This PR extend the preprocessing of well-founded recursive definitions
to bring assumptions like `h✝ : x ∈ xs` into scope automatically.
This fixes#5471, and follows (roughly) the design written there.
See the module docs at `src/Lean/Elab/PreDefinition/WF/AutoAttach.lean`
for details on the implementation.
This only works for higher-order functions that have a suitable setup.
See for example section “Well-founded recursion preprocessing setup” in
`src/Init/Data/List/Attach.lean`.
This does not change the `decreasing_tactic`, so in some cases there is
still the need for a manual termination proof some cases. We expect a
better termination tactic in the near future.
there was a check
if !Structural.recArgHasLooseBVarsAt recFnName fixedPrefixSize e then
that would avoid going through `.refineThrough`/`.addArg` for
matcher/casesOn applications. It seems it tries to detect when refining
the motive/param is pointless, but it was too eager, and cause confusion
with, for example, this reasonably reasonable function:
def foo : (n : Nat) → (i : Fin n) → Bool
| 0, _ => false
| 1, _ => false
| _+2, _ => foo 1 ⟨0, Nat.zero_lt_one⟩
decreasing_by simp_wf; simp_arith
In particular, the `GuessLex` code later expects that the (implict)
`PProd.casesOn` in the implementation of `foo._unary` will refine the
paramter, because else the (rather picky) `unpackArg` fails. But it also
prevents this from being provable.
So let's try without this shortcut.
Fixing this also revealed that `withRecApps` wasn’t looking in all
corners
of a matcherApp/casesOnApp.
Fixes#3175
