Defines `mergeSort`, a naive stable merge sort algorithm, replaces it
via a `@[csimp]` lemma with something faster at runtime, and proves the
following results:
* `mergeSort_sorted`: `mergeSort` produces a sorted list.
* `mergeSort_perm`: `mergeSort` is a permutation of the input list.
* `mergeSort_of_sorted`: `mergeSort` does not change a sorted list.
* `mergeSort_cons`: proves `mergeSort le (x :: xs) = l₁ ++ x :: l₂` for
some `l₁, l₂`
so that `mergeSort le xs = l₁ ++ l₂`, and no `a ∈ l₁` satisfies `le a
x`.
* `mergeSort_stable`: if `c` is a sorted sublist of `l`, then `c` is
still a sublist of `mergeSort le l`.
This change
* moves `termination_by` and `decreasing_by` next to the function they
apply to
* simplify the syntax of `termination_by`
* apply the `decreasing_by` goal to all goals at once, for better
interactive use.
See the section in `RELEASES.md` for more details and migration advise.
This is a hard breaking change, requiring developers to touch every
`termination_by` in their code base. We decided to still do it as a
hard-breaking change, because supporting both old and new syntax at the
same time would be non-trivial, and not save that much. Moreover, this
requires changes to some metaprograms that developers might have
written, and supporting both syntaxes at the same time would make
_their_ migration harder.
