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[Merged by Bors] - chore(logic/function/basic): remove classical decidable instance from a lemma statement #6488

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[Merged by Bors] - chore(logic/function/basic): remove classical decidable instance from a lemma statement #6488

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chore(logic/function/basic): remove classical decidable instance from…
eric-wieser Mar 1, 2021
64e5f2f
Update src/logic/function/basic.lean
eric-wieser Mar 1, 2021
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eric-wieser Mar 1, 2021
f4e8822
Update src/logic/function/basic.lean
eric-wieser Apr 6, 2021
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5 changes: 3 additions & 2 deletions src/logic/function/basic.lean
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Expand Up @@ -462,8 +462,9 @@ Mostly useful when `f` is injective. -/
def extend (f : α → β) (g : α → γ) (e' : β → γ) : β → γ :=
λ b, if h : ∃ a, f a = b then g (classical.some h) else e' b

lemma extend_def (f : α → β) (g : α → γ) (e' : β → γ) (b : β) :
extend f g e' b = if h : ∃ a, f a = b then g (classical.some h) else e' b := rfl
lemma extend_def (f : α → β) (g : α → γ) (e' : β → γ) (b : β) [decidable (∃ a, f a = b)] :
extend f g e' b = if h : ∃ a, f a = b then g (classical.some h) else e' b :=
by { unfold extend, congr }

@[simp] lemma extend_apply (hf : injective f) (g : α → γ) (e' : β → γ) (a : α) :
extend f g e' (f a) = g a :=
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