diff --git a/Mathbin/All.lean b/Mathbin/All.lean
index dacdd71294..f3127a1bf4 100644
--- a/Mathbin/All.lean
+++ b/Mathbin/All.lean
@@ -592,6 +592,7 @@ import Mathbin.Analysis.Convex.Uniform
 import Mathbin.Analysis.Convolution
 import Mathbin.Analysis.Fourier.AddCircle
 import Mathbin.Analysis.Fourier.FourierTransform
+import Mathbin.Analysis.Fourier.PoissonSummation
 import Mathbin.Analysis.Fourier.RiemannLebesgueLemma
 import Mathbin.Analysis.Hofer
 import Mathbin.Analysis.InnerProductSpace.Adjoint
@@ -2239,6 +2240,7 @@ import Mathbin.NumberTheory.Padics.PadicNumbers
 import Mathbin.NumberTheory.Padics.PadicVal
 import Mathbin.NumberTheory.Padics.RingHoms
 import Mathbin.NumberTheory.Pell
+import Mathbin.NumberTheory.PellGeneral
 import Mathbin.NumberTheory.PrimeCounting
 import Mathbin.NumberTheory.PrimesCongruentOne
 import Mathbin.NumberTheory.Primorial
diff --git a/Mathbin/Analysis/Fourier/FourierTransform.lean b/Mathbin/Analysis/Fourier/FourierTransform.lean
index c0353bc946..61ffc2de5d 100644
--- a/Mathbin/Analysis/Fourier/FourierTransform.lean
+++ b/Mathbin/Analysis/Fourier/FourierTransform.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Loeffler
 
 ! This file was ported from Lean 3 source module analysis.fourier.fourier_transform
-! leanprover-community/mathlib commit a231f964b9ec8d1e12a28326b556123258a52829
+! leanprover-community/mathlib commit 3353f3371120058977ce1e20bf7fc8986c0fb042
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -265,9 +265,12 @@ theorem fourierIntegral_def (f : ℝ → E) (w : ℝ) :
   rfl
 #align real.fourier_integral_def Real.fourierIntegral_def
 
+-- mathport name: fourier_integral
+scoped[FourierTransform] notation "𝓕" => Real.fourierIntegral
+
 theorem fourierIntegral_eq_integral_exp_smul {E : Type _} [NormedAddCommGroup E] [CompleteSpace E]
     [NormedSpace ℂ E] (f : ℝ → E) (w : ℝ) :
-    fourierIntegral f w = ∫ v : ℝ, Complex.exp (↑(-2 * π * v * w) * Complex.i) • f v := by
+    𝓕 f w = ∫ v : ℝ, Complex.exp (↑(-2 * π * v * w) * Complex.i) • f v := by
   simp_rw [fourier_integral_def, Real.fourierChar_apply, mul_neg, neg_mul, mul_assoc]
 #align real.fourier_integral_eq_integral_exp_smul Real.fourierIntegral_eq_integral_exp_smul
 
diff --git a/Mathbin/Analysis/Fourier/PoissonSummation.lean b/Mathbin/Analysis/Fourier/PoissonSummation.lean
new file mode 100644
index 0000000000..995d6bb3f2
--- /dev/null
+++ b/Mathbin/Analysis/Fourier/PoissonSummation.lean
@@ -0,0 +1,131 @@
+/-
+Copyright (c) 2023 David Loeffler. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: David Loeffler
+
+! This file was ported from Lean 3 source module analysis.fourier.poisson_summation
+! leanprover-community/mathlib commit 3353f3371120058977ce1e20bf7fc8986c0fb042
+! Please do not edit these lines, except to modify the commit id
+! if you have ported upstream changes.
+-/
+import Mathbin.Analysis.Fourier.AddCircle
+import Mathbin.Analysis.Fourier.FourierTransform
+
+/-!
+# Poisson's summation formula
+
+We prove Poisson's summation formula `∑ (n : ℤ), f n = ∑ (n : ℤ), 𝓕 f n`, where `𝓕 f` is the
+Fourier transform of `f`, under the following hypotheses:
+* `f` is a continuous function `ℝ → ℂ`.
+* The sum `∑ (n : ℤ), 𝓕 f n` is convergent.
+* For all compacts `K ⊂ ℝ`, the sum `∑ (n : ℤ), sup { ‖f(x + n)‖ | x ∈ K }` is convergent.
+
+## TODO
+
+* Show that the conditions on `f` are automatically satisfied for Schwartz functions.
+-/
+
+
+noncomputable section
+
+open Function hiding comp_apply
+
+open Complex Real
+
+open Set hiding restrict_apply
+
+open TopologicalSpace Filter MeasureTheory
+
+open Real BigOperators Filter FourierTransform
+
+attribute [local instance] Real.fact_zero_lt_one
+
+open ContinuousMap
+
+/-- The key lemma for Poisson summation: the `m`-th Fourier coefficient of the periodic function
+`∑' n : ℤ, f (x + n)` is the value at `m` of the Fourier transform of `f`. -/
+theorem Real.fourierCoeff_tsum_comp_add {f : C(ℝ, ℂ)}
+    (hf : ∀ K : Compacts ℝ, Summable fun n : ℤ => ‖(f.comp (ContinuousMap.addRight n)).restrict K‖)
+    (m : ℤ) : fourierCoeff (Periodic.lift <| f.periodic_tsum_comp_add_zsmul 1) m = 𝓕 f m :=
+  by
+  -- NB: This proof can be shortened somewhat by telescoping together some of the steps in the calc
+  -- block, but I think it's more legible this way. We start with preliminaries about the integrand.
+  let e : C(ℝ, ℂ) := (fourier (-m)).comp ⟨(coe : ℝ → UnitAddCircle), continuous_quotient_mk'⟩
+  have neK : ∀ (K : compacts ℝ) (g : C(ℝ, ℂ)), ‖(e * g).restrict K‖ = ‖g.restrict K‖ :=
+    by
+    have : ∀ x : ℝ, ‖e x‖ = 1 := fun x => abs_coe_circle _
+    intro K g
+    simp_rw [norm_eq_supr_norm, restrict_apply, mul_apply, norm_mul, this, one_mul]
+  have eadd : ∀ n : ℤ, e.comp (ContinuousMap.addRight n) = e :=
+    by
+    intro n
+    ext1 x
+    have : periodic e 1 := periodic.comp (fun x => AddCircle.coe_add_period 1 x) _
+    simpa only [mul_one] using this.int_mul n x
+  -- Now the main argument. First unwind some definitions.
+  calc
+    fourierCoeff (periodic.lift <| f.periodic_tsum_comp_add_zsmul 1) m =
+        ∫ x in 0 ..1, e x * (∑' n : ℤ, f.comp (ContinuousMap.addRight n)) x :=
+      by
+      simp_rw [fourierCoeff_eq_intervalIntegral _ m 0, div_one, one_smul, zero_add, comp_apply,
+        coe_mk, periodic.lift_coe, zsmul_one, smul_eq_mul]
+    -- Transform sum in C(ℝ, ℂ) evaluated at x into pointwise sum of values.
+        _ =
+        ∫ x in 0 ..1, ∑' n : ℤ, (e * f.comp (ContinuousMap.addRight n)) x :=
+      by
+      simp_rw [coe_mul, Pi.mul_apply, ← tsum_apply (summable_of_locally_summable_norm hf),
+        tsum_mul_left]
+    -- Swap sum and integral.
+        _ =
+        ∑' n : ℤ, ∫ x in 0 ..1, (e * f.comp (ContinuousMap.addRight n)) x :=
+      by
+      refine' (intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm _).symm
+      convert hf ⟨uIcc 0 1, isCompact_uIcc⟩
+      exact funext fun n => neK _ _
+    _ = ∑' n : ℤ, ∫ x in 0 ..1, (e * f).comp (ContinuousMap.addRight n) x :=
+      by
+      simp only [ContinuousMap.comp_apply, mul_comp] at eadd⊢
+      simp_rw [eadd]
+    -- Rearrange sum of interval integrals into an integral over `ℝ`.
+        _ =
+        ∫ x, e x * f x :=
+      by
+      suffices : integrable ⇑(e * f); exact this.has_sum_interval_integral_comp_add_int.tsum_eq
+      apply integrable_of_summable_norm_Icc
+      convert hf ⟨Icc 0 1, is_compact_Icc⟩
+      simp_rw [ContinuousMap.comp_apply, mul_comp] at eadd⊢
+      simp_rw [eadd]
+      exact funext fun n => neK ⟨Icc 0 1, is_compact_Icc⟩ _
+    -- Minor tidying to finish
+        _ =
+        𝓕 f m :=
+      by
+      rw [fourier_integral_eq_integral_exp_smul]
+      congr 1 with x : 1
+      rw [smul_eq_mul, comp_apply, coe_mk, fourier_coe_apply]
+      congr 2
+      push_cast
+      ring
+    
+#align real.fourier_coeff_tsum_comp_add Real.fourierCoeff_tsum_comp_add
+
+/-- **Poisson's summation formula**. -/
+theorem Real.tsum_eq_tsum_fourierIntegral {f : C(ℝ, ℂ)}
+    (h_norm :
+      ∀ K : Compacts ℝ, Summable fun n : ℤ => ‖(f.comp <| ContinuousMap.addRight n).restrict K‖)
+    (h_sum : Summable fun n : ℤ => 𝓕 f n) : (∑' n : ℤ, f n) = ∑' n : ℤ, 𝓕 f n :=
+  by
+  let F : C(UnitAddCircle, ℂ) :=
+    ⟨(f.periodic_tsum_comp_add_zsmul 1).lift, continuous_coinduced_dom.mpr (map_continuous _)⟩
+  have : Summable (fourierCoeff F) := by
+    convert h_sum
+    exact funext fun n => Real.fourierCoeff_tsum_comp_add h_norm n
+  convert (has_pointwise_sum_fourier_series_of_summable this 0).tsum_eq.symm using 1
+  · have := (has_sum_apply (summable_of_locally_summable_norm h_norm).HasSum 0).tsum_eq
+    simpa only [coe_mk, ← QuotientAddGroup.mk_zero, periodic.lift_coe, zsmul_one, comp_apply,
+      coe_add_right, zero_add] using this
+  · congr 1 with n : 1
+    rw [← Real.fourierCoeff_tsum_comp_add h_norm n, fourier_eval_zero, smul_eq_mul, mul_one]
+    rfl
+#align real.tsum_eq_tsum_fourier_integral Real.tsum_eq_tsum_fourierIntegral
+
diff --git a/Mathbin/Analysis/Fourier/RiemannLebesgueLemma.lean b/Mathbin/Analysis/Fourier/RiemannLebesgueLemma.lean
index 389a31795a..e2fbe5bbee 100644
--- a/Mathbin/Analysis/Fourier/RiemannLebesgueLemma.lean
+++ b/Mathbin/Analysis/Fourier/RiemannLebesgueLemma.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Loeffler
 
