This is in preparation for coq/coq#9274.

Adding a hint without a database now triggers a deprecation warning in
Coq master (https://github.com/coq/coq/pull/8987).

Works around Coq bug #7731

This followed from discussions in https://gitlab.mpi-sws.org/FP/iris-coq/merge_requests/134

`NoBackTrack P` requires `P` but will never backtrack on it
once a result for `P` has been found.

As we have for all classes for binary relations.

Enable one to import both stdpp's base and ssrfun.

Note that (f x.1) now parses as (f (fst x)) rather than (fst (f x)).
(This change affects one proof in Iris.)

This gets rid of the old hack to have specific notations for pairs
up to a fixed arity, and moreover allows to do fancy things like:

```
Record test := Test { t1 : nat; t2 : nat }.

Definition foo (x : option test) : option nat :=
  ''(Test a1 a2) ← x;
  Some a1.
```

This follows the associativity in Haskell. So, something like

  f <$> g <$> h

Is now parsed as:

  (f <$> g) <$> h

Since the functor is a generalized form of function application, this also now
also corresponds with the associativity of function application, which is also
left associative.

Infinity is described by having an injection from nat.

The documentation for some typeclasses used the wrong
names for these typeclasses.

This addresses some concerns in !5.

This way, we will be compabile with Iris's heap_lang, which puts ;;
at level 100.

This allows for more control over `Hint Mode`.