This way, it won't pick arbitrary (and possibly wrong!) inG instances
when multiple ones are available. We achieve this by declaring:

  Hint Mode inG - - +

So that type class inference only succeeds when the type of the ghost
variable does not include any evars.

This required me to make some minor changes throughout the whole
development making some types explicit.

The intropattern {H} also meant clear (both in ssreflect, and the logic
part of the introduction pattern).

This introduces n hypotheses and destructs the nth one.

be the same as .

This is a fairly intrusive change, but at least makes notations more
consistent, and often shorter because fewer parentheses are needed. Note
that viewshifts already had the same precedence as →.

It used to be: (P ={E}=> Q) := (True ⊢ (P → |={E}=> Q))
Now it is: (P ={E}=> Q) := (P ⊢ |={E}=> Q)

Changes:
- We no longer have a different syntax for specializing a term H : P -★ Q whose
  range P or domain Q is persistent. There is just one syntax, and the system
  automatically determines whether either P or Q is persistent.
- While specializing a term, always modalities are automatically stripped. This
  gets rid of the specialization pattern !.
- Make the syntax of specialization patterns more consistent. The syntax for
  generating a goal is [goal_spec] where goal_spec is one of the following:

    H1 .. Hn : generate a goal using hypotheses H1 .. Hn
   -H1 .. Hn : generate a goal using all hypotheses but H1 .. Hn
           # : generate a goal for the premise in which all hypotheses can be
               used. This is only allowed when specializing H : P -★ Q where
               either P or Q is persistent.
           % : generate a goal for a pure premise.

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

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

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

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

This way it behaves better for discrete CMRAs.

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.

barrier: strive for consistency between barrierGF and the inGF assumptions; also change some instance names

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