 ! This file was ported from Lean 3 source module analysis.fourier.riemann_lebesgue_lemma
-! leanprover-community/mathlib commit a231f964b9ec8d1e12a28326b556123258a52829
+! leanprover-community/mathlib commit 3353f3371120058977ce1e20bf7fc8986c0fb042
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -193,7 +193,7 @@ open FourierTransform
 /-- Riemann-Lebesgue lemma for continuous compactly-supported functions: the Fourier transform
 tends to 0 at infinity. -/
 theorem Real.fourierIntegral_zero_at_infty_of_continuous_compact_support (hc : Continuous f)
-    (hs : HasCompactSupport f) : Tendsto (Real.fourierIntegral f) (cocompact ℝ) (𝓝 0) :=
+    (hs : HasCompactSupport f) : Tendsto (𝓕 f) (cocompact ℝ) (𝓝 0) :=
   by
   refine'
     ((zero_at_infty_integral_mul_exp_of_continuous_compact_support hc hs).comp
diff --git a/Mathbin/Data/Finset/Basic.lean b/Mathbin/Data/Finset/Basic.lean
index 29203d06ea..7161d94216 100644
--- a/Mathbin/Data/Finset/Basic.lean
+++ b/Mathbin/Data/Finset/Basic.lean
@@ -4970,9 +4970,9 @@ theorem singleton_disjUnionᵢ (a : α) {h} : Finset.disjUnion {a} t h = t a :=
 
