This patch was created using

  find -name *.v | xargs -L 1 awk -i inplace '{from = 0} /^From/{ from = 1; ever_from = 1} { if (from == 0 && seen == 0 && ever_from == 1) { print "Set Default Proof Using \"Type*\"."; seen = 1 } }1 '

and some minor manual editing

This also solves a name clash with the extension order of CMRAs.

With Coq 8.6, you can no longer have intro patterns that give more names than
the constructor has.  Also, patterns with too few names are now interpreted as
filling up with "?", rather than putting the unnamed parts into the goal again.

Furthermore, it seems the behavior of "simplify_eq/=" changed, I guess
hypotheses are considered in different order now.  I managed to work around
this, but it all seem kind of fragile.

The next compilation failure is an "Anyomaly: ... Please report", so that's what I will do.

There was not really a need for the lattice type classes, so I removed
these.

These just make things more complicated, it would be more useful to
declare (efficient) decision procedures for each instance, so that
we can properly predict which instance we will get.

This class whose name is horrible and purpose is arbitrary seems to be a
leftover of some experiment with ch2o, a long time a ago.

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.

Also, use "set_solver by tac" to specify a tactic.

In most cases there is a lot of duplicate proof search performed by
both naive_solver and eauto. Especially since naive_solver calls its
tactic (in the case of set_solver this used to be eauto) quite eagerly
this made it very slow.

Note that set_solver is this too slow and should be improved.

In most cases there is a lot of duplicate proof search performed by
both naive_solver and eauto. Especially since naive_solver calls its
tactic (in the case of set_solver this used to be eauto) quite eagerly
this made it very slow.

Note that set_solver is this too slow and should be improved.

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.