4a111501eb
This PR fixes the `grind` invalid universe level regression reported in #11036 Closes #11036
22 lines
1.1 KiB
Text
22 lines
1.1 KiB
Text
variable {α : Sort u} {β : α → Sort v} {α' : Sort w} [DecidableEq α]
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{f : (a : α) → β a} {a : α} {b : β a}
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/-- Replacing the value of a function at a given point by a given value. -/
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def Function.update (f : ∀ a, β a) (a' : α) (v : β a') (a : α) : β a :=
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if h : a = a' then Eq.ndrec v h.symm else f a
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@[simp]
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theorem Function.update_self (a : α) (v : β a) (f : ∀ a, β a) : update f a v a = v :=
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dif_pos rfl
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@[simp]
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theorem Function.update_of_ne {a a' : α} (h : a ≠ a') (v : β a') (f : ∀ a, β a) : update f a' v a = f a :=
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dif_neg h
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theorem domDomRestrict_aux {ι : Sort u_1} [DecidableEq ι] (P : ι → Prop) [DecidablePred P] {M₁ : ι → Type u_2}
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[DecidableEq {a // P a}]
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(x : (i : {a // P a}) → M₁ i) (z : (i : {a // ¬ P a}) → M₁ i) (i : {a : ι // P a})
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(c : M₁ i) : (fun j ↦ if h : P j then Function.update x i c ⟨j, h⟩ else z ⟨j, h⟩) =
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Function.update (fun j => if h : P j then x ⟨j, h⟩ else z ⟨j, h⟩) i c := by
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ext j
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by_cases h : j = i <;> grind only [Function.update_self, Function.update_of_ne]
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