 /- warning: finset.disj_Union_disj_Union -> Finset.disjUnionᵢ_disjUnionᵢ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} (s : Finset.{u1} α) (f : α -> (Finset.{u2} β)) (g : β -> (Finset.{u3} γ)) (h1 : Set.PairwiseDisjoint.{u2, u1} (Finset.{u2} β) α (Finset.partialOrder.{u2} β) (Finset.orderBot.{u2} β) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s) f) (h2 : Set.PairwiseDisjoint.{u3, u2} (Finset.{u3} γ) β (Finset.partialOrder.{u3} γ) (Finset.orderBot.{u3} γ) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (Finset.disjUnionₓ.{u1, u2} α β s f h1)) g), Eq.{succ u3} (Finset.{u3} γ) (Finset.disjUnionₓ.{u2, u3} β γ (Finset.disjUnionₓ.{u1, u2} α β s f h1) g h2) (Finset.disjUnionₓ.{u1, u3} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) γ (Finset.attach.{u1} α s) (fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) (fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) (ha : Membership.Mem.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.hasMem.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Finset.Set.hasCoeT.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) (Finset.attach.{u1} α s))) (b : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) (hb : Membership.Mem.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.hasMem.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) b ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Finset.Set.hasCoeT.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) (Finset.attach.{u1} α s))) (hab : Ne.{succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) a b) => Iff.mpr (Disjoint.{u3} (Finset.{u3} γ) (Finset.partialOrder.{u3} γ) (Finset.orderBot.{u3} γ) ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) a) ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) b)) (forall {{a_1 : γ}}, (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) a_1 ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) a)) -> (Not (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) a_1 ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) b)))) (Finset.disjoint_left.{u3} γ ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) a) ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) b)) (fun (x : γ) (hxa : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) a)) (hxb : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) b)) => Exists.dcases_on.{succ u2} β (fun (a_1 : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g a_1))) (fun (_fresh.613.283405 : Exists.{succ u2} β (fun (a_1 : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g a_1)))) => False) (Iff.mp (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc)))))) (Exists.{succ u2} β (fun (a_1 : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g a_1)))) (Finset.mem_disjUnionᵢ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g x (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) hxa) (fun (xa : β) (h : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xa))) => Exists.dcases_on.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xa)) (fun (h : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xa))) => False) h (fun (hfa : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (hga : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xa)) => Exists.dcases_on.{succ u2} β (fun (a : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g a))) (fun (_fresh.613.283522 : Exists.{succ u2} β (fun (a : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g a)))) => False) (Iff.mp (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b)) g (fun (b_1 : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b_1 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b)))) => h2 b_1 (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b_1 h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) b) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) b) hc)))))) (Exists.{succ u2} β (fun (a : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g a)))) (Finset.mem_disjUnionᵢ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b)) g x (fun (b_1 : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b_1 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b)))) => h2 b_1 (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b_1 h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) b) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) b) hc))))) hxb) (fun (xb : β) (h : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xb))) => Exists.dcases_on.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xb)) (fun (h : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xb))) => False) h (fun (hfb : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (hgb : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xb)) => Iff.mp (Disjoint.{u3} (Finset.{u3} γ) (Finset.partialOrder.{u3} γ) (Finset.orderBot.{u3} γ) (g xa) (g xb)) (forall {{a : γ}}, (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) a (g xa)) -> (Not (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) a (g xb)))) (Finset.disjoint_left.{u3} γ (g xa) (g xb)) (h2 xa (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f xa h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hfa))) xb (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f xb h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) b) hfb))) (id.{0} (Ne.{succ u2} β xa xb) (fun (ᾰ : Eq.{succ u2} β xa xb) => Eq.ndrec.{0, succ u2} β xa (fun (xb : β) => (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) -> (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xb)) -> False) (fun (hfb : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (hgb : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xa)) => Iff.mp (Disjoint.{u2} (Finset.{u2} β) (Finset.partialOrder.{u2} β) (Finset.orderBot.{u2} β) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (forall {{a_1 : β}}, (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) -> (Not (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))))) (Finset.disjoint_left.{u2} β (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (h1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) b) (Function.Injective.ne.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)))))) (Subtype.coe_injective.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) a b hab)) xa hfa hfb) xb ᾰ hfb hgb))) x hga hgb)))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} (s : Finset.{u1} α) (f : α -> (Finset.{u2} β)) (g : β -> (Finset.{u3} γ)) (h1 : Set.PairwiseDisjoint.{u2, u1} (Finset.{u2} β) α (Finset.partialOrder.{u2} β) (Finset.orderBot.{u2} β) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s) f) (h2 : Set.PairwiseDisjoint.{u3, u2} (Finset.{u3} γ) β (Finset.partialOrder.{u3} γ) (Finset.orderBot.{u3} γ) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (Finset.disjUnionₓ.{u1, u2} α β s f h1)) g), Eq.{succ u3} (Finset.{u3} γ) (Finset.disjUnionₓ.{u2, u3} β γ (Finset.disjUnionₓ.{u1, u2} α β s f h1) g h2) (Finset.disjUnionₓ.{u1, u3} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) γ (Finset.attach.{u1} α s) (fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) (fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) (ha : Membership.Mem.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.hasMem.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Finset.Set.hasCoeT.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) (Finset.attach.{u1} α s))) (b : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) (hb : Membership.Mem.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.hasMem.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) b ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Set.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))) (Finset.Set.hasCoeT.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) (Finset.attach.{u1} α s))) (hab : Ne.{succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) a b) => Iff.mpr (Disjoint.{u3} (Finset.{u3} γ) (Finset.partialOrder.{u3} γ) (Finset.orderBot.{u3} γ) ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) a) ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) b)) (forall {{a_1 : γ}}, (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) a_1 ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) a)) -> (Not (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) a_1 ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) b)))) (Finset.disjoint_left.{u3} γ ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) a) ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) b)) (fun (x : γ) (hxa : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) a)) (hxb : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x ((fun (a : Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) => Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) b)) => Exists.dcases_on.{succ u2} β (fun (a_1 : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g a_1))) (fun (_fresh.532.21383 : Exists.{succ u2} β (fun (a_1 : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g a_1)))) => False) (Iff.mp (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc)))))) (Exists.{succ u2} β (fun (a_1 : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g a_1)))) (Finset.mem_disjUnionᵢ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) g x (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)))) => h2 b (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hc))))) hxa) (fun (xa : β) (h : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xa))) => Exists.dcases_on.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xa)) (fun (h : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xa))) => False) h (fun (hfa : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (hga : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xa)) => Exists.dcases_on.{succ u2} β (fun (a : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g a))) (fun (_fresh.532.21500 : Exists.{succ u2} β (fun (a : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g a)))) => False) (Iff.mp (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (Finset.disjUnionₓ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b)) g (fun (b_1 : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b_1 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b)))) => h2 b_1 (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b_1 h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) b) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) b) hc)))))) (Exists.{succ u2} β (fun (a : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g a)))) (Finset.mem_disjUnionᵢ.{u2, u3} β γ (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b)) g x (fun (b_1 : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b_1 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b)))) (c : β) (hc : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b)))) => h2 b_1 (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f b_1 h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) b_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) b) hb))) c (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f c h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) c (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) b) hc))))) hxb) (fun (xb : β) (h : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xb))) => Exists.dcases_on.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xb)) (fun (h : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) => Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xb))) => False) h (fun (hfb : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (hgb : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xb)) => Iff.mp (Disjoint.{u3} (Finset.{u3} γ) (Finset.partialOrder.{u3} γ) (Finset.orderBot.{u3} γ) (g xa) (g xb)) (forall {{a : γ}}, (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) a (g xa)) -> (Not (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) a (g xb)))) (Finset.disjoint_left.{u3} γ (g xa) (g xb)) (h2 xa (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f xa h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) hfa))) xb (Iff.mpr (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (Finset.disjUnionₓ.{u1, u2} α β s f h1)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f a)))) (Finset.mem_disjUnionᵢ.{u1, u2} α β s f xb h1) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f a))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) (fun (H : Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) s) => Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) b) hfb))) (id.{0} (Ne.{succ u2} β xa xb) (fun (ᾰ : Eq.{succ u2} β xa xb) => Eq.ndrec.{0, succ u2} β xa (fun (xb : β) => (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) -> (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xb)) -> False) (fun (hfb : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (hgb : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (g xa)) => Iff.mp (Disjoint.{u2} (Finset.{u2} β) (Finset.partialOrder.{u2} β) (Finset.orderBot.{u2} β) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (forall {{a_1 : β}}, (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a))) -> (Not (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))))) (Finset.disjoint_left.{u2} β (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a)) (f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b))) (h1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) a) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) a) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s))))) b) (Subtype.prop.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s) b) (Function.Injective.ne.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)))))) (Subtype.coe_injective.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) x s)) a b hab)) xa hfa hfb) xb ᾰ hfb hgb))) x hga hgb)))))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} (s : Finset.{u3} α) (f : α -> (Finset.{u2} β)) (g : β -> (Finset.{u1} γ)) (h1 : Set.PairwiseDisjoint.{u2, u3} (Finset.{u2} β) α (Finset.partialOrder.{u2} β) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u2} β) (Finset.toSet.{u3} α s) f) (h2 : Set.PairwiseDisjoint.{u1, u2} (Finset.{u1} γ) β (Finset.partialOrder.{u1} γ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} γ) (Finset.toSet.{u2} β (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) g), Eq.{succ u1} (Finset.{u1} γ) (Finset.disjUnionᵢ.{u2, u1} β γ (Finset.disjUnionᵢ.{u3, u2} α β s f h1) g h2) (Finset.disjUnionᵢ.{u3, u1} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) γ (Finset.attach.{u3} α s) (fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) (fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) (ha : Membership.mem.{u3, u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) (Set.{u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s))) (Set.instMembershipSet.{u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s))) a (Finset.toSet.{u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) (Finset.attach.{u3} α s))) (b : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) (hb : Membership.mem.{u3, u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) (Set.{u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s))) (Set.instMembershipSet.{u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s))) b (Finset.toSet.{u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) (Finset.attach.{u3} α s))) (hab : Ne.{succ u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) a b) => Iff.mpr (Disjoint.{u1} (Finset.{u1} γ) (Finset.partialOrder.{u1} γ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} γ) ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) a) ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) b)) (forall {{a_1 : γ}}, (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) a_1 ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) a)) -> (Not (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) a_1 ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) b)))) (Finset.disjoint_left.{u1} γ ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) a) ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) b)) (fun (x : γ) (hxa : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) a)) (hxb : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) b)) => Exists.casesOn.{succ u2} β (fun (a_1 : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g a_1))) (fun (_fresh.613.283405 : Exists.{succ u2} β (fun (a_1 : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g a_1)))) => False) (Iff.mp (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc)))))) (Exists.{succ u2} β (fun (a_1 : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g a_1)))) (Finset.mem_disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g x (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) hxa) (fun (xa : β) (h : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xa))) => And.casesOn.{0} (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xa)) (fun (h : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xa))) => False) h (fun (hfa : Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (hga : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xa)) => Exists.casesOn.{succ u2} β (fun (a : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g a))) (fun (_fresh.613.283522 : Exists.{succ u2} β (fun (a : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g a)))) => False) (Iff.mp (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b)) g (fun (b_1 : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b_1 (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b)))) => h2 b_1 (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b_1 h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) hc)))))) (Exists.{succ u2} β (fun (a : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g a)))) (Finset.mem_disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b)) g x (fun (b_1 : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b_1 (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b)))) => h2 b_1 (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b_1 h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) hc))))) hxb) (fun (xb : β) (h : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xb))) => And.casesOn.{0} (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xb)) (fun (h : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xb))) => False) h (fun (hfb : Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (hgb : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xb)) => Iff.mp (Disjoint.{u1} (Finset.{u1} γ) (Finset.partialOrder.{u1} γ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} γ) (g xa) (g xb)) (forall {{a : γ}}, (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) a (g xa)) -> (Not (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) a (g xb)))) (Finset.disjoint_left.{u1} γ (g xa) (g xb)) (h2 xa (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f xa h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hfa))) xb (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f xb h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) hfb))) (fun (a._@.Init.Prelude.139.Mathlib.Data.Finset.Basic._hyg.32538 : Eq.{succ u2} β xa xb) => Eq.ndrec.{0, succ u2} β xa (fun (xb : β) => (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) -> (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xb)) -> False) (fun (hfb : Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (hgb : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xa)) => Iff.mp (Disjoint.{u2} (Finset.{u2} β) (Finset.partialOrder.{u2} β) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u2} β) (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (forall {{a_1 : β}}, (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) -> (Not (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))))) (Finset.disjoint_left.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (h1 (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (Function.Injective.ne.{succ u3, succ u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) α (fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (Subtype.coe_injective.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) a b hab)) xa hfa hfb) xb a._@.Init.Prelude.139.Mathlib.Data.Finset.Basic._hyg.32538 hfb hgb)) x hga hgb)))))))
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} (s : Finset.{u3} α) (f : α -> (Finset.{u2} β)) (g : β -> (Finset.{u1} γ)) (h1 : Set.PairwiseDisjoint.{u2, u3} (Finset.{u2} β) α (Finset.partialOrder.{u2} β) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u2} β) (Finset.toSet.{u3} α s) f) (h2 : Set.PairwiseDisjoint.{u1, u2} (Finset.{u1} γ) β (Finset.partialOrder.{u1} γ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} γ) (Finset.toSet.{u2} β (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) g), Eq.{succ u1} (Finset.{u1} γ) (Finset.disjUnionᵢ.{u2, u1} β γ (Finset.disjUnionᵢ.{u3, u2} α β s f h1) g h2) (Finset.disjUnionᵢ.{u3, u1} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) γ (Finset.attach.{u3} α s) (fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) (fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) (ha : Membership.mem.{u3, u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) (Set.{u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s))) (Set.instMembershipSet.{u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s))) a (Finset.toSet.{u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) (Finset.attach.{u3} α s))) (b : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) (hb : Membership.mem.{u3, u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) (Set.{u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s))) (Set.instMembershipSet.{u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s))) b (Finset.toSet.{u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) (Finset.attach.{u3} α s))) (hab : Ne.{succ u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) a b) => Iff.mpr (Disjoint.{u1} (Finset.{u1} γ) (Finset.partialOrder.{u1} γ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} γ) ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) a) ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) b)) (forall {{a_1 : γ}}, (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) a_1 ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) a)) -> (Not (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) a_1 ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) b)))) (Finset.disjoint_left.{u1} γ ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) a) ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) b)) (fun (x : γ) (hxa : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) a)) (hxb : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x ((fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) b)) => Exists.casesOn.{succ u2} β (fun (a_1 : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g a_1))) (fun (_fresh.532.21383 : Exists.{succ u2} β (fun (a_1 : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g a_1)))) => False) (Iff.mp (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc)))))) (Exists.{succ u2} β (fun (a_1 : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g a_1)))) (Finset.mem_disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) g x (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)))) => h2 b (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hc))))) hxa) (fun (xa : β) (h : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xa))) => And.casesOn.{0} (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xa)) (fun (h : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xa))) => False) h (fun (hfa : Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (hga : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xa)) => Exists.casesOn.{succ u2} β (fun (a : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g a))) (fun (_fresh.532.21500 : Exists.{succ u2} β (fun (a : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g a)))) => False) (Iff.mp (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (Finset.disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b)) g (fun (b_1 : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b_1 (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b)))) => h2 b_1 (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b_1 h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) hc)))))) (Exists.{succ u2} β (fun (a : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g a)))) (Finset.mem_disjUnionᵢ.{u2, u1} β γ (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b)) g x (fun (b_1 : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b_1 (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b)))) (c : β) (hc : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c (Finset.toSet.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b)))) => h2 b_1 (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f b_1 h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) b_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) hb))) c (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f c h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) c (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) hc))))) hxb) (fun (xb : β) (h : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xb))) => And.casesOn.{0} (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xb)) (fun (h : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xb))) => False) h (fun (hfb : Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (hgb : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xb)) => Iff.mp (Disjoint.{u1} (Finset.{u1} γ) (Finset.partialOrder.{u1} γ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} γ) (g xa) (g xb)) (forall {{a : γ}}, (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) a (g xa)) -> (Not (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) a (g xb)))) (Finset.disjoint_left.{u1} γ (g xa) (g xb)) (h2 xa (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f xa h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) hfa))) xb (Iff.mpr (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (Finset.disjUnionᵢ.{u3, u2} α β s f h1)) (Exists.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f a)))) (Finset.mem_disjUnionᵢ.{u3, u2} α β s f xb h1) (Exists.intro.{succ u3} α (fun (a : α) => And (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) a s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f a))) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (And.intro (Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) s) (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) hfb))) (fun (a._@.Init.Prelude.139.Mathlib.Data.Finset.Basic._hyg.32538 : Eq.{succ u2} β xa xb) => Eq.ndrec.{0, succ u2} β xa (fun (xb : β) => (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) -> (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xb)) -> False) (fun (hfb : Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (hgb : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (g xa)) => Iff.mp (Disjoint.{u2} (Finset.{u2} β) (Finset.partialOrder.{u2} β) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u2} β) (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (forall {{a_1 : β}}, (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a))) -> (Not (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))))) (Finset.disjoint_left.{u2} β (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a)) (f (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b))) (h1 (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (Subtype.prop.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) b) (Function.Injective.ne.{succ u3, succ u3} (Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) α (fun (a : Subtype.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) => Subtype.val.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s) a) (Subtype.coe_injective.{succ u3} α (fun (x : α) => Membership.mem.{u3, u3} α (Finset.{u3} α) (Finset.instMembershipFinset.{u3} α) x s)) a b hab)) xa hfa hfb) xb a._@.Init.Prelude.139.Mathlib.Data.Finset.Basic._hyg.32538 hfb hgb)) x hga hgb)))))))
 Case conversion may be inaccurate. Consider using '#align finset.disj_Union_disj_Union Finset.disjUnionᵢ_disjUnionᵢₓ'. -/
 theorem disjUnionᵢ_disjUnionᵢ (s : Finset α) (f : α → Finset β) (g : β → Finset γ) (h1 h2) :
     (s.disjUnionₓ f h1).disjUnionₓ g h2 =
diff --git a/Mathbin/Data/Finset/Image.lean b/Mathbin/Data/Finset/Image.lean
index d3f1b7b93b..6848f54ebc 100644
--- a/Mathbin/Data/Finset/Image.lean
+++ b/Mathbin/Data/Finset/Image.lean
@@ -487,9 +487,9 @@ theorem map_disjUnionᵢ {f : α ↪ β} {s : Finset α} {t : β → Finset γ}
 
