GitLab

write tactics to move particular assertions to the front, and to introduce a (*) while taking paticular assertions to the left/right

For consistency's sake.

This cleans up some ad-hoc stuff and prepares for a generalization
of saved propositions.

It now also contains a non-expansiveness proof.

I have simplified the following CMRA axioms:

  cmra_unit_preservingN n x y : x ≼{n} y → unit x ≼{n} unit y;
  cmra_op_minus n x y : x ≼{n} y → x ⋅ y ⩪ x ≡{n}≡ y;

By dropping off the step-index, so into:

  cmra_unit_preservingN x y : x ≼ y → unit x ≼ unit y;
  cmra_op_minus x y : x ≼ y → x ⋅ y ⩪ x ≡ y;

The old axioms can be derived.

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

The performance gain seems neglectable, unfortunatelly...

* Use sig instead of sigT: the proof is a Prop after all
* Tweak implicit arguments
* Shorten proof of sigma

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 better seals off their definition. Although it did not give
much of a speedup, I think it is conceptually nicer.