feat: better support for reducing Nat.rec
#3616
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closes #3022 With this commit, given the declaration ``` def foo : Nat → Nat | 0 => 2 | n + 1 => foo n ``` when we unfold `foo (n+1)`, we now obtain `foo n` instead of `foo (Nat.add n 0)`.
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| @@ -64,9 +65,17 @@ def constructorApp? (e : Expr) : MetaM (Option (ConstructorVal × Array Expr)) : | |||
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| Similar to `constructorApp?`, but on failure it puts `e` in WHNF and tries again. | |||
| It also `isOffset?` | |||
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…utiful eliminators for `Nat` (#3629) Replaces `@[eliminator]` with two attributes `@[induction_eliminator]` and `@[cases_eliminator]` for defining custom eliminators for the `induction` and `cases` tactics, respectively. Adds `Nat.recAux` and `Nat.casesAuxOn`, which are eliminators that are defeq to `Nat.rec` and `Nat.casesOn`, but these use `0` and `n + 1` rather than `Nat.zero` and `Nat.succ n`. For example, using `induction` to prove that the factorial function is positive now has the following goal states (thanks also to #3616 for the goal state after unfolding). ```lean example : 0 < fact x := by induction x with | zero => decide | succ x ih => /- x : Nat ih : 0 < fact x ⊢ 0 < fact (x + 1) -/ unfold fact /- ... ⊢ 0 < (x + 1) * fact x -/ simpa using ih ``` Thanks to @adamtopaz for initial work on splitting the `@[eliminator]` attribute.
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Mar 11, 2024
closes leanprover#3022 With this commit, given the declaration ``` def foo : Nat → Nat | 0 => 2 | n + 1 => foo n ``` when we unfold `foo (n+1)`, we now obtain `foo n` instead of `foo (Nat.add n 0)`.
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closes #3022
With this commit, given the declaration
when we unfold
foo (n+1), we now obtainfoo ninstead offoo (Nat.add n 0).