 /- warning: finset.disj_Union_map -> Finset.disjUnionᵢ_map is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} {s : Finset.{u1} α} {t : α -> (Finset.{u2} β)} {f : Function.Embedding.{succ u2, succ u3} β γ} {h : Set.PairwiseDisjoint.{u2, u1} (Finset.{u2} β) α (Finset.partialOrder.{u2} β) (Finset.orderBot.{u2} β) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s) t}, Eq.{succ u3} (Finset.{u3} γ) (Finset.map.{u2, u3} β γ f (Finset.disjUnionₓ.{u1, u2} α β s t h)) (Finset.disjUnionₓ.{u1, u3} α γ s (fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) (fun (a : α) (ha : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (b : α) (hb : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (hab : Ne.{succ u1} α a b) => Iff.mpr (Disjoint.{u3} (Finset.{u3} γ) (Finset.partialOrder.{u3} γ) (Finset.orderBot.{u3} γ) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) (forall {{a_1 : γ}}, (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) a_1 ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a)) -> (Not (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) a_1 ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)))) (Finset.disjoint_left.{u3} γ ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) (fun (x : γ) (hxa : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a)) (hxb : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) => Exists.dcases_on.{succ u2} β (fun (a_1 : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f a_1) x)) (fun (_fresh.637.76962 : Exists.{succ u2} β (fun (a_1 : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f a_1) x))) => False) (Iff.mp (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (Finset.map.{u2, u3} β γ f (t a))) (Exists.{succ u2} β (fun (a_1 : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f a_1) x))) (Finset.mem_map.{u2, u3} β γ f (t a) x) hxa) (fun (xa : β) (h_1 : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) x)) => Exists.dcases_on.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) x) (fun (h_1 : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) x)) => False) h_1 (fun (hfa : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) (h_1_h : Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) x) => Eq.ndrec.{0, succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) (fun (x : γ) => (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a)) -> (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) -> False) (fun (hxa : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a)) (hxb : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) => Exists.dcases_on.{succ u2} β (fun (a : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (t b)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (t b)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f a) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa))) (fun (_fresh.637.77048 : Exists.{succ u2} β (fun (a : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (t b)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (t b)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f a) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa)))) => False) (Iff.mp (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) (Finset.map.{u2, u3} β γ f (t b))) (Exists.{succ u2} β (fun (a : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (t b)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (t b)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f a) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa)))) (Finset.mem_map.{u2, u3} β γ f (t b) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa)) hxb) (fun (xb : β) (h_1 : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa))) => Exists.dcases_on.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa)) (fun (h_1 : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa))) => False) h_1 (fun (hfb : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) (hfab : Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa)) => Eq.ndrec.{0, succ u2} β xb (fun (xa : β) => (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) -> (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a)) -> (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) -> (Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa)) -> False) (fun (hfa : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t a)) (hxa : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a)) (hxb : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) (hfab : Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb)) => Iff.mp (Disjoint.{u2} (Finset.{u2} β) (Finset.partialOrder.{u2} β) (Finset.orderBot.{u2} β) (t a) (t b)) (forall {{a_1 : β}}, (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) -> (Not (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t b)))) (Finset.disjoint_left.{u2} β (t a) (t b)) (h a ha b hb hab) xb hfa hfb) xa (Function.Embedding.injective.{succ u2, succ u3} β γ f xb xa hfab) hfa hxa hxb hfab))) x h_1_h hxa hxb)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} {s : Finset.{u1} α} {t : α -> (Finset.{u2} β)} {f : Function.Embedding.{succ u2, succ u3} β γ} {h : Set.PairwiseDisjoint.{u2, u1} (Finset.{u2} β) α (Finset.partialOrder.{u2} β) (Finset.orderBot.{u2} β) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s) t}, Eq.{succ u3} (Finset.{u3} γ) (Finset.map.{u2, u3} β γ f (Finset.disjUnionₓ.{u1, u2} α β s t h)) (Finset.disjUnionₓ.{u1, u3} α γ s (fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) (fun (a : α) (ha : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (b : α) (hb : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (hab : Ne.{succ u1} α a b) => Iff.mpr (Disjoint.{u3} (Finset.{u3} γ) (Finset.partialOrder.{u3} γ) (Finset.orderBot.{u3} γ) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) (forall {{a_1 : γ}}, (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) a_1 ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a)) -> (Not (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) a_1 ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)))) (Finset.disjoint_left.{u3} γ ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) (fun (x : γ) (hxa : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a)) (hxb : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) => Exists.dcases_on.{succ u2} β (fun (a_1 : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f a_1) x)) (fun (_fresh.497.345555 : Exists.{succ u2} β (fun (a_1 : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f a_1) x))) => False) (Iff.mp (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x (Finset.map.{u2, u3} β γ f (t a))) (Exists.{succ u2} β (fun (a_1 : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f a_1) x))) (Finset.mem_map.{u2, u3} β γ f (t a) x) hxa) (fun (xa : β) (h_1 : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) x)) => Exists.dcases_on.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) x) (fun (h_1 : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) x)) => False) h_1 (fun (hfa : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) (h_1_h : Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) x) => Eq.ndrec.{0, succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) (fun (x : γ) => (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a)) -> (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) x ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) -> False) (fun (hxa : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a)) (hxb : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) => Exists.dcases_on.{succ u2} β (fun (a : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (t b)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (t b)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f a) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa))) (fun (_fresh.497.345641 : Exists.{succ u2} β (fun (a : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (t b)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (t b)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f a) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa)))) => False) (Iff.mp (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) (Finset.map.{u2, u3} β γ f (t b))) (Exists.{succ u2} β (fun (a : β) => Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (t b)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a (t b)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f a) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa)))) (Finset.mem_map.{u2, u3} β γ f (t b) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa)) hxb) (fun (xb : β) (h_1 : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa))) => Exists.dcases_on.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa)) (fun (h_1 : Exists.{0} (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) (fun (H : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) => Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa))) => False) h_1 (fun (hfb : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t b)) (hfab : Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa)) => Eq.ndrec.{0, succ u2} β xb (fun (xa : β) => (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xa (t a)) -> (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a)) -> (Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) -> (Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xa)) -> False) (fun (hfa : Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) xb (t a)) (hxa : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) a)) (hxb : Membership.Mem.{u3, u3} γ (Finset.{u3} γ) (Finset.hasMem.{u3} γ) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) ((fun (a : α) => Finset.map.{u2, u3} β γ f (t a)) b)) (hfab : Eq.{succ u3} γ (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb) (coeFn.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Function.Embedding.{succ u2, succ u3} β γ) (fun (_x : Function.Embedding.{succ u2, succ u3} β γ) => β -> γ) (Function.Embedding.hasCoeToFun.{succ u2, succ u3} β γ) f xb)) => Iff.mp (Disjoint.{u2} (Finset.{u2} β) (Finset.partialOrder.{u2} β) (Finset.orderBot.{u2} β) (t a) (t b)) (forall {{a_1 : β}}, (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t a)) -> (Not (Membership.Mem.{u2, u2} β (Finset.{u2} β) (Finset.hasMem.{u2} β) a_1 (t b)))) (Finset.disjoint_left.{u2} β (t a) (t b)) (h a ha b hb hab) xb hfa hfb) xa (Function.Embedding.injective.{succ u2, succ u3} β γ f xb xa hfab) hfa hxa hxb hfab))) x h_1_h hxa hxb)))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} {s : Finset.{u3} α} {t : α -> (Finset.{u2} β)} {f : Function.Embedding.{succ u2, succ u1} β γ} {h : Set.PairwiseDisjoint.{u2, u3} (Finset.{u2} β) α (Finset.partialOrder.{u2} β) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u2} β) (Finset.toSet.{u3} α s) t}, Eq.{succ u1} (Finset.{u1} γ) (Finset.map.{u2, u1} β γ f (Finset.disjUnionᵢ.{u3, u2} α β s t h)) (Finset.disjUnionᵢ.{u3, u1} α γ s (fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) (fun (a : α) (ha : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a (Finset.toSet.{u3} α s)) (b : α) (hb : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) b (Finset.toSet.{u3} α s)) (hab : Ne.{succ u3} α a b) => Iff.mpr (Disjoint.{u1} (Finset.{u1} γ) (Finset.partialOrder.{u1} γ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} γ) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) (forall {{a_1 : γ}}, (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) a_1 ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a)) -> (Not (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) a_1 ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)))) (Finset.disjoint_left.{u1} γ ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) (fun (x : γ) (hxa : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a)) (hxb : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) => Exists.casesOn.{succ u2} β (fun (a_1 : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (t a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a_1) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f a_1) x)) (fun (_fresh.637.76962 : Exists.{succ u2} β (fun (a_1 : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (t a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a_1) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f a_1) x))) => False) (Iff.mp (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (Finset.map.{u2, u1} β γ f (t a))) (Exists.{succ u2} β (fun (a_1 : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (t a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a_1) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f a_1) x))) (Finset.mem_map.{u2, u1} β γ f (t a) x) hxa) (fun (xa : β) (h_1 : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (t a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xa) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) x)) => And.casesOn.{0} (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (t a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xa) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) x) (fun (h_1 : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (t a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xa) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) x)) => False) h_1 (fun (hfa : Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (t a)) (h_1_h : Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xa) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) x) => Eq.ndrec.{0, succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xa) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) (fun (x : γ) => (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a)) -> (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) -> False) (fun (hxa : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a)) (hxb : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) => Exists.casesOn.{succ u2} β (fun (a : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a (t b)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa))) (fun (_fresh.637.77048 : Exists.{succ u2} β (fun (a : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a (t b)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa)))) => False) (Iff.mp (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) (Finset.map.{u2, u1} β γ f (t b))) (Exists.{succ u2} β (fun (a : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a (t b)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa)))) (Finset.mem_map.{u2, u1} β γ f (t b) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa)) hxb) (fun (xb : β) (h_1 : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (t b)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa))) => And.casesOn.{0} (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (t b)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa)) (fun (h_1 : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (t b)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa))) => False) h_1 (fun (hfb : Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (t b)) (hfab : Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa)) => Eq.ndrec.{0, succ u2} β xb (fun (xa : β) => (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (t a)) -> (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a)) -> (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa)) -> False) (fun (hfa : Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (t a)) (hxa : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a)) (hxb : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) (hfab : Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb)) => Iff.mp (Disjoint.{u2} (Finset.{u2} β) (Finset.partialOrder.{u2} β) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u2} β) (t a) (t b)) (forall {{a_1 : β}}, (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (t a)) -> (Not (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (t b)))) (Finset.disjoint_left.{u2} β (t a) (t b)) (h a ha b hb hab) xb hfa hfb) xa (Function.Embedding.injective.{succ u1, succ u2} β γ f xb xa hfab) hfa hxa hxb hfab))) x h_1_h hxa hxb)))))
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} {s : Finset.{u3} α} {t : α -> (Finset.{u2} β)} {f : Function.Embedding.{succ u2, succ u1} β γ} {h : Set.PairwiseDisjoint.{u2, u3} (Finset.{u2} β) α (Finset.partialOrder.{u2} β) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u2} β) (Finset.toSet.{u3} α s) t}, Eq.{succ u1} (Finset.{u1} γ) (Finset.map.{u2, u1} β γ f (Finset.disjUnionᵢ.{u3, u2} α β s t h)) (Finset.disjUnionᵢ.{u3, u1} α γ s (fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) (fun (a : α) (ha : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a (Finset.toSet.{u3} α s)) (b : α) (hb : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) b (Finset.toSet.{u3} α s)) (hab : Ne.{succ u3} α a b) => Iff.mpr (Disjoint.{u1} (Finset.{u1} γ) (Finset.partialOrder.{u1} γ) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} γ) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) (forall {{a_1 : γ}}, (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) a_1 ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a)) -> (Not (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) a_1 ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)))) (Finset.disjoint_left.{u1} γ ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) (fun (x : γ) (hxa : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a)) (hxb : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) => Exists.casesOn.{succ u2} β (fun (a_1 : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (t a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a_1) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f a_1) x)) (fun (_fresh.497.345555 : Exists.{succ u2} β (fun (a_1 : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (t a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a_1) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f a_1) x))) => False) (Iff.mp (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x (Finset.map.{u2, u1} β γ f (t a))) (Exists.{succ u2} β (fun (a_1 : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (t a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a_1) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f a_1) x))) (Finset.mem_map.{u2, u1} β γ f (t a) x) hxa) (fun (xa : β) (h_1 : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (t a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xa) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) x)) => And.casesOn.{0} (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (t a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xa) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) x) (fun (h_1 : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (t a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xa) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) x)) => False) h_1 (fun (hfa : Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (t a)) (h_1_h : Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xa) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) x) => Eq.ndrec.{0, succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xa) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) (fun (x : γ) => (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a)) -> (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) x ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) -> False) (fun (hxa : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a)) (hxb : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) => Exists.casesOn.{succ u2} β (fun (a : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a (t b)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa))) (fun (_fresh.497.345641 : Exists.{succ u2} β (fun (a : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a (t b)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa)))) => False) (Iff.mp (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) (Finset.map.{u2, u1} β γ f (t b))) (Exists.{succ u2} β (fun (a : β) => And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a (t b)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa)))) (Finset.mem_map.{u2, u1} β γ f (t b) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa)) hxb) (fun (xb : β) (h_1 : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (t b)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa))) => And.casesOn.{0} (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (t b)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa)) (fun (h_1 : And (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (t b)) (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (a : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa))) => False) h_1 (fun (hfb : Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (t b)) (hfab : Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa)) => Eq.ndrec.{0, succ u2} β xb (fun (xa : β) => (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xa (t a)) -> (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a)) -> (Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xa)) -> False) (fun (hfa : Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) xb (t a)) (hxa : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) a)) (hxb : Membership.mem.{u1, u1} γ (Finset.{u1} γ) (Finset.instMembershipFinset.{u1} γ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) ((fun (a : α) => Finset.map.{u2, u1} β γ f (t a)) b)) (hfab : Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β γ)) f xb)) => Iff.mp (Disjoint.{u2} (Finset.{u2} β) (Finset.partialOrder.{u2} β) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u2} β) (t a) (t b)) (forall {{a_1 : β}}, (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (t a)) -> (Not (Membership.mem.{u2, u2} β (Finset.{u2} β) (Finset.instMembershipFinset.{u2} β) a_1 (t b)))) (Finset.disjoint_left.{u2} β (t a) (t b)) (h a ha b hb hab) xb hfa hfb) xa (Function.Embedding.injective.{succ u1, succ u2} β γ f xb xa hfab) hfa hxa hxb hfab))) x h_1_h hxa hxb)))))
 Case conversion may be inaccurate. Consider using '#align finset.disj_Union_map Finset.disjUnionᵢ_mapₓ'. -/
 theorem disjUnionᵢ_map {s : Finset α} {t : α → Finset β} {f : β ↪ γ} {h} :
     (s.disjUnionₓ t h).map f =
diff --git a/Mathbin/MeasureTheory/Group/Measure.lean b/Mathbin/MeasureTheory/Group/Measure.lean
index eccdafb9e1..f0398a61c1 100644
--- a/Mathbin/MeasureTheory/Group/Measure.lean
+++ b/Mathbin/MeasureTheory/Group/Measure.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
 
