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Fix some #aligns in Order.CompleteLattice (#1211)
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urkud committed Dec 25, 2022
1 parent ea82bbc commit 3cd4748
Showing 1 changed file with 10 additions and 10 deletions.
20 changes: 10 additions & 10 deletions Mathlib/Order/CompleteLattice.lean
Expand Up @@ -160,11 +160,11 @@ theorem supₛ_le : (∀ b ∈ s, b ≤ a) → supₛ s ≤ a :=

theorem isLUB_supₛ (s : Set α) : IsLUB s (supₛ s) :=
fun _ ↦ le_supₛ, fun _ ↦ supₛ_le⟩
#align isLUB_Sup isLUB_supₛ
#align is_lub_Sup isLUB_supₛ

theorem IsLUB.supₛ_eq (h : IsLUB s a) : supₛ s = a :=
(isLUB_supₛ s).unique h
#align isLUB.Sup_eq IsLUB.supₛ_eq
#align is_lub.Sup_eq IsLUB.supₛ_eq

theorem le_supₛ_of_le (hb : b ∈ s) (h : a ≤ b) : a ≤ supₛ s :=
le_trans h (le_supₛ hb)
Expand Down Expand Up @@ -228,11 +228,11 @@ theorem le_infₛ : (∀ b ∈ s, a ≤ b) → a ≤ infₛ s :=

theorem isGLB_infₛ (s : Set α) : IsGLB s (infₛ s) :=
fun _ => infₛ_le, fun _ => le_infₛ⟩
#align isGLB_Inf isGLB_infₛ
#align is_glb_Inf isGLB_infₛ

theorem IsGLB.infₛ_eq (h : IsGLB s a) : infₛ s = a :=
(isGLB_infₛ s).unique h
#align isGLB.Inf_eq IsGLB.infₛ_eq
#align is_glb.Inf_eq IsGLB.infₛ_eq

theorem infₛ_le_of_le (hb : b ∈ s) (h : b ≤ a) : infₛ s ≤ a :=
le_trans (infₛ_le hb) h
Expand Down Expand Up @@ -778,19 +778,19 @@ le_supₛ ⟨i, rfl⟩
-/
theorem isLUB_supᵢ : IsLUB (range f) (⨆ j, f j) :=
isLUB_supₛ _
#align isLUB_supr isLUB_supᵢ
#align is_lub_supr isLUB_supᵢ

theorem isGLB_infᵢ : IsGLB (range f) (⨅ j, f j) :=
isGLB_infₛ _
#align isGLB_infi isGLB_infᵢ
#align is_glb_infi isGLB_infᵢ

theorem IsLUB.supᵢ_eq (h : IsLUB (range f) a) : (⨆ j, f j) = a :=
h.supₛ_eq
#align isLUB.supr_eq IsLUB.supᵢ_eq
#align is_lub.supr_eq IsLUB.supᵢ_eq

theorem IsGLB.infᵢ_eq (h : IsGLB (range f) a) : (⨅ j, f j) = a :=
h.infₛ_eq
#align isGLB.infi_eq IsGLB.infᵢ_eq
#align is_glb.infi_eq IsGLB.infᵢ_eq

theorem le_supᵢ_of_le (i : ι) (h : a ≤ f i) : a ≤ supᵢ f :=
h.trans <| le_supᵢ _ i
Expand Down Expand Up @@ -1536,12 +1536,12 @@ theorem inf_eq_infᵢ (x y : α) : x ⊓ y = ⨅ b : Bool, cond b x y :=
theorem isGLB_binfᵢ {s : Set β} {f : β → α} : IsGLB (f '' s) (⨅ x ∈ s, f x) := by
simpa only [range_comp, Subtype.range_coe, infᵢ_subtype'] using
@isGLB_infᵢ α s _ (f ∘ fun x => (x : β))
#align isGLB_binfi isGLB_binfᵢ
#align is_glb_binfi isGLB_binfᵢ

theorem isLUB_bsupᵢ {s : Set β} {f : β → α} : IsLUB (f '' s) (⨆ x ∈ s, f x) := by
simpa only [range_comp, Subtype.range_coe, supᵢ_subtype'] using
@isLUB_supᵢ α s _ (f ∘ fun x => (x : β))
#align isLUB_bsupr isLUB_bsupᵢ
#align is_lub_bsupr isLUB_bsupᵢ

theorem supᵢ_sigma {p : β → Type _} {f : Sigma p → α} : (⨆ x, f x) = ⨆ (i) (j), f ⟨i, j⟩ :=
eq_of_forall_ge_iff fun c => by simp only [supᵢ_le_iff, Sigma.forall]
Expand Down

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