Alternate take on
https://gitlab.inria.fr/bertot/stdpp/-/commit/895121f919c6f1332f41f658ce7f850e391eb49e,
which is used as an overlay in Coq for
https://github.com/coq/coq/pull/13448.

rename elem_of_equiv -> set_equiv and set_equiv_spec -> set_equiv_subseteq, and rename some instances to get out of the way

names for big operators in Iris.

Robbert Krebbers authored 4 years ago and Ralf Jung committed 4 years ago

* Add lemma `map_omap_union`.
* Add lemmas `map_disjoint_fmap` and `map_disjoint_omap`.
* Add lemmas `fmap_merge` and `omap_merge`.
* Add lemma `omap_delete`.
* Generalize `omap_insert` and `omap_singleton` to cover both the `Some` and `None` case. Add `_Some` and `_None` versions of the lemmas for the specific cases.
* Generalize `map_size_insert` and `map_size_delete` in the same way.
* Add lemmas `lookup_fmap_Some`, `lookup_omap_Some`, and `lookup_omap_id_Some`.

See https://github.com/coq/coq/pull/13741#issuecomment-762761112

Proofs by Tej