 ! This file was ported from Lean 3 source module measure_theory.group.measure
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 950605e4b9b4e2827681f637ba997307814a5ca9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -249,9 +249,9 @@ end HasMeasurableMul
 
 end Mul
 
-section Group
+section DivInvMonoid
 
-variable [Group G]
+variable [DivInvMonoid G]
 
 @[to_additive]
 theorem map_div_right_eq_self (μ : Measure G) [IsMulRightInvariant μ] (g : G) : map (· / g) μ = μ :=
@@ -259,7 +259,11 @@ theorem map_div_right_eq_self (μ : Measure G) [IsMulRightInvariant μ] (g : G)
 #align measure_theory.map_div_right_eq_self MeasureTheory.map_div_right_eq_self
 #align measure_theory.map_sub_right_eq_self MeasureTheory.map_sub_right_eq_self
 
-variable [HasMeasurableMul G]
+end DivInvMonoid
+
+section Group
+
+variable [Group G] [HasMeasurableMul G]
 
 @[to_additive]
 theorem measurePreservingDivRight (μ : Measure G) [IsMulRightInvariant μ] (g : G) :
@@ -427,9 +431,9 @@ instance (μ : Measure G) [SigmaFinite μ] : SigmaFinite μ.inv :=
 
 end InvolutiveInv
 
-section mul_inv
+section DivisionMonoid
 
-variable [Group G] [HasMeasurableMul G] [HasMeasurableInv G] {μ : Measure G}
+variable [DivisionMonoid G] [HasMeasurableMul G] [HasMeasurableInv G] {μ : Measure G}
 
 @[to_additive]
 instance [IsMulLeftInvariant μ] : IsMulRightInvariant μ.inv :=
@@ -479,6 +483,12 @@ theorem map_mul_right_inv_eq_self (μ : Measure G) [IsInvInvariant μ] [IsMulLef
 #align measure_theory.measure.map_mul_right_inv_eq_self MeasureTheory.Measure.map_mul_right_inv_eq_self
 #align measure_theory.measure.map_add_right_neg_eq_self MeasureTheory.Measure.map_add_right_neg_eq_self
 
