diff --git a/Mathbin/Analysis/Asymptotics/Asymptotics.lean b/Mathbin/Analysis/Asymptotics/Asymptotics.lean
index 5740be6154..1027df0a15 100644
--- a/Mathbin/Analysis/Asymptotics/Asymptotics.lean
+++ b/Mathbin/Analysis/Asymptotics/Asymptotics.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.asymptotics.asymptotics
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 9a48a083b390d9b84a71efbdc4e8dfa26a687104
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.LocalHomeomorph
 /-!
 # Asymptotics
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We introduce these relations:
 
 * `is_O_with c l f g` : "f is big O of g along l with constant c";
diff --git a/Mathbin/Analysis/Convex/Quasiconvex.lean b/Mathbin/Analysis/Convex/Quasiconvex.lean
index bfb33ce8d0..8fa52f49e7 100644
--- a/Mathbin/Analysis/Convex/Quasiconvex.lean
+++ b/Mathbin/Analysis/Convex/Quasiconvex.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
 
 ! This file was ported from Lean 3 source module analysis.convex.quasiconvex
-! leanprover-community/mathlib commit 9003f28797c0664a49e4179487267c494477d853
+! leanprover-community/mathlib commit 9a48a083b390d9b84a71efbdc4e8dfa26a687104
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.Convex.Function
 /-!
 # Quasiconvex and quasiconcave functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines quasiconvexity, quasiconcavity and quasilinearity of functions, which are
 generalizations of unimodality and monotonicity. Convexity implies quasiconvexity, concavity implies
 quasiconcavity, and monotonicity implies quasilinearity.
diff --git a/Mathbin/Analysis/LocallyConvex/Basic.lean b/Mathbin/Analysis/LocallyConvex/Basic.lean
index 5c560e99d3..cc15aa6ed7 100644
--- a/Mathbin/Analysis/LocallyConvex/Basic.lean
+++ b/Mathbin/Analysis/LocallyConvex/Basic.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jean Lo, Bhavik Mehta, Yaël Dillies
 
 ! This file was ported from Lean 3 source module analysis.locally_convex.basic
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 9a48a083b390d9b84a71efbdc4e8dfa26a687104
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.NormedSpace.Basic
 /-!
 # Local convexity
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines absorbent and balanced sets.
 
 An absorbent set is one that "surrounds" the origin. The idea is made precise by requiring that any
diff --git a/Mathbin/Analysis/Normed/Order/UpperLower.lean b/Mathbin/Analysis/Normed/Order/UpperLower.lean
index 2557829b22..1eeb636da1 100644
--- a/Mathbin/Analysis/Normed/Order/UpperLower.lean
+++ b/Mathbin/Analysis/Normed/Order/UpperLower.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
 
 ! This file was ported from Lean 3 source module analysis.normed.order.upper_lower
-! leanprover-community/mathlib commit 992efbda6f85a5c9074375d3c7cb9764c64d8f72
+! leanprover-community/mathlib commit 9a48a083b390d9b84a71efbdc4e8dfa26a687104
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Algebra.Order.UpperLower
 /-!
 # Upper/lower/order-connected sets in normed groups
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The topological closure and interior of an upper/lower/order-connected set is an
 upper/lower/order-connected set (with the notable exception of the closure of an order-connected
 set).
diff --git a/Mathbin/Analysis/NormedSpace/ContinuousLinearMap.lean b/Mathbin/Analysis/NormedSpace/ContinuousLinearMap.lean
index 322789dda0..a063d98721 100644
--- a/Mathbin/Analysis/NormedSpace/ContinuousLinearMap.lean
+++ b/Mathbin/Analysis/NormedSpace/ContinuousLinearMap.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
 
 ! This file was ported from Lean 3 source module analysis.normed_space.continuous_linear_map
-! leanprover-community/mathlib commit e0e2f10d64d8a5fd11140de398eaa1322eb46c07
+! leanprover-community/mathlib commit 9a48a083b390d9b84a71efbdc4e8dfa26a687104
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -12,6 +12,9 @@ import Mathbin.Analysis.NormedSpace.Basic
 
 /-! # Constructions of continuous linear maps between (semi-)normed spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A fundamental fact about (semi-)linear maps between normed spaces over sensible fields is that
 continuity and boundedness are equivalent conditions.  That is, for normed spaces `E`, `F`, a
 `linear_map` `f : E →ₛₗ[σ] F` is the coercion of some `continuous_linear_map` `f' : E →SL[σ] F`, if
diff --git a/Mathbin/Analysis/NormedSpace/Ray.lean b/Mathbin/Analysis/NormedSpace/Ray.lean
index 0e8f35426f..33905acd5d 100644
--- a/Mathbin/Analysis/NormedSpace/Ray.lean
+++ b/Mathbin/Analysis/NormedSpace/Ray.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Yaël Dillies
 
