1.) iDestruct is able turns  into two implications (because uPred_iff
    is (type classes) transparent).
2.) iApply only backtracks on turning P  Q into P → Q or Q → P when
    there are no future premises. This is not the case for
    'P  □ (P → False)'.

It not behaves more consistently with iExact and thus also works in the
case H : P -★ □^n Q |- Q.

show that even \later^n False is inconsistent (for any fixed n); properly use pvs in counter_examples

The new implementation ensures that type class arguments are only infered
in the very end. This avoids the need for the inG hack in a0348d7c.

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 reverts commit 20b4ae55, which does
not seem to work with Coq 8.5pl2 (I accidentally tested with 8.5pl1).

This makes type checking more directed, and somewhat more predictable.

On the downside, it makes it impossible to declare the singleton on
lists as an instance of SingletonM and the insert and alter operations
on functions as instances of Alter and Insert. However, these were not
used often anyway.

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.

Similar files (gmap, listset, ...) were already in singular form and
matched the name of the set/map data type.

In particular, remove ectx_language.atomic, because it seems unused
expect for a smart constructor for language.atomic.

Also, remove some unused lemmas about agree.

* Values are considered as atomic expressions (this does not hurt, and
  this makes the proofs of atomicity simpler).

Both ndot and nclose involve encodings of countable types, and conversion
should thus never unfold these definitions.

I also reverted 7952bca4 since there is no need for atomic to be a
boolean predicate anymore. Moreover, I introduced a hint database
fsaV for solving side-conditions related to FSAs, in particular,
side-conditions related to expressions being atomic.

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

Lifting lemmas : make the initial state appear under an existential under the view shift. This is still sound, but slightly more expressive.

In particular, it no longer uses set_solver (which made it often slow
or diverge) but a more specific lemma about subseteq.

Concretely, when execution of any of the wp_ tactics does not yield
another wp, it will make sure that a view shift is kept. This
behavior was already partially there, but now it is hopefully more
consistent.

This is more consistent with the proofmode, where we also call it pure.

Fixes issue #20.