+end DivisionMonoid
+
+section Group
+
+variable [Group G] [HasMeasurableMul G] [HasMeasurableInv G] {μ : Measure G}
+
 @[to_additive]
 theorem map_div_left_ae (μ : Measure G) [IsMulLeftInvariant μ] [IsInvInvariant μ] (x : G) :
     Filter.map (fun t => x / t) μ.ae = μ.ae :=
@@ -486,22 +496,22 @@ theorem map_div_left_ae (μ : Measure G) [IsMulLeftInvariant μ] [IsInvInvariant
 #align measure_theory.measure.map_div_left_ae MeasureTheory.Measure.map_div_left_ae
 #align measure_theory.measure.map_sub_left_ae MeasureTheory.Measure.map_sub_left_ae
 
-end mul_inv
+end Group
 
 end Measure
 
 section TopologicalGroup
 
-variable [TopologicalSpace G] [BorelSpace G] {μ : Measure G}
-
-variable [Group G] [TopologicalGroup G]
+variable [TopologicalSpace G] [BorelSpace G] {μ : Measure G} [Group G]
 
 @[to_additive]
-instance Measure.Regular.inv [T2Space G] [Regular μ] : Regular μ.inv :=
+instance Measure.Regular.inv [ContinuousInv G] [T2Space G] [Regular μ] : Regular μ.inv :=
   Regular.map (Homeomorph.inv G)
 #align measure_theory.measure.regular.inv MeasureTheory.Measure.Regular.inv
 #align measure_theory.measure.regular.neg MeasureTheory.Measure.Regular.neg
 
+variable [TopologicalGroup G]
+
 @[to_additive]
 theorem regular_inv_iff [T2Space G] : μ.inv.regular ↔ μ.regular :=
   by
@@ -657,9 +667,9 @@ theorem measure_univ_of_isMulLeftInvariant [LocallyCompactSpace G] [NoncompactSp
 
 end TopologicalGroup
 
-section CommGroup
+section CommSemigroup
 
-variable [CommGroup G]
+variable [CommSemigroup G]
 
 /-- In an abelian group every left invariant measure is also right-invariant.
   We don't declare the converse as an instance, since that would loop type-class inference, and
@@ -672,7 +682,7 @@ instance (priority := 100) IsMulLeftInvariant.isMulRightInvariant {μ : Measure
 #align measure_theory.is_mul_left_invariant.is_mul_right_invariant MeasureTheory.IsMulLeftInvariant.isMulRightInvariant
 #align is_add_left_invariant.is_add_right_invariant IsAddLeftInvariant.is_add_right_invariant
 
-end CommGroup
+end CommSemigroup
 
 section Haar
 
diff --git a/Mathbin/MeasureTheory/Measure/MeasureSpace.lean b/Mathbin/MeasureTheory/Measure/MeasureSpace.lean
index 7326aae30f..d156dcc44f 100644
--- a/Mathbin/MeasureTheory/Measure/MeasureSpace.lean
+++ b/Mathbin/MeasureTheory/Measure/MeasureSpace.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro
 
 ! This file was ported from Lean 3 source module measure_theory.measure.measure_space
-! leanprover-community/mathlib commit a75898643b2d774cced9ae7c0b28c21663b99666
+! leanprover-community/mathlib commit 3f5c9d30716c775bda043456728a1a3ee31412e7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -2143,6 +2143,19 @@ theorem sum_smul_dirac [Countable α] [MeasurableSingletonClass α] (μ : Measur
     (sum fun a => μ {a} • dirac a) = μ := by simpa using (map_eq_sum μ id measurable_id).symm
 #align measure_theory.measure.sum_smul_dirac MeasureTheory.Measure.sum_smul_dirac
 
+/-- Given that `α` is a countable, measurable space with all singleton sets measurable,
+write the measure of a set `s` as the sum of the measure of `{x}` for all `x ∈ s`. -/
+theorem tsum_indicator_apply_singleton [Countable α] [MeasurableSingletonClass α] (μ : Measure α)
+    (s : Set α) (hs : MeasurableSet s) : (∑' x : α, s.indicator (fun x => μ {x}) x) = μ s :=
+  calc
+    (∑' x : α, s.indicator (fun x => μ {x}) x) = Measure.sum (fun a => μ {a} • Measure.dirac a) s :=
+      by
+      simp only [measure.sum_apply _ hs, measure.smul_apply, smul_eq_mul, measure.dirac_apply,
+        Set.indicator_apply, mul_ite, Pi.one_apply, mul_one, mul_zero]
+    _ = μ s := by rw [μ.sum_smul_dirac]
+    
+#align measure_theory.measure.tsum_indicator_apply_singleton MeasureTheory.Measure.tsum_indicator_apply_singleton
+
 omit m0
 
 end Sum
diff --git a/Mathbin/NumberTheory/PellGeneral.lean b/Mathbin/NumberTheory/PellGeneral.lean
new file mode 100644
index 0000000000..090aa0fb35
--- /dev/null
+++ b/Mathbin/NumberTheory/PellGeneral.lean
@@ -0,0 +1,140 @@
+/-
+Copyright (c) 2023 Michael Stoll. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Michael Geißer, Michael Stoll
+
+! This file was ported from Lean 3 source module number_theory.pell_general
+! leanprover-community/mathlib commit c23aca359d4be6975b2a577d5cdb9d77b82c7407
+! Please do not edit these lines, except to modify the commit id
+! if you have ported upstream changes.
+-/
+import Mathbin.Tactic.Qify
+import Mathbin.Tactic.LinearCombination
+import Mathbin.Data.Zmod.Basic
+import Mathbin.NumberTheory.DiophantineApproximation
+
+/-!
+# Pell's Equation
+
+We prove the following
+
+**Theorem.** Let $d$ be a positive integer that is not a square. Then the equation
+$x^2 - d y^2 = 1$ has a nontrivial (i.e., with $y \ne 0$) solution in integers.
+
+See `pell.exists_of_not_is_square`.
+
+This is the beginning of a development that aims at providing all of the essential theory
+of Pell's Equation for general $d$ (as opposed to the contents of `number_theory.pell`,
+which is specific to the case $d = a^2 - 1$ for some $a > 1$).
+
+## References
+
+* [K. Ireland, M. Rosen, *A classical introduction to modern number theory*
+   (Section 17.5)][IrelandRosen1990]
+
+## Tags
+
+Pell's equation
+-/
+
+
+namespace Pell
+
+section Existence
+
+open Set Real
+
+/-- If `d` is a positive integer that is not a square, then there is a nontrivial solution
+to the Pell equation `x^2 - d*y^2 = 1`. -/
+theorem exists_of_not_isSquare {d : ℤ} (h₀ : 0 < d) (hd : ¬IsSquare d) :
+    ∃ x y : ℤ, x ^ 2 - d * y ^ 2 = 1 ∧ y ≠ 0 :=
+  by
+  let ξ : ℝ := sqrt d
+  have hξ : Irrational ξ :=
+    by
+    refine' irrational_nrt_of_notint_nrt 2 d (sq_sqrt <| int.cast_nonneg.mpr h₀.le) _ two_pos
+    rintro ⟨x, hx⟩
+    refine' hd ⟨x, @Int.cast_injective ℝ _ _ d (x * x) _⟩
+    rw [← sq_sqrt <| int.cast_nonneg.mpr h₀.le, Int.cast_mul, ← hx, sq]
+  obtain ⟨M, hM₁⟩ := exists_int_gt (2 * |ξ| + 1)
+  have hM : { q : ℚ | |q.1 ^ 2 - d * q.2 ^ 2| < M }.Infinite :=
+    by
+    refine' infinite.mono (fun q h => _) (infinite_rat_abs_sub_lt_one_div_denom_sq_of_irrational hξ)
+    have h0 : 0 < (q.2 : ℝ) ^ 2 := pow_pos (nat.cast_pos.mpr q.pos) 2
+    have h1 : (q.num : ℝ) / (q.denom : ℝ) = q := by exact_mod_cast q.num_div_denom
+    rw [mem_set_of, abs_sub_comm, ← @Int.cast_lt ℝ, ← div_lt_div_right (abs_pos_of_pos h0)]
+    push_cast
+    rw [← abs_div, abs_sq, sub_div, mul_div_cancel _ h0.ne', ← div_pow, h1, ←
+      sq_sqrt (int.cast_pos.mpr h₀).le, sq_sub_sq, abs_mul, ← mul_one_div]
+    refine' mul_lt_mul'' (((abs_add ξ q).trans _).trans_lt hM₁) h (abs_nonneg _) (abs_nonneg _)
+    rw [two_mul, add_assoc, add_le_add_iff_left, ← sub_le_iff_le_add']
+    rw [mem_set_of, abs_sub_comm] at h
+    refine' (abs_sub_abs_le_abs_sub (q : ℝ) ξ).trans (h.le.trans _)
+    rw [div_le_one h0, one_le_sq_iff_one_le_abs, Nat.abs_cast, Nat.one_le_cast]
+    exact q.pos
+  obtain ⟨m, hm⟩ : ∃ m : ℤ, { q : ℚ | q.1 ^ 2 - d * q.2 ^ 2 = m }.Infinite :=
+    by
+    contrapose! hM
+    simp only [not_infinite] at hM⊢
+    refine' (congr_arg _ (ext fun x => _)).mp (finite.bUnion (finite_Ioo (-M) M) fun m _ => hM m)
+    simp only [abs_lt, mem_set_of_eq, mem_Ioo, mem_Union, exists_prop, exists_eq_right']
+  have hm₀ : m ≠ 0 := by
+    rintro rfl
+    obtain ⟨q, hq⟩ := hm.nonempty
+    rw [mem_set_of, sub_eq_zero, mul_comm] at hq
+    obtain ⟨a, ha⟩ := (Int.pow_dvd_pow_iff two_pos).mp ⟨d, hq⟩
+    rw [ha, mul_pow, mul_right_inj' (pow_pos (int.coe_nat_pos.mpr q.pos) 2).ne'] at hq
+    exact hd ⟨a, sq a ▸ hq.symm⟩
+  haveI := ne_zero_iff.mpr (int.nat_abs_ne_zero.mpr hm₀)
+  let f : ℚ → ZMod m.nat_abs × ZMod m.nat_abs := fun q => (q.1, q.2)
+  obtain ⟨q₁, h₁ : q₁.1 ^ 2 - d * q₁.2 ^ 2 = m, q₂, h₂ : q₂.1 ^ 2 - d * q₂.2 ^ 2 = m, hne, hqf⟩ :=
+    hm.exists_ne_map_eq_of_maps_to (maps_to_univ f _) finite_univ
+  obtain ⟨hq1 : (q₁.1 : ZMod m.nat_abs) = q₂.1, hq2 : (q₁.2 : ZMod m.nat_abs) = q₂.2⟩ :=
+    prod.ext_iff.mp hqf
+  have hd₁ : m ∣ q₁.1 * q₂.1 - d * (q₁.2 * q₂.2) :=
+    by
+    rw [← Int.natAbs_dvd, ← ZMod.int_coe_zMod_eq_zero_iff_dvd]
+    push_cast
+    rw [hq1, hq2, ← sq, ← sq]
+    norm_cast
+    rw [ZMod.int_coe_zMod_eq_zero_iff_dvd, Int.natAbs_dvd, Nat.cast_pow, ← h₂]
+  have hd₂ : m ∣ q₁.1 * q₂.2 - q₂.1 * q₁.2 :=
+    by
+    rw [← Int.natAbs_dvd, ← ZMod.int_coe_eq_int_coe_iff_dvd_sub]
+    push_cast
+    rw [hq1, hq2]
+  replace hm₀ : (m : ℚ) ≠ 0 := int.cast_ne_zero.mpr hm₀
+  refine' ⟨(q₁.1 * q₂.1 - d * (q₁.2 * q₂.2)) / m, (q₁.1 * q₂.2 - q₂.1 * q₁.2) / m, _, _⟩
+  · qify [hd₁, hd₂]
+    field_simp [hm₀]
+    norm_cast
+    conv_rhs =>
+      congr
+      rw [sq]
+      congr
+      rw [← h₁]
+      skip
+      rw [← h₂]
+    push_cast
+    ring
+  · qify [hd₂]
+    refine' div_ne_zero_iff.mpr ⟨_, hm₀⟩
+    exact_mod_cast mt sub_eq_zero.mp (mt rat.eq_iff_mul_eq_mul.mpr hne)
+#align pell.exists_of_not_is_square Pell.exists_of_not_isSquare
+
+/-- If `d` is a positive integer, then there is a nontrivial solution
+to the Pell equation `x^2 - d*y^2 = 1` if and only if `d` is not a square. -/
+theorem exists_iff_not_isSquare {d : ℤ} (h₀ : 0 < d) :
+    (∃ x y : ℤ, x ^ 2 - d * y ^ 2 = 1 ∧ y ≠ 0) ↔ ¬IsSquare d :=
+  by
+  refine' ⟨_, exists_of_not_is_square h₀⟩
+  rintro ⟨x, y, hxy, hy⟩ ⟨a, rfl⟩
+  rw [← sq, ← mul_pow, sq_sub_sq, Int.mul_eq_one_iff_eq_one_or_neg_one] at hxy
+  replace hxy := hxy.elim (fun h => h.1.trans h.2.symm) fun h => h.1.trans h.2.symm
+  simpa [mul_self_pos.mp h₀, sub_eq_add_neg, eq_neg_self_iff] using hxy
+#align pell.exists_iff_not_is_square Pell.exists_iff_not_isSquare
+
+end Existence
+
+end Pell
+
diff --git a/Mathbin/Probability/ProbabilityMassFunction/Basic.lean b/Mathbin/Probability/ProbabilityMassFunction/Basic.lean
index d4f2d7013b..90d4356b4c 100644
--- a/Mathbin/Probability/ProbabilityMassFunction/Basic.lean
+++ b/Mathbin/Probability/ProbabilityMassFunction/Basic.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
 