 ! This file was ported from Lean 3 source module analysis.normed_space.ray
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
+! leanprover-community/mathlib commit 9a48a083b390d9b84a71efbdc4e8dfa26a687104
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.NormedSpace.Basic
 /-!
 # Rays in a real normed vector space
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove some lemmas about the `same_ray` predicate in case of a real normed space. In
 this case, for two vectors `x y` in the same ray, the norm of their sum is equal to the sum of their
 norms and `‖y‖ • x = ‖x‖ • y`.
diff --git a/Mathbin/Analysis/NormedSpace/RieszLemma.lean b/Mathbin/Analysis/NormedSpace/RieszLemma.lean
index 6a196bcdc8..c04577d6f8 100644
--- a/Mathbin/Analysis/NormedSpace/RieszLemma.lean
+++ b/Mathbin/Analysis/NormedSpace/RieszLemma.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jean Lo, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.normed_space.riesz_lemma
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 9a48a083b390d9b84a71efbdc4e8dfa26a687104
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Topology.MetricSpace.HausdorffDistance
 /-!
 # Applications of the Hausdorff distance in normed spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Riesz's lemma, stated for a normed space over a normed field: for any
 closed proper subspace `F` of `E`, there is a nonzero `x` such that `‖x - F‖`
 is at least `r * ‖x‖` for any `r < 1`. This is `riesz_lemma`.
diff --git a/Mathbin/Analysis/Seminorm.lean b/Mathbin/Analysis/Seminorm.lean
index c4eacf3531..918f9343dc 100644
--- a/Mathbin/Analysis/Seminorm.lean
+++ b/Mathbin/Analysis/Seminorm.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jean Lo, Yaël Dillies, Moritz Doll
 
 ! This file was ported from Lean 3 source module analysis.seminorm
-! leanprover-community/mathlib commit 832a8ba8f10f11fea99367c469ff802e69a5b8ec
+! leanprover-community/mathlib commit 7ebf83ed9c262adbf983ef64d5e8c2ae94b625f4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -255,12 +255,22 @@ theorem smul_sup [SMul R ℝ] [SMul R ℝ≥0] [IsScalarTower R ℝ≥0 ℝ] (r
 instance : PartialOrder (Seminorm 𝕜 E) :=
   PartialOrder.lift _ FunLike.coe_injective
 
-theorem le_def (p q : Seminorm 𝕜 E) : p ≤ q ↔ (p : E → ℝ) ≤ q :=
+@[simp, norm_cast]
+theorem coe_le_coe {p q : Seminorm 𝕜 E} : (p : E → ℝ) ≤ q ↔ p ≤ q :=
   Iff.rfl
-#align seminorm.le_def Seminorm.le_def
+#align seminorm.coe_le_coe Seminorm.coe_le_coe
+
+@[simp, norm_cast]
+theorem coe_lt_coe {p q : Seminorm 𝕜 E} : (p : E → ℝ) < q ↔ p < q :=
+  Iff.rfl
+#align seminorm.coe_lt_coe Seminorm.coe_lt_coe
 
-theorem lt_def (p q : Seminorm 𝕜 E) : p < q ↔ (p : E → ℝ) < q :=
+theorem le_def {p q : Seminorm 𝕜 E} : p ≤ q ↔ ∀ x, p x ≤ q x :=
   Iff.rfl
+#align seminorm.le_def Seminorm.le_def
+
+theorem lt_def {p q : Seminorm 𝕜 E} : p < q ↔ p ≤ q ∧ ∃ x, p x < q x :=
+  Pi.lt_def
 #align seminorm.lt_def Seminorm.lt_def
 
 instance : SemilatticeSup (Seminorm 𝕜 E) :=
@@ -364,7 +374,7 @@ theorem bot_eq_zero : (⊥ : Seminorm 𝕜 E) = 0 :=
 
 theorem smul_le_smul {p q : Seminorm 𝕜 E} {a b : ℝ≥0} (hpq : p ≤ q) (hab : a ≤ b) : a • p ≤ b • q :=
   by
-  simp_rw [le_def, Pi.le_def, coe_smul]
+  simp_rw [le_def, coe_smul]
   intro x
   simp_rw [Pi.smul_apply, NNReal.smul_def, smul_eq_mul]
   exact mul_le_mul hab (hpq x) (map_nonneg p x) (NNReal.coe_nonneg b)
diff --git a/Mathbin/CategoryTheory/Idempotents/SimplicialObject.lean b/Mathbin/CategoryTheory/Idempotents/SimplicialObject.lean
index 39d39fa82c..c4b8d96aac 100644
--- a/Mathbin/CategoryTheory/Idempotents/SimplicialObject.lean
+++ b/Mathbin/CategoryTheory/Idempotents/SimplicialObject.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 
 ! This file was ported from Lean 3 source module category_theory.idempotents.simplicial_object
-! leanprover-community/mathlib commit 163d1a6d98caf9f0431704169027e49c5c6c6cc0
+! leanprover-community/mathlib commit 9a48a083b390d9b84a71efbdc4e8dfa26a687104
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.Idempotents.FunctorCategories
 
