Should be restored later.

The only drawback is that we have to restrict iprod to finite types,
but that is fine.

Thanks to Amin Timany for the suggestion.

Contrary to destruct_conj from Program.

This replaces f_equiv and solve_proper with our own, hopefully better, versions

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.

This way it behaves better for discrete CMRAs.

This reverts commit 7266d16b

due to an accidental git commit --amend after a git push.

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.

This is all still pretty ad hoc, but oh well. Also, I have no idea why I had to make those instances in sta_dra global, but it complained about missing instances. Actually, I wonder how they could *not* be global previously...

This strengthens some lemmas that are written using the notion of closednes, shortening some proofs all the way up to barrier.v

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.

* Clearly separate the file algebra/sts in three parts:
  1.) The definition of an STS, step relations, and closure stuff
  2.) The construction as a disjoint RA (this module should never be used)
  3.) The construction as a CMRA with many derived properties
* Turn stsT into a canonical structure so that we can make more of its arguments
  implicit.
* Rename the underlying step relation of STSs to prim_step (similar naming as
  for languages, but here in a module to avoid ambiguity)
* Refactor program_logic/sts by moving general properties of the STS CMRA to
  algebra/sts.v
* Make naming and use of modules in program_logic/sts more consistent with
  program_logic/auth and program_logic/saved_prop
* Prove setoid properties of all definitions in program_logic/sts

Turns out it only holds as a view shift, not as an implication