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2 commits

Author SHA1 Message Date
Kyle Miller
45fccc5906
feat: custom eliminators for induction and cases tactics, and beautiful 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.
2024-03-09 15:31:51 +00:00
Leonardo de Moura
fed7ff27e8 fix: issue reported on Zulip
https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Annoying.20LCNF.20errors/near/302056742
2022-10-03 09:51:32 -07:00