 # Idempotent completeness of categories of simplicial objects
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, we provide an instance expressing that `simplicial_object C`
 and `cosimplicial_object C` are idempotent complete categories when the
 category `C` is.
diff --git a/Mathbin/Data/Finset/Basic.lean b/Mathbin/Data/Finset/Basic.lean
index 3417be6143..066b05d77a 100644
--- a/Mathbin/Data/Finset/Basic.lean
+++ b/Mathbin/Data/Finset/Basic.lean
@@ -4980,9 +4980,9 @@ 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
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 but is expected to have type
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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) 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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)) 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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.605.97219 : 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 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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 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(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.33048 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)) 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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 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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.657.96664 : 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) 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(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.33048 : 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.33048 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 3c4dce2115..a7ac2c26c2 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
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 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/Data/Matrix/Rank.lean b/Mathbin/Data/Matrix/Rank.lean
index 4aebf30c9c..a2b4825db6 100644
--- a/Mathbin/Data/Matrix/Rank.lean
+++ b/Mathbin/Data/Matrix/Rank.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module data.matrix.rank
-! leanprover-community/mathlib commit b5b5dd5a47b5744260e2c9185013075ce9dadccd
+! leanprover-community/mathlib commit 86add5ce96b35c2cc6ee6946ab458e7302584e21
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -23,7 +23,7 @@ This definition does not depend on the choice of basis, see `matrix.rank_eq_finr
 
 ## TODO
 
-* Show that `matrix.rank` is equal to the row-rank and column-rank
+* Show that `matrix.rank` is equal to the row-rank, and that `rank Aᵀ = rank A`.
 
 -/
 
@@ -34,30 +34,31 @@ namespace Matrix
 
 open FiniteDimensional
 
-variable {m n o R : Type _} [m_fin : Fintype m] [Fintype n] [Fintype o]
+variable {l m n o R : Type _} [m_fin : Fintype m] [Fintype n] [Fintype o]
 
-variable [DecidableEq n] [DecidableEq o] [CommRing R]
+variable [CommRing R]
 
 /-- The rank of a matrix is the rank of its image. -/
 noncomputable def rank (A : Matrix m n R) : ℕ :=
-  finrank R A.toLin'.range
+  finrank R A.mulVecLin.range
 #align matrix.rank Matrix.rank
 
 @[simp]
-theorem rank_one [StrongRankCondition R] : rank (1 : Matrix n n R) = Fintype.card n := by
-  rw [rank, to_lin'_one, LinearMap.range_id, finrank_top, finrank_pi]
+theorem rank_one [StrongRankCondition R] [DecidableEq n] :
+    rank (1 : Matrix n n R) = Fintype.card n := by
+  rw [rank, mul_vec_lin_one, LinearMap.range_id, finrank_top, finrank_pi]
 #align matrix.rank_one Matrix.rank_one
 
 @[simp]
 theorem rank_zero [Nontrivial R] : rank (0 : Matrix m n R) = 0 := by
-  rw [rank, LinearEquiv.map_zero, LinearMap.range_zero, finrank_bot]
+  rw [rank, mul_vec_lin_zero, LinearMap.range_zero, finrank_bot]
 #align matrix.rank_zero Matrix.rank_zero
 
 theorem rank_le_card_width [StrongRankCondition R] (A : Matrix m n R) : A.rank ≤ Fintype.card n :=
   by
   haveI : Module.Finite R (n → R) := Module.Finite.pi
   haveI : Module.Free R (n → R) := Module.Free.pi _ _
-  exact A.to_lin'.finrank_range_le.trans_eq (finrank_pi _)
+  exact A.mul_vec_lin.finrank_range_le.trans_eq (finrank_pi _)
 #align matrix.rank_le_card_width Matrix.rank_le_card_width
 
 theorem rank_le_width [StrongRankCondition R] {m n : ℕ} (A : Matrix (Fin m) (Fin n) R) :
@@ -65,21 +66,37 @@ theorem rank_le_width [StrongRankCondition R] {m n : ℕ} (A : Matrix (Fin m) (F
   A.rank_le_card_width.trans <| (Fintype.card_fin n).le
 #align matrix.rank_le_width Matrix.rank_le_width
 
-theorem rank_mul_le [StrongRankCondition R] (A : Matrix m n R) (B : Matrix n o R) :
+theorem rank_mul_le_left [StrongRankCondition R] (A : Matrix m n R) (B : Matrix n o R) :
     (A ⬝ B).rank ≤ A.rank := by
-  rw [rank, rank, to_lin'_mul]
+  rw [rank, rank, mul_vec_lin_mul]
   exact Cardinal.toNat_le_of_le_of_lt_aleph0 (rank_lt_aleph_0 _ _) (LinearMap.rank_comp_le_left _ _)
+#align matrix.rank_mul_le_left Matrix.rank_mul_le_left
+
+include m_fin
+
+theorem rank_mul_le_right [StrongRankCondition R] (A : Matrix l m R) (B : Matrix m n R) :
+    (A ⬝ B).rank ≤ B.rank := by
+  rw [rank, rank, mul_vec_lin_mul]
+  exact
+    finrank_le_finrank_of_rank_le_rank (LinearMap.lift_rank_comp_le_right _ _) (rank_lt_aleph_0 _ _)
+#align matrix.rank_mul_le_right Matrix.rank_mul_le_right
+
+omit m_fin
+
+theorem rank_mul_le [StrongRankCondition R] (A : Matrix m n R) (B : Matrix n o R) :
+    (A ⬝ B).rank ≤ min A.rank B.rank :=
+  le_min (rank_mul_le_left _ _) (rank_mul_le_right _ _)
 #align matrix.rank_mul_le Matrix.rank_mul_le
 
