lean4-htt/tests/lean/indimpltarget.lean.expected.out
Joachim Breitner 550fa6994e
feat: induction using <term> (#3188)
right now, the `induction` tactic accepts a custom eliminator using the
`using <ident>` syntax, but is restricted to identifiers. This
limitation becomes annoying when the elminator has explicit parameters
that are not targets, and the user (naturally) wants to be able to write
```
induction a, b, c using foo (x := …)
```

This generalizes the syntax to expressions and changes the code
accordingly.

This can be used to instantiate a multi-motive induction:
```
example (a : A) : True := by
  induction a using A.rec (motive_2 := fun b => True)
  case mkA b IH => exact trivial
  case A => exact trivial
  case mkB b IH => exact trivial
```

For this to work the term elaborator learned the `heedElabAsElim` flag,
`true` by default. But in the default setting, `A.rec (motive_2 := fun b
=> True)`
would fail to elaborate, because there is no expected type. So the
induction
tactic will elaborate in a mode where that attribute is simply ignored.

As a side effect, the “failed to infer implicit target” error message 
is improved and prints the name of the implicit target that could not be
instantiated.
2024-01-25 16:57:41 +00:00

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indimpltarget.lean:6:2-6:45: error: failed to infer implicit target m
indimpltarget.lean:16:2-16:45: error: failed to infer implicit target n
indimpltarget.lean:26:0-26:7: warning: declaration uses 'sorry'
indimpltarget.lean:40:2-40:45: error: failed to infer implicit target