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.
49 lines
2 KiB
Text
49 lines
2 KiB
Text
open Sum Function
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-- This needs to be in the library!
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-- https://github.com/leanprover/lean4/pull/11085
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attribute [grind =] Prod.map_fst Prod.map_snd
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-- Copy the definition of `Equiv` from Mathlib.
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structure Equiv (α : Sort _) (β : Sort _) where
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protected toFun : α → β
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protected invFun : β → α
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protected left_inv : LeftInverse invFun toFun := by intro; first | rfl | ext <;> rfl
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protected right_inv : RightInverse invFun toFun := by intro; first | rfl | ext <;> rfl
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infixl:25 " ≃ " => Equiv
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def sumProdDistrib (α β γ) : (α ⊕ β) × γ ≃ α × γ ⊕ β × γ :=
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⟨fun p => p.1.map (fun x => (x, p.2)) fun x => (x, p.2),
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fun s => s.elim (Prod.map inl id) (Prod.map inr id), by
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rintro ⟨_ | _, _⟩ <;> rfl, by
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rintro (⟨_, _⟩ | ⟨_, _⟩)
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· grind
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· grind⟩
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def sumProdDistrib' (α β γ) : (α ⊕ β) × γ ≃ α × γ ⊕ β × γ :=
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⟨fun p => p.1.map (fun x => (x, p.2)) fun x => (x, p.2),
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fun s => s.elim (Prod.map inl id) (Prod.map inr id), by
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rintro ⟨_ | _, _⟩ <;> rfl, by
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rintro (⟨_, _⟩ | ⟨_, _⟩)
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· grind +abstractProof
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· grind +abstractProof⟩
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def sumProdDistrib'' (α β γ) : (α ⊕ β) × γ ≃ α × γ ⊕ β × γ :=
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⟨fun p => p.1.map (fun x => (x, p.2)) fun x => (x, p.2),
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fun s => s.elim (Prod.map inl id) (Prod.map inr id), by
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rintro ⟨_ | _, _⟩ <;> rfl, by
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rintro (⟨_, _⟩ | ⟨_, _⟩)
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· grind?
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· grind?⟩
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example (α β γ) (fst : α) (snd : γ) :
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(fun p : (α ⊕ β) × γ ↦ Sum.map (fun x ↦ (x, p.snd)) (fun x ↦ (x, p.snd)) p.fst)
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((fun s ↦ Sum.elim (Prod.map inl id) (Prod.map inr id) s) (inl (fst, snd))) =
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inl (fst, snd) := by
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grind
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example (α β γ) :
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RightInverse (fun s : α × γ ⊕ β × γ ↦ Sum.elim (Prod.map inl id) (Prod.map inr id) s) fun p ↦
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Sum.map (fun x ↦ (x, p.snd)) (fun x ↦ (x, p.snd)) p.fst := by
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rintro (⟨_, _⟩ | ⟨_, _⟩) <;> grind
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