-theorem rank_unit [StrongRankCondition R] (A : (Matrix n n R)ˣ) :
+theorem rank_unit [StrongRankCondition R] [DecidableEq n] (A : (Matrix n n R)ˣ) :
     (A : Matrix n n R).rank = Fintype.card n :=
   by
   refine' le_antisymm (rank_le_card_width A) _
-  have := rank_mul_le (A : Matrix n n R) (↑A⁻¹ : Matrix n n R)
+  have := rank_mul_le_left (A : Matrix n n R) (↑A⁻¹ : Matrix n n R)
   rwa [← mul_eq_mul, ← Units.val_mul, mul_inv_self, Units.val_one, rank_one] at this
 #align matrix.rank_unit Matrix.rank_unit
 
-theorem rank_of_isUnit [StrongRankCondition R] (A : Matrix n n R) (h : IsUnit A) :
+theorem rank_of_isUnit [StrongRankCondition R] [DecidableEq n] (A : Matrix n n R) (h : IsUnit A) :
     A.rank = Fintype.card n := by
   obtain ⟨A, rfl⟩ := h
   exact rank_unit A
@@ -87,9 +104,9 @@ theorem rank_of_isUnit [StrongRankCondition R] (A : Matrix n n R) (h : IsUnit A)
 
 include m_fin
 
-theorem rank_eq_finrank_range_toLin {M₁ M₂ : Type _} [AddCommGroup M₁] [AddCommGroup M₂]
-    [Module R M₁] [Module R M₂] (A : Matrix m n R) (v₁ : Basis m R M₁) (v₂ : Basis n R M₂) :
-    A.rank = finrank R (toLin v₂ v₁ A).range :=
+theorem rank_eq_finrank_range_toLin [DecidableEq n] {M₁ M₂ : Type _} [AddCommGroup M₁]
+    [AddCommGroup M₂] [Module R M₁] [Module R M₂] (A : Matrix m n R) (v₁ : Basis m R M₁)
+    (v₂ : Basis n R M₂) : A.rank = finrank R (toLin v₂ v₁ A).range :=
   by
   let e₁ := (Pi.basisFun R m).Equiv v₁ (Equiv.refl _)
   let e₂ := (Pi.basisFun R n).Equiv v₂ (Equiv.refl _)
@@ -105,7 +122,7 @@ theorem rank_eq_finrank_range_toLin {M₁ M₂ : Type _} [AddCommGroup M₁] [Ad
   apply LinearMap.ext_ring
   have aux₁ := to_lin_self (Pi.basisFun R n) (Pi.basisFun R m) A i
   have aux₂ := Basis.equiv_apply (Pi.basisFun R n) i v₂
-  rw [to_lin_eq_to_lin'] at aux₁
+  rw [to_lin_eq_to_lin', to_lin'_apply'] at aux₁
   rw [Pi.basisFun_apply, LinearMap.coe_stdBasis] at aux₁ aux₂
   simp only [LinearMap.comp_apply, e₁, e₂, LinearEquiv.coe_coe, Equiv.refl_apply, aux₁, aux₂,
     LinearMap.coe_single, to_lin_self, LinearEquiv.map_sum, LinearEquiv.map_smul, Basis.equiv_apply]
@@ -125,5 +142,10 @@ theorem rank_le_height [StrongRankCondition R] {m n : ℕ} (A : Matrix (Fin m) (
   A.rank_le_card_height.trans <| (Fintype.card_fin m).le
 #align matrix.rank_le_height Matrix.rank_le_height
 
+/-- The rank of a matrix is the rank of the space spanned by its columns. -/
+theorem rank_eq_finrank_span_cols (A : Matrix m n R) :
+    A.rank = finrank R (Submodule.span R (Set.range Aᵀ)) := by rw [rank, Matrix.range_mulVecLin]
+#align matrix.rank_eq_finrank_span_cols Matrix.rank_eq_finrank_span_cols
+
 end Matrix
 
diff --git a/Mathbin/GroupTheory/SpecificGroups/Alternating.lean b/Mathbin/GroupTheory/SpecificGroups/Alternating.lean
index a1bb7e8d4a..e293db16f8 100644
--- a/Mathbin/GroupTheory/SpecificGroups/Alternating.lean
+++ b/Mathbin/GroupTheory/SpecificGroups/Alternating.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 
 ! This file was ported from Lean 3 source module group_theory.specific_groups.alternating
-! leanprover-community/mathlib commit 0f6670b8af2dff699de1c0b4b49039b31bc13c46
+! leanprover-community/mathlib commit 9a48a083b390d9b84a71efbdc4e8dfa26a687104
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Tactic.IntervalCases
 /-!
 # Alternating Groups
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The alternating group on a finite type `α` is the subgroup of the permutation group `perm α`
 consisting of the even permutations.
 
diff --git a/Mathbin/LinearAlgebra/Dimension.lean b/Mathbin/LinearAlgebra/Dimension.lean
index 3ec7aa390d..58c850d135 100644
--- a/Mathbin/LinearAlgebra/Dimension.lean
+++ b/Mathbin/LinearAlgebra/Dimension.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit b5b5dd5a47b5744260e2c9185013075ce9dadccd
+! leanprover-community/mathlib commit 47a5f8186becdbc826190ced4312f8199f9db6a5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1876,14 +1876,34 @@ theorem rank_comp_le_left (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') : rank (f.
 #align linear_map.rank_comp_le_left LinearMap.rank_comp_le_left
 -/
 
