In particular, it no longer uses set_solver (which made it often slow
or diverge) but a more specific lemma about subseteq.

Thanks to Amin Timany for the suggestion.

It now traverses terms at most once, whereas the setoid_rewrite
approach was travering terms many times. Also, the tactic can now
be extended by defining type class instances.

The non applied one should be only parsing.

It is doing much more than just dealing with ∈, it solves all kinds
of goals involving set operations (including ≡ and ⊆).

simplify_equality        => simplify_eq
simplify_equality'       => simplify_eq/=
simplify_map_equality    => simplify_map_eq
simplify_map_equality'   => simplify_map_eq/=
simplify_option_equality => simplify_option_eq
simplify_list_equality   => simplify_list_eq
f_equal'                 => f_equal/=

The /= suffixes (meaning: do simpl) are inspired by ssreflect.

Now that there is more of it, it deserves its own place :).