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dagurtomas committed Sep 27, 2023
1 parent 539ded3 commit c098098
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions Mathlib/Topology/LocallyConstant/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -637,8 +637,8 @@ def piecewise {C₁ C₂ : Set X} (h₁ : IsClosed C₁) (h₂ : IsClosed C₂)
exact hf

@[simp]
lemma piecewise_apply_left {C₁ C₂ : Set X} (h₁ : IsClosed C₁) (h₂ : IsClosed C₂) (h : C₁ ∪ C₂ = Set.univ)
(f : LocallyConstant C₁ Z) (g : LocallyConstant C₂ Z)
lemma piecewise_apply_left {C₁ C₂ : Set X} (h₁ : IsClosed C₁) (h₂ : IsClosed C₂)
(h : C₁ ∪ C₂ = Set.univ) (f : LocallyConstant C₁ Z) (g : LocallyConstant C₂ Z)
(hfg : ∀ (x : X) (hx : x ∈ C₁ ∩ C₂), f ⟨x, hx.1⟩ = g ⟨x, hx.2⟩)
[DecidablePred (· ∈ C₁)] (x : X) (hx : x ∈ C₁) :
piecewise h₁ h₂ h f g hfg x = f ⟨x, hx⟩ := by
Expand All @@ -647,8 +647,8 @@ lemma piecewise_apply_left {C₁ C₂ : Set X} (h₁ : IsClosed C₁) (h₂ : Is
rw [dif_pos hx]

@[simp]
lemma piecewise_apply_right {C₁ C₂ : Set X} (h₁ : IsClosed C₁) (h₂ : IsClosed C₂) (h : C₁ ∪ C₂ = Set.univ)
(f : LocallyConstant C₁ Z) (g : LocallyConstant C₂ Z)
lemma piecewise_apply_right {C₁ C₂ : Set X} (h₁ : IsClosed C₁) (h₂ : IsClosed C₂)
(h : C₁ ∪ C₂ = Set.univ) (f : LocallyConstant C₁ Z) (g : LocallyConstant C₂ Z)
(hfg : ∀ (x : X) (hx : x ∈ C₁ ∩ C₂), f ⟨x, hx.1⟩ = g ⟨x, hx.2⟩)
[DecidablePred (· ∈ C₁)] (x : X) (hx : x ∈ C₂) :
piecewise h₁ h₂ h f g hfg x = g ⟨x, hx⟩ := by
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