fix: more robust match equation generation

[nomeata]

This PR, still an experiment, changes how match equations are generated, to fix issues like #11342 (which would arise more frequently once we have #11105).

When proving a matcher equation, we may encounter casesOn that do not reduce right away (it is not applied to a constructor), and that we thus want to split. But splitting can be blocked when the scrutine is not a free variable, which can be the case when this target is also the index of a later target, see #11342.

A more robust approach at equation generation to to prove it in the form of the “congruence equation” from #8284, where the arguments to the matcher are free variables, and the information that these arguments are actually equal to the current pattern is put into hypotheses. In this form, we should reliably be able to split the match into all its branches, avoiding the issue above. At each branch there are three possibilities:

• We are in the right branch. We may need to substitute some variable and apply injection to the assumed assumption to unify the goal, and then are done. This can be handled by a (restrictively configured) call to grind, now that grind handles heterogeneous equality between constructors better (feat: heterogeneous contructor injectivity in grind #11491).

• We are in a wrong branch and the patterns do not unify. Then we should have a (possibly heterogeneous) equality between different constructors somewhere in the context, and grind can handle it.

• We are in a wrong branch and it’s overlapping the one we care about. Then there should be a no-overlap assumption in the context, and we need to use that. The code for that exists in contradiction (but maybe we can make that even more targetted?)

This is a more expensive approach than the current one, which can avoid many case splits. We'll see how bad it is, and whether we can tweak this to be faster, or whether we need both algorithms and this one is the fallback, or whether the common case is rfl anyways, so either refl or this one suffices.

[nomeata]

Just a note to future myself:

The next issue is that during proveCondEqThm we want the overlap assumptions to be applied to the abstract discrs, but the final theorem needs them applied to the concrete pattern and simpHlified, to match the splitter and be convenient.

This requires a bit of refactoring, and in particular simpH needs to return an actual proof of equivalence between the two (possibly only since this week since #11474).

[leanprover-bot]

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