Thanks to Amin Timany for the suggestion.

Add both non-expansive and contractive functors, and bundle them for the general Iris instance as well as the global functor construction

This allows us to move the \later in the user-defined functor to any place we want.
In particular, we can now have "\later (iProp -> iProp)" in the ghost CMRA.

make the global functor stuff in the various constructions more uniform; change it such that barrier/proof does not have to repeat the functors it needs

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

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

I am now also using reification to obtain the indexes corresponding to
the stuff we want to cancel instead of relying on matching using Ltac.

And now the part that I forgot to commit.

Also, give all these global functors the suffix GF to avoid shadowing
such as we had with authF.

And add some type annotations for clarity.

I added a new typeclass "inGF" to witness that a particular *functor* is part of \Sigma. inG, in contrast, witnesses a particular *CMRA* to be in there, after applying the functor to "\later iProp".
inGF can be inferred if that functor is consed to the head of \Sigma, and it is preserved by consing a new functor to \Sigma. This is not the case for inG since the recursive occurence of \Sigma also changes.
For evry construction (auth, sts, saved_prop), there is an instance infering the respective authG, stsG, savedPropG from an inGF. There is also a global inG_inGF, but Coq is unable to use it.

I tried to instead have *only* inGF, since having both typeclasses seemed weird. However, then the actual type that e.g. "own" is about is the result of applying a functor, and Coq entirely fails to infer anything.

I had to add a few type annotations in heap.v, because Coq tried to use the "authG_inGF" instance before the A got fixed, and ended up looping and expanding endlessly on that proof of timelessness.
This does not seem entirely unreasonable, I was honestly surprised Coq was able to infer the types previously.

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

* These type classes bundle an identifier into the global CMRA with a proof
  that the identifier points to the correct CMRA. Bundling allows us to get
  rid of many arguments everywhere.

* I have setup the type classes so that we no longer have to keep track of the
  global CMRA identifiers. These are implicit and resolved automatically.

* For heap I am also bundling the name of the heap RA instance. There always
  should be at most one heap instance so this does not introduce ambiguities.

* We now have a "maps to" notation!

Whenever clients get this stuff out of invariants, this is much more convenient for them, compared to applying timelessness themselves.
On the other hand, this makes the test proofs slightly more annoying, since they have to manually strip away that later. I am not sure if it is worth having separate lemmas (well, tactics, soon) for that.
Eventually, we should have a tactic which, given "... * P * ... |- ... * \later^n P * ...", automatically gets rid of the P.