There are now two proof mode tactics for dealing with modalities:

- `iModIntro` : introduction of a modality
- `iMod pm_trm as (x1 ... xn) "ipat"` : eliminate a modality

The behavior of these tactics can be controlled by instances of the `IntroModal`
and `ElimModal` type class. We have declared instances for later, except 0,
basic updates and fancy updates. The tactic `iMod` is flexible enough that it
can also eliminate an updates around a weakest pre, and so forth.

The corresponding introduction patterns of these tactics are `!>` and `>`.

These tactics replace the tactics `iUpdIntro`, `iUpd` and `iTimeless`.

Source of backwards incompatability: the introduction pattern `!>` is used for
introduction of arbitrary modalities. It used to introduce laters by stripping
of a later of each hypotheses.

And also rename the corresponding proof mode tactics.

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

Before this commit, given "HP" : P and "H" : P -★ Q with Q persistent, one
could write:

  iSpecialize ("H" with "#HP")

to eliminate the wand in "H" while keeping the resource "HP". The lemma:

  own_valid : own γ x ⊢ ✓ x

was the prototypical example where this pattern (using the #) was used.

However, the pattern was too limited. For example, given "H" : P₁ -★ P₂ -★ Q",
one could not write iSpecialize ("H" with "#HP₁") because P₂ -★ Q is not
persistent, even when Q is.

So, instead, this commit introduces the following tactic:

  iSpecialize pm_trm as #

which allows one to eliminate implications and wands while being able to use
all hypotheses to prove the premises, as well as being able to use all
hypotheses to prove the resulting goal.

In the case of iDestruct, we now check whether all branches of the introduction
pattern start with an `#` (moving the hypothesis to the persistent context) or
`%` (moving the hypothesis to the pure Coq context). If this is the case, we
allow one to use all hypotheses for proving the premises, as well as for proving
the resulting goal.

By using the global ghost maps instead of our own ones.

This makes stuff more uniform and also removes the need for the [inGFs]
type class. Instead, there is now a type class [subG Σ1 Σ2] which expresses
that a list of functors [Σ1] is contained in [Σ2].

Also make those for introduction and elimination more symmetric:

  !%   pure introduction         %        pure elimination
  !#   always introduction       #        always elimination
  !>   later introduction        > pat    timeless later elimination
  !==> view shift introduction   ==> pat  view shift elimination

This commit features:

- A simpler model. The recursive domain equation no longer involves a triple
  containing invariants, physical state and ghost state, but just ghost state.
  Invariants and physical state are encoded using (higher-order) ghost state.

- (Primitive) view shifts are formalized in the logic and all properties about
  it are proven in the logic instead of the model. Instead, the core logic
  features only a notion of raw view shifts which internalizing performing frame
  preserving updates.

- A better behaved notion of mask changing view shifts. In particular, we no
  longer have side-conditions on transitivity of view shifts, and we have a
  rule for introduction of mask changing view shifts |={E1,E2}=> P with
  E2 ⊆ E1 which allows to postpone performing a view shift.

- The weakest precondition connective is formalized in the logic using Banach's
  fixpoint. All properties about the connective are proven in the logic instead
  of directly in the model.

- Adequacy is proven in the logic and uses a primitive form of adequacy for
  uPred that only involves raw views shifts and laters.

Some remarks:

- I have removed binary view shifts. I did not see a way to describe all rules
  of the new mask changing view shifts using those.
- There is no longer the need for the notion of "frame shifting assertions" and
  these are thus removed. The rules for Hoare triples are thus also stated in
  terms of primitive view shifts.

TODO:

- Maybe rename primitive view shift into something more sensible
- Figure out a way to deal with closed proofs (see the commented out stuff in
  tests/heap_lang and tests/barrier_client).

This way type class inference is not invokved when used in tactics
like iPvs while not having to write an @.

(Idea suggested by Ralf.)

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