08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
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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