 ! This file was ported from Lean 3 source module probability.probability_mass_function.basic
-! leanprover-community/mathlib commit e50b8c261b0a000b806ec0e1356b41945eda61f7
+! leanprover-community/mathlib commit 3f5c9d30716c775bda043456728a1a3ee31412e7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -25,6 +25,9 @@ by assigning each set the sum of the probabilities of each of its elements.
 Under this outer measure, every set is Carathéodory-measurable,
 so we can further extend this to a `measure` on `α`, see `pmf.to_measure`.
 `pmf.to_measure.is_probability_measure` shows this associated measure is a probability measure.
+Conversely, given a probability measure `μ` on a measurable space `α` with all singleton sets
+measurable, `μ.to_pmf` constructs a `pmf` on `α`, setting the probability mass of a point `x`
+to be the measure of the singleton set `{x}`.
 
 ## Tags
 
@@ -36,7 +39,7 @@ noncomputable section
 
 variable {α β γ : Type _}
 
-open Classical BigOperators NNReal Ennreal
+open Classical BigOperators NNReal Ennreal MeasureTheory
 
 /-- A probability mass function, or discrete probability measures is a function `α → ℝ≥0∞` such
   that the values have (infinite) sum `1`. -/
@@ -154,6 +157,15 @@ theorem toOuterMeasure_apply : p.toOuterMeasure s = ∑' x, s.indicator p x :=
   tsum_congr fun x => smul_dirac_apply (p x) x s
 #align pmf.to_outer_measure_apply Pmf.toOuterMeasure_apply
 
+@[simp]
+theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ :=
+  by
+  refine' eq_top_iff.2 <| le_trans (le_infₛ fun x hx => _) (le_sum_caratheodory _)
+  exact
+    let ⟨y, hy⟩ := hx
+    ((le_of_eq (dirac_caratheodory y).symm).trans (le_smul_caratheodory _ _)).trans (le_of_eq hy)
+#align pmf.to_outer_measure_caratheodory Pmf.toOuterMeasure_caratheodory
+
 @[simp]
 theorem toOuterMeasure_apply_finset (s : Finset α) : p.toOuterMeasure s = ∑ x in s, p x :=
   by
@@ -169,6 +181,18 @@ theorem toOuterMeasure_apply_singleton (a : α) : p.toOuterMeasure {a} = p a :=
   · exact ite_eq_left_iff.2 fun ha' => False.elim <| ha' rfl
 #align pmf.to_outer_measure_apply_singleton Pmf.toOuterMeasure_apply_singleton
 
+theorem toOuterMeasure_injective : (toOuterMeasure : Pmf α → OuterMeasure α).Injective :=
+  fun p q h =>
+  Pmf.ext fun x =>
+    (p.toOuterMeasure_apply_singleton x).symm.trans
+      ((congr_fun (congr_arg _ h) _).trans <| q.toOuterMeasure_apply_singleton x)
+#align pmf.to_outer_measure_injective Pmf.toOuterMeasure_injective
+
+@[simp]
+theorem toOuterMeasure_inj {p q : Pmf α} : p.toOuterMeasure = q.toOuterMeasure ↔ p = q :=
+  toOuterMeasure_injective.eq_iff
+#align pmf.to_outer_measure_inj Pmf.toOuterMeasure_inj
+
 theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p.support s :=
   by
   rw [to_outer_measure_apply, Ennreal.tsum_eq_zero]
@@ -216,15 +240,6 @@ theorem toOuterMeasure_apply_fintype [Fintype α] : p.toOuterMeasure s = ∑ x,
   (p.toOuterMeasure_apply s).trans (tsum_eq_sum fun x h => absurd (Finset.mem_univ x) h)
 #align pmf.to_outer_measure_apply_fintype Pmf.toOuterMeasure_apply_fintype
 
-@[simp]
-theorem toOuterMeasure_caratheodory (p : Pmf α) : (toOuterMeasure p).caratheodory = ⊤ :=
-  by
-  refine' eq_top_iff.2 <| le_trans (le_infₛ fun x hx => _) (le_sum_caratheodory _)
-  obtain ⟨y, hy⟩ := hx
-  exact
-    ((le_of_eq (dirac_caratheodory y).symm).trans (le_smul_caratheodory _ _)).trans (le_of_eq hy)
-#align pmf.to_outer_measure_caratheodory Pmf.toOuterMeasure_caratheodory
-
 end OuterMeasure
 
 section Measure
@@ -254,7 +269,7 @@ theorem toMeasure_apply (hs : MeasurableSet s) : p.toMeasure s = ∑' x, s.indic
 
 theorem toMeasure_apply_singleton (a : α) (h : MeasurableSet ({a} : Set α)) :
     p.toMeasure {a} = p a := by
-  simp [to_measure_apply_eq_to_outer_measure_apply p {a} h, to_outer_measure_apply_singleton]
+  simp [to_measure_apply_eq_to_outer_measure_apply _ _ h, to_outer_measure_apply_singleton]
 #align pmf.to_measure_apply_singleton Pmf.toMeasure_apply_singleton
 
 theorem toMeasure_apply_eq_zero_iff (hs : MeasurableSet s) :
@@ -289,6 +304,18 @@ section MeasurableSingletonClass
 
 variable [MeasurableSingletonClass α]
 
