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

Terminology taken from "A Fresh Look at Separation Algebras and Share"
by Dockins et al.

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 allows for more control over `Hint Mode`.

See also Coq bug #5712.

This patch was created using

  find -name *.v | xargs -L 1 awk -i inplace '{from = 0} /^From/{ from = 1; ever_from = 1} { if (from == 0 && seen == 0 && ever_from == 1) { print "Set Default Proof Using \"Type*\"."; seen = 1 } }1 '

and some minor manual editing

The previous commit is not really necesarry anymore, but my proof
for UIP of types with decidable equality is a bit more general, so
I won't revert it.

Also cleanup the file a bit.

simplify_equality        => simplify_eq
simplify_equality'       => simplify_eq/=
simplify_map_equality    => simplify_map_eq
simplify_map_equality'   => simplify_map_eq/=
simplify_option_equality => simplify_option_eq
simplify_list_equality   => simplify_list_eq
f_equal'                 => f_equal/=

The /= suffixes (meaning: do simpl) are inspired by ssreflect.