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This fix removes superflous white space in pretty printing. For example
✓{S n} x was pretty printed incorrectly as ✓{(S n)} x.

turns out we can import with shorter names (and we actually already do that frequently in "From Coq Import")

This avoids ambiguity with P and Q that we were using before for both
uPreds/iProps and indexed uPreds/iProps.

- The direction of big_sepS_later and big_sepM_later is now like later_sep.
- Do not use generated variables in the proofs.

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.

Also, specialize the big ops to gmap and gset because that is all that
we are using. For the big ops on sets this also means we can use Leibniz
equality on sets.

This prevent the assumption from being dragged into lemmas that do not even need it

The singleton maps notation is now also more consistent with the
insert <[_ := _]> _ notation for maps.

We now have:

  Π★{map Q } ...
  Π★{set Q } ...

to differentiate between sets and maps.

* 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

With nicely overloaded notations for sets and maps.

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