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https://github.com/leanprover/lean4.git
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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.
27 lines
825 B
Lean4
27 lines
825 B
Lean4
structure Equiv (α : Sort _) (β : Sort _) where
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toFun : α → β
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invFun : β → α
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left_inv : ∀ x, invFun (toFun x) = x
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infixl:25 " ≃ " => Equiv
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/-- A product of types can be split as the binary product of one of the types and the product
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of all the remaining types. -/
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def piSplitAt {α : Type _} [DecidableEq α] (i : α) (β : α → Type _) :
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(∀ j, β j) ≃ β i × ∀ j : { j // j ≠ i }, β j where
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toFun f := ⟨f i, fun j => f j⟩
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invFun f j := if h : j = i then h.symm.rec f.1 else f.2 ⟨j, h⟩
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left_inv f := by
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apply funext
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intro x
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/- Goal is now:
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```
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(fun f j => if h : j = i then (_ : i = j) ▸ f.fst else Prod.snd f { val := j, property := h })
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((fun f => (f i, fun j => f j.val)) f) x =
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f x
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```
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-/
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dsimp
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trace_state
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sorry
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