This PR improves the functional cases principles, by making a more
educated guess which function parameters should be targets and which
should remain parameters (or be dropped). This simplifies the
principles, and increases the chance that `fun_cases` can unfold the
function call.
Fixes#8296 (at least for the common cases, I hope.)
This PR makes `fun_induction` and `fun_cases` (try to) unfold the
function application of interest in the goal. The old behavior can be
enabled with `set_option tactic.fun_induction.unfolding false`. For
`fun_cases` this does not work yet when the function’s result type
depends on one of the arguments, see issue #8296.
This PR adds `foo.fun_cases`, an automatically generated theorem that
splits the goal according to the branching structure of `foo`, much like
the Functional Induction Principle, but for all functions (not just
recursive ones), and without providing inductive hypotheses.
The design isn't quite final yet as to which function parameters should
become targets of the motive, and which parameters of the theorem, but
the current version is already proven to be useful, so start with this
and iterate later.