+theorem lift_rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
+    Cardinal.lift.{v'} (rank (f.comp g)) ≤ Cardinal.lift.{v''} (rank g) := by
+  rw [rank, rank, LinearMap.range_comp] <;> exact lift_rank_map_le _ _
+#align linear_map.lift_rank_comp_le_right LinearMap.lift_rank_comp_le_right
+
+/-- The rank of the composition of two maps is less than the minimum of their ranks. -/
+theorem lift_rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
+    Cardinal.lift.{v'} (rank (f.comp g)) ≤
+      min (Cardinal.lift.{v'} (rank f)) (Cardinal.lift.{v''} (rank g)) :=
+  le_min (Cardinal.lift_le.mpr <| rank_comp_le_left _ _) (lift_rank_comp_le_right _ _)
+#align linear_map.lift_rank_comp_le LinearMap.lift_rank_comp_le
+
 variable [AddCommGroup V'₁] [Module K V'₁]
 
 #print LinearMap.rank_comp_le_right /-
 theorem rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank (f.comp g) ≤ rank g := by
-  rw [rank, rank, LinearMap.range_comp] <;> exact rank_map_le _ _
+  simpa only [Cardinal.lift_id] using lift_rank_comp_le_right g f
 #align linear_map.rank_comp_le_right LinearMap.rank_comp_le_right
 -/
 
+/-- The rank of the composition of two maps is less than the minimum of their ranks.
+
+See `lift_rank_comp_le` for the universe-polymorphic version. -/
+theorem rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) :
+    rank (f.comp g) ≤ min (rank f) (rank g) := by
+  simpa only [Cardinal.lift_id] using lift_rank_comp_le g f
+#align linear_map.rank_comp_le LinearMap.rank_comp_le
+
 end Ring
 
 section DivisionRing
diff --git a/Mathbin/LinearAlgebra/Finrank.lean b/Mathbin/LinearAlgebra/Finrank.lean
index 081a05f70f..2fe7658cbd 100644
--- a/Mathbin/LinearAlgebra/Finrank.lean
+++ b/Mathbin/LinearAlgebra/Finrank.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.finrank
-! leanprover-community/mathlib commit 347636a7a80595d55bedf6e6fbd996a3c39da69a
+! leanprover-community/mathlib commit 9a48a083b390d9b84a71efbdc4e8dfa26a687104
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.LinearAlgebra.Dimension
 /-!
 # Finite dimension of vector spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Definition of the rank of a module, or dimension of a vector space, as a natural number.
 
 ## Main definitions
diff --git a/Mathbin/LinearAlgebra/FreeModule/Rank.lean b/Mathbin/LinearAlgebra/FreeModule/Rank.lean
index 156439df07..f81d8eb438 100644
--- a/Mathbin/LinearAlgebra/FreeModule/Rank.lean
+++ b/Mathbin/LinearAlgebra/FreeModule/Rank.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 
 ! This file was ported from Lean 3 source module linear_algebra.free_module.rank
-! leanprover-community/mathlib commit 5aa3c1de9f3c642eac76e11071c852766f220fd0
+! leanprover-community/mathlib commit 465d4301d8da5945ef1dc1b29fb34c2f2b315ac4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -114,12 +114,9 @@ open Module.Free
 theorem rank_tensorProduct :
     Module.rank R (M ⊗[R] N) = lift.{w, v} (Module.rank R M) * lift.{v, w} (Module.rank R N) :=
   by
-  let ιM := choose_basis_index R M
-  let ιN := choose_basis_index R N
-  have h₁ := LinearEquiv.lift_rank_eq (TensorProduct.congr (repr R M) (repr R N))
-  let b : Basis (ιM × ιN) R (_ →₀ R) := Finsupp.basisSingleOne
-  rw [LinearEquiv.rank_eq (finsuppTensorFinsupp' R ιM ιN), ← b.mk_eq_rank, mk_prod] at h₁
-  rw [lift_inj.1 h₁, rank_eq_card_choose_basis_index R M, rank_eq_card_choose_basis_index R N]
+  obtain ⟨⟨_, bM⟩⟩ := Module.Free.exists_basis R M
+  obtain ⟨⟨_, bN⟩⟩ := Module.Free.exists_basis R N
+  rw [← bM.mk_eq_rank'', ← bN.mk_eq_rank'', ← (bM.tensor_product bN).mk_eq_rank'', Cardinal.mk_prod]
 #align rank_tensor_product rank_tensorProduct
 
 /-- If `M` and `N` lie in the same universe, the rank of `M ⊗[R] N` is
diff --git a/Mathbin/LinearAlgebra/Matrix/DotProduct.lean b/Mathbin/LinearAlgebra/Matrix/DotProduct.lean
index f3e340792c..cc34f21f07 100644
--- a/Mathbin/LinearAlgebra/Matrix/DotProduct.lean
+++ b/Mathbin/LinearAlgebra/Matrix/DotProduct.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.dot_product
-! leanprover-community/mathlib commit 46822d96c0c0a8e58a41a0cba1291620967575c5
+! leanprover-community/mathlib commit 5ac1dab1670014b4c07a82c86a67f3d064a1b3e1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -133,30 +133,30 @@ theorem dotProduct_self_eq_zero [LinearOrderedRing R] {v : n → R} : dotProduct
 
