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.
62 lines
2.1 KiB
Text
62 lines
2.1 KiB
Text
variable {α β γ : Type}
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structure Equiv (α β : Type) where
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toFun : α → β
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invFun : β → α
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infixl:25 " ≃ " => Equiv
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namespace Equiv
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instance : CoeFun (α ≃ β) (fun _ => α → β) := ⟨toFun⟩
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@[ext, grind ext] theorem ext {f g : Equiv α β} (H : ∀ x, f x = g x) : f = g := sorry
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theorem congr_fun {f g : Equiv α β} (h : f = g) (x : α) : f x = g x := by rw [h]
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def symm (e : α ≃ β) : β ≃ α := ⟨e.invFun, e.toFun⟩
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def trans (e₁ : α ≃ β) (e₂ : β ≃ γ) : α ≃ γ := ⟨e₂ ∘ e₁, e₁.symm ∘ e₂.symm⟩
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def sigmaCongrRight {α : Type} {β₁ β₂ : α → Type} (F : ∀ a, β₁ a ≃ β₂ a) : (Σ a, β₁ a) ≃ Σ a, β₂ a where
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toFun a := ⟨a.1, F a.1 a.2⟩
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invFun a := ⟨a.1, (F a.1).symm a.2⟩
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def sigmaEquivProd (α β : Type) : (Σ _ : α, β) ≃ α × β where
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toFun a := ⟨a.1, a.2⟩
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invFun a := ⟨a.1, a.2⟩
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end Equiv
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variable {α₁ β₁ β₂ : Type} (e : α₁ → β₁ ≃ β₂)
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def prodCongrRight : α₁ × β₁ ≃ α₁ × β₂ where
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toFun ab := ⟨ab.1, e ab.1 ab.2⟩
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invFun ab := ⟨ab.1, (e ab.1).symm ab.2⟩
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example :
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(Equiv.sigmaCongrRight e).trans (Equiv.sigmaEquivProd α₁ β₂)
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= (Equiv.sigmaEquivProd α₁ β₁).trans (prodCongrRight e) := by
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grind -reducible only [Equiv.congr_fun]
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example :
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(Equiv.sigmaCongrRight e).trans (Equiv.sigmaEquivProd α₁ β₂)
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= (Equiv.sigmaEquivProd α₁ β₁).trans (prodCongrRight e) := by
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grind -reducible only => finish only [Equiv.congr_fun]
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example :
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(Equiv.sigmaCongrRight e).trans (Equiv.sigmaEquivProd α₁ β₂)
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= (Equiv.sigmaEquivProd α₁ β₁).trans (prodCongrRight e) := by
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grind -reducible => cases #d592 <;> instantiate only [Equiv.congr_fun]
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/--
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info: Try these:
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[apply] grind -reducible only [Equiv.congr_fun, #d592]
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[apply] grind -reducible only [Equiv.congr_fun]
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[apply] grind -reducible => cases #d592 <;> instantiate only [Equiv.congr_fun]
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-/
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#guard_msgs in
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example :
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(Equiv.sigmaCongrRight e).trans (Equiv.sigmaEquivProd α₁ β₂)
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= (Equiv.sigmaEquivProd α₁ β₁).trans (prodCongrRight e) := by
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grind? -reducible [Equiv.congr_fun]
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