45fccc5906
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.
5 lines
268 B
Text
5 lines
268 B
Text
{"textDocument": {"uri": "file:///anonHyp.lean"},
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"position": {"line": 2, "character": 4}}
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{"rendered":
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"```lean\ncase succ\nn✝ : Nat\na✝ : n✝ + 1 > 0\n⊢ n✝ + 1 + 1 > 0\n```",
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"goals": ["case succ\nn✝ : Nat\na✝ : n✝ + 1 > 0\n⊢ n✝ + 1 + 1 > 0"]}
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