 /- warning: matrix.dot_product_star_self_eq_zero -> Matrix.dotProduct_star_self_eq_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2))] [_inst_4 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2)) _inst_3))) (Star.star.{max u2 u1} (n -> R) (Pi.hasStar.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2)) _inst_3))))) v) v) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))))))))
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : PartialOrder.{u1} R] [_inst_3 : NonUnitalRing.{u1} R] [_inst_4 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2] [_inst_5 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R _inst_3 _inst_2 _inst_4))) (Star.star.{max u2 u1} (n -> R) (Pi.hasStar.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2 _inst_4))))) v) v) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2)] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))) (Star.star.{max u2 u1} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2) _inst_3))))) v) v) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))) (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.521 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))))
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2)] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))] {_inst_5 : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))) (Star.star.{max u2 u1} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.6390 : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2) _inst_3))))) _inst_5) _inst_5) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))) (Eq.{max (succ u1) (succ u2)} (n -> R) _inst_5 (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.521 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zeroₓ'. -/
 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp]
-theorem dotProduct_star_self_eq_zero [StrictOrderedRing R] [StarOrderedRing R] [NoZeroDivisors R]
-    {v : n → R} : dotProduct (star v) v = 0 ↔ v = 0 :=
-  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => @star_mul_self_nonneg _ _ _ _ (v i)).trans <| by
-    simp [Function.funext_iff, mul_eq_zero]
+theorem dotProduct_star_self_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R]
+    [NoZeroDivisors R] {v : n → R} : dotProduct (star v) v = 0 ↔ v = 0 :=
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@star_mul_self_nonneg _ _ _ _ (v i) : _)).trans <|
+    by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zero
 
 /- warning: matrix.dot_product_self_star_eq_zero -> Matrix.dotProduct_self_star_eq_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2))] [_inst_4 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2)) _inst_3))) v (Star.star.{max u2 u1} (n -> R) (Pi.hasStar.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2)) _inst_3))))) v)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))))))))
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : PartialOrder.{u1} R] [_inst_3 : NonUnitalRing.{u1} R] [_inst_4 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2] [_inst_5 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R _inst_3 _inst_2 _inst_4))) v (Star.star.{max u2 u1} (n -> R) (Pi.hasStar.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2 _inst_4))))) v)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2)] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))) v (Star.star.{max u1 u2} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2) _inst_3))))) v)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))) (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.579 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))))
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2)] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))] {_inst_5 : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))) _inst_5 (Star.star.{max u1 u2} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.6393 : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2) _inst_3))))) _inst_5)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))) (Eq.{max (succ u1) (succ u2)} (n -> R) _inst_5 (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.579 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zeroₓ'. -/
 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp]
-theorem dotProduct_self_star_eq_zero [StrictOrderedRing R] [StarOrderedRing R] [NoZeroDivisors R]
-    {v : n → R} : dotProduct v (star v) = 0 ↔ v = 0 :=
-  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => @star_mul_self_nonneg' _ _ _ _ (v i)).trans <| by
-    simp [Function.funext_iff, mul_eq_zero]
+theorem dotProduct_self_star_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R]
+    [NoZeroDivisors R] {v : n → R} : dotProduct v (star v) = 0 ↔ v = 0 :=
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@star_mul_self_nonneg' _ _ _ _ (v i) : _)).trans <|
+    by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zero
 
 end Self
diff --git a/Mathbin/LinearAlgebra/Matrix/ToLin.lean b/Mathbin/LinearAlgebra/Matrix/ToLin.lean
index cf125696b5..b5d0b9c55e 100644
--- a/Mathbin/LinearAlgebra/Matrix/ToLin.lean
+++ b/Mathbin/LinearAlgebra/Matrix/ToLin.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.to_lin
-! leanprover-community/mathlib commit b1c23399f01266afe392a0d8f71f599a0dad4f7b
+! leanprover-community/mathlib commit 86add5ce96b35c2cc6ee6946ab458e7302584e21
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -198,7 +198,6 @@ variable {R : Type _} [CommSemiring R]
 variable {l m n : Type _}
 
 /-- `matrix.mul_vec M` is a linear map. -/
-@[simps]
 def Matrix.mulVecLin [Fintype n] (M : Matrix m n R) : (n → R) →ₗ[R] m → R
     where
   toFun := M.mulVec
@@ -206,19 +205,64 @@ def Matrix.mulVecLin [Fintype n] (M : Matrix m n R) : (n → R) →ₗ[R] m →
   map_smul' c v := funext fun i => dotProduct_smul _ _ _
 #align matrix.mul_vec_lin Matrix.mulVecLin
 