+theorem toMeasure_injective : (toMeasure : Pmf α → Measure α).Injective := fun p q h =>
+  Pmf.ext fun x =>
+    (p.toMeasure_apply_singleton x <| measurableSet_singleton x).symm.trans
+      ((congr_fun (congr_arg _ h) _).trans <|
+        q.toMeasure_apply_singleton x <| measurableSet_singleton x)
+#align pmf.to_measure_injective Pmf.toMeasure_injective
+
+@[simp]
+theorem toMeasure_inj {p q : Pmf α} : p.toMeasure = q.toMeasure ↔ p = q :=
+  toMeasure_injective.eq_iff
+#align pmf.to_measure_inj Pmf.toMeasure_inj
+
 @[simp]
 theorem toMeasure_apply_finset (s : Finset α) : p.toMeasure s = ∑ x in s, p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s s.MeasurableSet).trans
@@ -307,14 +334,75 @@ theorem toMeasure_apply_fintype [Fintype α] : p.toMeasure s = ∑ x, s.indicato
 
 end MeasurableSingletonClass
 
+end Measure
+
+end Pmf
+
+namespace MeasureTheory
+
+open Pmf
+
+namespace Measure
+
+/-- Given that `α` is a countable, measurable space with all singleton sets measurable,
+we can convert any probability measure into a `pmf`, where the mass of a point
+is the measure of the singleton set under the original measure. -/
+def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
+    [h : IsProbabilityMeasure μ] : Pmf α :=
+  ⟨fun x => μ ({x} : Set α),
+    Ennreal.summable.hasSum_iff.2
+      (trans
+        (symm <|
+          (tsum_indicator_apply_singleton μ Set.univ MeasurableSet.univ).symm.trans
+            (tsum_congr fun x => congr_fun (Set.indicator_univ _) x))
+        h.measure_univ)⟩
+#align measure_theory.measure.to_pmf MeasureTheory.Measure.toPmf
+
+variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
+  [IsProbabilityMeasure μ]
+
+theorem toPmf_apply (x : α) : μ.toPmf x = μ {x} :=
+  rfl
+#align measure_theory.measure.to_pmf_apply MeasureTheory.Measure.toPmf_apply
+
+@[simp]
+theorem toPmf_toMeasure : μ.toPmf.toMeasure = μ :=
+  Measure.ext fun s hs => by
+    simpa only [μ.to_pmf.to_measure_apply s hs, ← μ.tsum_indicator_apply_singleton s hs]
+#align measure_theory.measure.to_pmf_to_measure MeasureTheory.Measure.toPmf_toMeasure
+
+end Measure
+
+end MeasureTheory
+
+namespace Pmf
+
+open MeasureTheory
+
 /-- The measure associated to a `pmf` by `to_measure` is a probability measure -/
-instance toMeasure.isProbabilityMeasure (p : Pmf α) : IsProbabilityMeasure p.toMeasure :=
+instance toMeasure.isProbabilityMeasure [MeasurableSpace α] (p : Pmf α) :
+    IsProbabilityMeasure p.toMeasure :=
   ⟨by
     simpa only [MeasurableSet.univ, to_measure_apply_eq_to_outer_measure_apply, Set.indicator_univ,
       to_outer_measure_apply, Ennreal.coe_eq_one] using tsum_coe p⟩
 #align pmf.to_measure.is_probability_measure Pmf.toMeasure.isProbabilityMeasure
 
-end Measure
+variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (p : Pmf α) (μ : Measure α)
+  [IsProbabilityMeasure μ]
+
+@[simp]
+theorem toMeasure_toPmf : p.toMeasure.toPmf = p :=
+  Pmf.ext fun x => by
+    rw [← p.to_measure_apply_singleton x (measurable_set_singleton x), p.to_measure.to_pmf_apply]
+#align pmf.to_measure_to_pmf Pmf.toMeasure_toPmf
+
+theorem toMeasure_eq_iff_eq_toPmf (μ : Measure α) [IsProbabilityMeasure μ] :
+    p.toMeasure = μ ↔ p = μ.toPmf := by rw [← to_measure_inj, measure.to_pmf_to_measure]
+#align pmf.to_measure_eq_iff_eq_to_pmf Pmf.toMeasure_eq_iff_eq_toPmf
+
+theorem toPmf_eq_iff_toMeasure_eq (μ : Measure α) [IsProbabilityMeasure μ] :
+    μ.toPmf = p ↔ μ = p.toMeasure := by rw [← to_measure_inj, measure.to_pmf_to_measure]
+#align pmf.to_pmf_eq_iff_to_measure_eq Pmf.toPmf_eq_iff_toMeasure_eq
 
 end Pmf
 
diff --git a/Mathbin/Probability/ProbabilityMassFunction/Monad.lean b/Mathbin/Probability/ProbabilityMassFunction/Monad.lean
index 841ad2b3bd..d5dcc5266d 100644
--- a/Mathbin/Probability/ProbabilityMassFunction/Monad.lean
+++ b/Mathbin/Probability/ProbabilityMassFunction/Monad.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
 
 ! This file was ported from Lean 3 source module probability.probability_mass_function.monad
-! leanprover-community/mathlib commit feb165c980c918bb296fede8c3b21dbb4b85bb56
+! leanprover-community/mathlib commit 3f5c9d30716c775bda043456728a1a3ee31412e7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -30,6 +30,8 @@ variable {α β γ : Type _}
 
 open Classical BigOperators NNReal Ennreal
 
+open MeasureTheory
+
 namespace Pmf
 
 section Pure
@@ -73,13 +75,24 @@ theorem toOuterMeasure_pure_apply : (pure a).toOuterMeasure s = if a ∈ s then
     exact ite_eq_right_iff.2 fun hb => ite_eq_right_iff.2 fun h => (ha <| h ▸ hb).elim
 #align pmf.to_outer_measure_pure_apply Pmf.toOuterMeasure_pure_apply
 
+variable [MeasurableSpace α]
+
 /-- The measure of a set under `pure a` is `1` for sets containing `a` and `0` otherwise -/
 @[simp]
-theorem toMeasure_pure_apply [MeasurableSpace α] (hs : MeasurableSet s) :
+theorem toMeasure_pure_apply (hs : MeasurableSet s) :
     (pure a).toMeasure s = if a ∈ s then 1 else 0 :=
   (toMeasure_apply_eq_toOuterMeasure_apply (pure a) s hs).trans (toOuterMeasure_pure_apply a s)
 #align pmf.to_measure_pure_apply Pmf.toMeasure_pure_apply
 
+theorem toMeasure_pure : (pure a).toMeasure = Measure.dirac a :=
+  Measure.ext fun s hs => by simpa only [to_measure_pure_apply a s hs, measure.dirac_apply' a hs]
+#align pmf.to_measure_pure Pmf.toMeasure_pure
+
+@[simp]
+theorem toPmf_dirac [Countable α] [h : MeasurableSingletonClass α] :
+    (Measure.dirac a).toPmf = pure a := by rw [to_pmf_eq_iff_to_measure_eq, to_measure_pure]
+#align pmf.to_pmf_dirac Pmf.toPmf_dirac
+
 end Measure
 
 end Pure
diff --git a/README.md b/README.md
index 8b356fa8da..f1ce04ce37 100644
--- a/README.md
+++ b/README.md
@@ -1,4 +1,4 @@
-Tracking mathlib commit: [`271bf175e6c51b8d31d6c0107b7bb4a967c7277e`](https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e)
+Tracking mathlib commit: [`c23aca359d4be6975b2a577d5cdb9d77b82c7407`](https://github.com/leanprover-community/mathlib/commit/c23aca359d4be6975b2a577d5cdb9d77b82c7407)
 
 You should use this repository to inspect the Lean 4 files that `mathport` has generated from mathlib3.
 Please run `lake build` first, to download a copy of the generated `.olean` files.
diff --git a/lake-manifest.json b/lake-manifest.json
index 7d514e8bc6..b1c341393c 100644
--- a/lake-manifest.json
+++ b/lake-manifest.json
@@ -4,9 +4,9 @@
  [{"git":
    {"url": "https://github.com/leanprover-community/lean3port.git",
     "subDir?": null,
-    "rev": "279881c83f3c6d5d336a57c8a134dd2684728d86",
+    "rev": "ff073d896a9d45fbc7bc674c6002562500a1507f",
     "name": "lean3port",
-    "inputRev?": "279881c83f3c6d5d336a57c8a134dd2684728d86"}},
+    "inputRev?": "ff073d896a9d45fbc7bc674c6002562500a1507f"}},
   {"git":
    {"url": "https://github.com/leanprover-community/mathlib4.git",
     "subDir?": null,
diff --git a/lakefile.lean b/lakefile.lean
index 1fb64e0e89..1c11b0ce49 100644
--- a/lakefile.lean
+++ b/lakefile.lean
@@ -4,7 +4,7 @@ open Lake DSL System
 -- Usually the `tag` will be of the form `nightly-2021-11-22`.
 -- If you would like to use an artifact from a PR build,
 -- it will be of the form `pr-branchname-sha`.
-def tag : String := "nightly-2023-02-26-00"
+def tag : String := "nightly-2023-02-26-03"
 def releaseRepo : String := "leanprover-community/mathport"
 def oleanTarName : String := "mathlib3-binport.tar.gz"
 
@@ -38,7 +38,7 @@ target fetchOleans (_pkg : Package) : Unit := do
     untarReleaseArtifact releaseRepo tag oleanTarName libDir
   return .nil
 
-require lean3port from git "https://github.com/leanprover-community/lean3port.git"@"279881c83f3c6d5d336a57c8a134dd2684728d86"
+require lean3port from git "https://github.com/leanprover-community/lean3port.git"@"ff073d896a9d45fbc7bc674c6002562500a1507f"
 
 @[default_target]
 lean_lib Mathbin where
diff --git a/upstream-rev b/upstream-rev
index f354fd92ff..bdf18a5f0a 100644
--- a/upstream-rev
+++ b/upstream-rev
@@ -1 +1 @@
-271bf175e6c51b8d31d6c0107b7bb4a967c7277e
+c23aca359d4be6975b2a577d5cdb9d77b82c7407