The `induction h` tactic tries to clear hypothesis `h` after it is
applied. But, before this commit, `cases h` would only try to clear `h`
when performing non-dependent elimination. This was problematic when
writing tactic scripts for automating proofs.
The `no_confusion` construction is only generated for inductive
datatypes supported in the kernel.
Before this commit, given `h : T`, `cases h` could leak the internal encoding
used by the inductive compiler WHEN a nested and/or mutual inductive
datatype is used to index the inductive datatype `T`.
The new test exposes the problem.
The solution implemented in this commit uses inj_arrow lemmas
generated by the inductive compiler. We only use the lemmas
if the target is a proposition. If it is not, we sign an error.
The reason for this limitation is documented in the source code.
cc @jroesch @dselsam
Jared: the information leakage has been fixed. So, students will not be
confused by the internal encoding used in the inductive compiler.
I added the example I posted on slack as a new test.
Note that, the workaround I used has been removed.
`{s with ...}` is now `{..., ..s}`, which more clearly expresses that the
result type is not necessarily equal to the type of `s` (in absence of an
expected type and a structure name, we still default to the type of `s`).
Multiple fallback sources can be given: `{..., ..s, ..t}` will fall back to
searching a field in `s`, then in `t`. The last component can also be `..`,
which will replace any missing fields with a placeholder.
The old notation will be removed in the future.
Function applications `(f ...)` were not being elaborated correctly when
`f` has implicit parameters occurring after auto_params.
The new test exposes the problem.
This bug was found when developing the red black tree module.
This commit also fixes the following bugs:
- Invoke type class resolution again after tactic execution at
synthesize method. Reason: metavariables occurring in type
class instances may have been synthesized by tactics.
- mctx.assign optimization at invoke_tactic was incorrect
when the metavariable was assigned by typing rules.
Now, `cmp` is just a fixed helper function.
In the future, we will be able to use (more efficient) specialized
versions during code generation by defining simp rules.