-variable [Fintype n] [DecidableEq n]
+@[simp]
+theorem Matrix.mulVecLin_apply [Fintype n] (M : Matrix m n R) (v : n → R) :
+    M.mulVecLin v = M.mulVec v :=
+  rfl
+#align matrix.mul_vec_lin_apply Matrix.mulVecLin_apply
+
+@[simp]
+theorem Matrix.mulVecLin_zero [Fintype n] : Matrix.mulVecLin (0 : Matrix m n R) = 0 :=
+  LinearMap.ext zero_mulVec
+#align matrix.mul_vec_lin_zero Matrix.mulVecLin_zero
+
+@[simp]
+theorem Matrix.mulVecLin_add [Fintype n] (M N : Matrix m n R) :
+    (M + N).mulVecLin = M.mulVecLin + N.mulVecLin :=
+  LinearMap.ext fun _ => add_mulVec _ _ _
+#align matrix.mul_vec_lin_add Matrix.mulVecLin_add
+
+variable [Fintype n]
+
+@[simp]
+theorem Matrix.mulVecLin_one [DecidableEq n] : Matrix.mulVecLin (1 : Matrix n n R) = id :=
+  by
+  ext
+  simp [LinearMap.one_apply, std_basis_apply]
+#align matrix.mul_vec_lin_one Matrix.mulVecLin_one
+
+@[simp]
+theorem Matrix.mulVecLin_mul [Fintype m] (M : Matrix l m R) (N : Matrix m n R) :
+    Matrix.mulVecLin (M ⬝ N) = (Matrix.mulVecLin M).comp (Matrix.mulVecLin N) :=
+  LinearMap.ext fun x => (mulVec_mulVec _ _ _).symm
+#align matrix.mul_vec_lin_mul Matrix.mulVecLin_mul
 
-theorem Matrix.mulVec_stdBasis (M : Matrix m n R) (i j) :
+theorem Matrix.ker_mulVecLin_eq_bot_iff {M : Matrix n n R} :
+    M.mulVecLin.ker = ⊥ ↔ ∀ v, M.mulVec v = 0 → v = 0 := by
+  simp only [Submodule.eq_bot_iff, LinearMap.mem_ker, Matrix.mulVecLin_apply]
+#align matrix.ker_mul_vec_lin_eq_bot_iff Matrix.ker_mulVecLin_eq_bot_iff
+
+theorem Matrix.mulVec_stdBasis [DecidableEq n] (M : Matrix m n R) (i j) :
     M.mulVec (stdBasis R (fun _ => R) j 1) i = M i j :=
   (congr_fun (Matrix.mulVec_single _ _ (1 : R)) i).trans <| mul_one _
 #align matrix.mul_vec_std_basis Matrix.mulVec_stdBasis
 
 @[simp]
-theorem Matrix.mulVec_stdBasis_apply (M : Matrix m n R) (j) :
+theorem Matrix.mulVec_stdBasis_apply [DecidableEq n] (M : Matrix m n R) (j) :
     M.mulVec (stdBasis R (fun _ => R) j 1) = Mᵀ j :=
   funext fun i => Matrix.mulVec_stdBasis M i j
 #align matrix.mul_vec_std_basis_apply Matrix.mulVec_stdBasis_apply
 
+theorem Matrix.range_mulVecLin (M : Matrix m n R) : M.mulVecLin.range = span R (range Mᵀ) :=
+  by
+  letI := Classical.decEq n
+  simp_rw [range_eq_map, ← supr_range_std_basis, Submodule.map_supᵢ, range_eq_map, ←
+    Ideal.span_singleton_one, Ideal.span, Submodule.map_span, image_image, image_singleton,
+    Matrix.mulVecLin_apply, M.mul_vec_std_basis_apply, supr_span, range_eq_Union]
+#align matrix.range_mul_vec_lin Matrix.range_mulVecLin
+
+variable [DecidableEq n]
+
 /-- Linear maps `(n → R) →ₗ[R] (m → R)` are linearly equivalent to `matrix m n R`. -/
 def LinearMap.toMatrix' : ((n → R) →ₗ[R] m → R) ≃ₗ[R] Matrix m n R
     where
@@ -239,11 +283,17 @@ def LinearMap.toMatrix' : ((n → R) →ₗ[R] m → R) ≃ₗ[R] Matrix m n R
     simp only [Pi.smul_apply, LinearMap.smul_apply, RingHom.id_apply, of_apply]
 #align linear_map.to_matrix' LinearMap.toMatrix'
 
-/-- A `matrix m n R` is linearly equivalent to a linear map `(n → R) →ₗ[R] (m → R)`. -/
+/-- A `matrix m n R` is linearly equivalent to a linear map `(n → R) →ₗ[R] (m → R)`.
+
+Note that the forward-direction does not require `decidable_eq` and is `matrix.vec_mul_lin`. -/
 def Matrix.toLin' : Matrix m n R ≃ₗ[R] (n → R) →ₗ[R] m → R :=
   LinearMap.toMatrix'.symm
 #align matrix.to_lin' Matrix.toLin'
 
+theorem Matrix.toLin'_apply' (M : Matrix m n R) : Matrix.toLin' M = M.mulVecLin :=
+  rfl
+#align matrix.to_lin'_apply' Matrix.toLin'_apply'
+
 @[simp]
 theorem LinearMap.toMatrix'_symm :
     (LinearMap.toMatrix'.symm : Matrix m n R ≃ₗ[R] _) = Matrix.toLin' :=
@@ -286,9 +336,7 @@ theorem Matrix.toLin'_apply (M : Matrix m n R) (v : n → R) : Matrix.toLin' M v
 
 @[simp]
 theorem Matrix.toLin'_one : Matrix.toLin' (1 : Matrix n n R) = id :=
-  by
-  ext
-  simp [LinearMap.one_apply, std_basis_apply]
+  Matrix.mulVecLin_one
 #align matrix.to_lin'_one Matrix.toLin'_one
 
