fa058ed228
Else the `case` will now allow introducing all necessary variables. Induction principles with `let` in the types of the cases will be more common with #3432. This implementation no longer reduces the type as it goes, but really only counts manifest foralls and lets. I find this more sensible and predictable: If you have ``` theorem induction₂_symm {P : EReal → EReal → Prop} (symm : Symmetric P) … ``` then previously, writing ``` case symm => ``` would actually bring a fresh `x` and `y` and variable `h : P x y` into scope and produce a goal of `P y x`, because `Symmetric P` happens to be ``` def Symmetric := ∀ ⦃x y⦄, x ≺ y → y ≺ x ``` After this change, after `case symm =>` will leave `Symmetric P` as the goal. This gives more control to the author of the induction hypothesis about the actual goal of the cases. This shows up in mathlib in two places; fixes in https://github.com/leanprover-community/mathlib4/pull/11023. I consider these improvements.
14 lines
367 B
Text
14 lines
367 B
Text
theorem some_induction
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{motive : Nat → Prop}
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(zero : motive 0)
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(succ : forall n, 0 < n → let m := n - 1; motive m → motive n) :
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∀ n, motive n
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| 0 => zero
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| n+1 => succ (n+1) (Nat.zero_lt_succ n) (some_induction zero succ n)
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example (n : Nat) : n = n := by
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induction n using some_induction
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case zero => rfl
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case succ n _h _m _IH =>
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rfl
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