This PR adds some missing `List/Array/Vector lemmas` about
`isSome_idxOf?`, `isSome_finIdxOf?`, `isSome_findFinIdx?,
`isSome_findIdx?` and the corresponding `isNone` versions.
This PR changes definitions and theorems not to use the membership
instance on `Option` unless the theorem is specifically about the
membership instance.
The reasoning for this change is that the lemma `a ∈ o ↔ o = some a` is
a `simp` lemma, and we generally want theorem statements to use `simp`
normal forms.
One notable exception is the `ForIn'` instance, which must use
`Membership` because unlike `GetElem`, `ForIn'` requires the validity
predicate to be expressed via `Membership`.
This PR reviews the implicitness of arguments across List/Array/Vector,
generally trying to make arguments implicit where possible, although
sometimes correcting propositional arguments which were incorrectly
implicit to explicit.
This PR makes functions defined by well-founded recursion use an
`opaque` well-founded proof by default. This reliably prevents kernel
reduction of such definitions and proofs, which tends to be
prohibitively slow (fixes#2171), and which regularly causes
hard-to-debug kernel type-checking failures. This changes renders
`unseal` ineffective for such definitions. To avoid the opaque proof,
annotate the function definition with `@[semireducible]`.
This PR adds `Array.replace` and `Vector.replace`, proves the
correspondences with `List.replace`, and reproduces the basic API. In
order to do so, it fills in some gaps in the `List.findX` APIs.
This PR aligns current coverage of `find`-type theorems across
`List`/`Array`/`Vector`. There are still quite a few holes in this API,
which will be filled later.
This PR completes aligning `List`/`Array`/`Vector` lemmas about
`flatten`. `Vector.flatten` was previously missing, and has been added
(for rectangular sizes only). A small number of missing `Option` lemmas
were also need to get the proofs to go through.
