algebra.sts as the wrong file, the affected lemmas are in base_logic.lib.sts (already fixed by Robbert)

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

Using this new definition we can express being contractive using a
Proper. This has the following advantages:

- It makes it easier to state that a function with multiple arguments
  is contractive (in all or some arguments).
- A solve_contractive tactic can be implemented by extending the
  solve_proper tactic.

Initial proof by Jan-Oliver Kaiser, adapted by Robbert Krebbers.

Initial proof by Jan-Oliver Kaiser, adapted by Robbert Krebbers.

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

Similar files (gmap, listset, ...) were already in singular form and
matched the name of the set/map data type.

- Make the carrier argument of the constructors for the canonical structures
  cofeT and cmraT explicit. This way we make sure the carrier is properly
  exposed, instead of some alias of the carrier.
- Make derived constructions (such as discreteC and discreteR) notations
  instead of definitions. This is yet again to make sure that the carrier is
  properly exposed.
- Turn DRA into a canonical structure (it used to be a type class).

This fixes some issues, notably it fixes some broken rewrites in algebra/sts
and it makes canonical structures work properly with dec_agree.

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