 @[simp]
@@ -301,7 +349,7 @@ theorem LinearMap.toMatrix'_id : LinearMap.toMatrix' (LinearMap.id : (n → R) 
 @[simp]
 theorem Matrix.toLin'_mul [Fintype m] [DecidableEq m] (M : Matrix l m R) (N : Matrix m n R) :
     Matrix.toLin' (M ⬝ N) = (Matrix.toLin' M).comp (Matrix.toLin' N) :=
-  LinearMap.ext fun x => (mulVec_mulVec _ _ _).symm
+  Matrix.mulVecLin_mul _ _
 #align matrix.to_lin'_mul Matrix.toLin'_mul
 
 /-- Shortcut lemma for `matrix.to_lin'_mul` and `linear_map.comp_apply` -/
@@ -329,14 +377,12 @@ theorem LinearMap.toMatrix'_algebraMap (x : R) :
 #align linear_map.to_matrix'_algebra_map LinearMap.toMatrix'_algebraMap
 
 theorem Matrix.ker_toLin'_eq_bot_iff {M : Matrix n n R} :
-    M.toLin'.ker = ⊥ ↔ ∀ v, M.mulVec v = 0 → v = 0 := by
-  simp only [Submodule.eq_bot_iff, LinearMap.mem_ker, Matrix.toLin'_apply]
+    M.toLin'.ker = ⊥ ↔ ∀ v, M.mulVec v = 0 → v = 0 :=
+  Matrix.ker_mulVecLin_eq_bot_iff
 #align matrix.ker_to_lin'_eq_bot_iff Matrix.ker_toLin'_eq_bot_iff
 
-theorem Matrix.range_toLin' (M : Matrix m n R) : M.toLin'.range = span R (range Mᵀ) := by
-  simp_rw [range_eq_map, ← supr_range_std_basis, Submodule.map_supᵢ, range_eq_map, ←
-    Ideal.span_singleton_one, Ideal.span, Submodule.map_span, image_image, image_singleton,
-    Matrix.toLin'_apply, M.mul_vec_std_basis_apply, supr_span, range_eq_Union]
+theorem Matrix.range_toLin' (M : Matrix m n R) : M.toLin'.range = span R (range Mᵀ) :=
+  Matrix.range_mulVecLin _
 #align matrix.range_to_lin' Matrix.range_toLin'
 
 /-- If `M` and `M'` are each other's inverse matrices, they provide an equivalence between `m → A`
diff --git a/Mathbin/ModelTheory/LanguageMap.lean b/Mathbin/ModelTheory/LanguageMap.lean
index ba2e1b709f..74e2c009bb 100644
--- a/Mathbin/ModelTheory/LanguageMap.lean
+++ b/Mathbin/ModelTheory/LanguageMap.lean
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson, Jesse Michael Han, Floris van Doorn
 
 ! This file was ported from Lean 3 source module model_theory.language_map
-! leanprover-community/mathlib commit b3951c65c6e797ff162ae8b69eab0063bcfb3d73
+! leanprover-community/mathlib commit 9a48a083b390d9b84a71efbdc4e8dfa26a687104
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -12,6 +12,9 @@ import Mathbin.ModelTheory.Basic
 
 /-!
 # Language Maps
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 Maps between first-order languages in the style of the
 [Flypitch project](https://flypitch.github.io/), as well as several important maps between
 structures.
diff --git a/README.md b/README.md
index e2ef7aad4e..dcbfeac613 100644
--- a/README.md
+++ b/README.md
@@ -1,4 +1,4 @@
-Tracking mathlib commit: [`347636a7a80595d55bedf6e6fbd996a3c39da69a`](https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a)
+Tracking mathlib commit: [`7ebf83ed9c262adbf983ef64d5e8c2ae94b625f4`](https://github.com/leanprover-community/mathlib/commit/7ebf83ed9c262adbf983ef64d5e8c2ae94b625f4)
 
 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 3897dfab18..0238e7977c 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": "45463d75681bb17c38fff1094fd82c3d13928877",
+    "rev": "b841ad13a760405a48f75b9a72f9a2dd6e13edb7",
     "name": "lean3port",
-    "inputRev?": "45463d75681bb17c38fff1094fd82c3d13928877"}},
+    "inputRev?": "b841ad13a760405a48f75b9a72f9a2dd6e13edb7"}},
   {"git":
    {"url": "https://github.com/leanprover-community/mathlib4.git",
     "subDir?": null,
diff --git a/lakefile.lean b/lakefile.lean
index f8b220e6b0..da97382246 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-2023-04-14-00"
+def tag : String := "nightly-2023-04-14-02"
 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"@"45463d75681bb17c38fff1094fd82c3d13928877"
+require lean3port from git "https://github.com/leanprover-community/lean3port.git"@"b841ad13a760405a48f75b9a72f9a2dd6e13edb7"
 
 @[default_target]
 lean_lib Mathbin where
diff --git a/upstream-rev b/upstream-rev
index 780d1460bb..5df2e8462a 100644
--- a/upstream-rev
+++ b/upstream-rev
@@ -1 +1 @@
-347636a7a80595d55bedf6e6fbd996a3c39da69a
+7ebf83ed9c262adbf983ef64d5e8c2ae94b625f4