Fixes new Coq master warning deprecated-hint-without-locality.

Moreover, and suitable lemmas.

This follows the standard naming for Coq numbers, and avoids one using
the old lemma to break abstraction accidentally.

- Remove the coercion from `Qp` to `Qc`, and remove it into from `Qp_car` into
  `Qp_to_Qc` to be consistent with other conversion functions.
- Use `let '(..) = ...` in the definitions of `Qp_plus`/`Qp_mult`/`Qp_div` to
  avoid Coq tactics (like `injection`) to unfold these definitions eagerly.
- Define orders `Qp_le` and `Qp_lt`, instead of relying on the orders on `Qc`,
  which were obtained through the removed coercion into `Qc`.
- Lift lemmas about the orders from `Qc` to `Qp`.
- Improve variable names and use of notation scopes.

Tej Chajed authored 4 years ago and Robbert Krebbers committed 4 years ago

Set Default Goal Selector "!" makes it illegal to ever apply a tactic
with more than one goal (instead, must focus with bullets or braces).

Code not affected by a00d9bd8.

All occurrences are gone, except for one in `base.v` where you'd need different
functions.

However, I'm unsure this is an improvement: in lots of cases here, the function
didn't need to be guessed, but could be deduced by "simple" higher-order
unification, the one where unifying `?f ?a` against `g args last_arg` sets `?f =
g args`.

This was done using `sed --in-place 's/[[:space:]]\+$//' theories/*.v`.

This follows iris/iris!387
This closes issue #54.

For example, change `(!! i)` into `(.!! x)` so that `!!` can also be used as
a prefix, as done in VST for example.

This closes issue #42.

I have used the `sed` script below. This script took care of nearly all uses
apart from a few occurrences where a space was missing, e.g. `(,foo)`. In
this case, `coqc` will just fail, allowing one to patch up things manually.

The script is slightly too eager on Iris developments, where it also replaces
`($ ...)` introduction patterns. When porting Iris developments you thus may
want to remove the line for `$`.

```
sed '
s/(= /(.= /g;
s/ =)/ =.)/g;
s/(≠ /(.≠ /g;
s/ ≠)/ ≠.)/g;
s/(≡ /(.≡ /g;
s/ ≡)/ ≡.)/g;
s/(≢ /(.≢ /g;
s/ ≢)/ ≢.)/g;
s/(∧ /(.∧ /g;
s/ ∧)/ ∧.)/g;
s/(∨ /(.∨ /g;
s/ ∨)/ ∨.)/g;
s/( /(. /g;
s/ )/ .)/g;
s/(→ /(.→ /g;
s/ →)/ →.)/g;
s/($ /(.$ /g;
s/(∘ /(.∘ /g;
s/ ∘)/ ∘.)/g;
s/(, /(., /g;
s/ ,)/ ,.)/g;
s/(∘ /(.∘ /g;
s/ ∘)/ ∘.)/g;
s/(∪ /(.∪ /g;
s/ ∪)/ ∪.)/g;
s/(⊎ /(.⊎ /g;
s/ ⊎)/ ⊎.)/g;
s/(∩ /(.∩ /g;
s/ ∩)/ ∩.)/g;
s/(∖ /(.∖ /g;
s/ ∖)/ ∖.)/g;
s/(⊆ /(.⊆ /g;
s/ ⊆)/ ⊆.)/g;
s/(⊈ /(.⊈ /g;
s/ ⊈)/ ⊈.)/g;
s/(⊂ /(.⊂ /g;
s/ ⊂)/ ⊂.)/g;
s/(⊄ /(.⊄ /g;
s/ ⊄)/ ⊄.)/g;
s/(∈ /(.∈ /g;
s/ ∈)/ ∈.)/g;
s/(∉ /(.∉ /g;
s/ ∉)/ ∉.)/g;
s/(≫= /(.≫= /g;
s/ ≫=)/ ≫=.)/g;
s/(!! /(.!! /g;
s/ !!)/ !!.)/g;
s/(⊑ /(.⊑ /g;
s/ ⊑)/ ⊑.)/g;
s/(⊓ /(.⊓ /g;
s/ ⊓)/ ⊓.)/g;
s/(⊔ /(.⊔ /g;
s/ ⊔)/ ⊔.)/g;
s/(:: /(.:: /g;
s/ ::)/ ::.)/g;
s/(++ /(.++ /g;
s/ ++)/ ++.)/g;
s/(≡ₚ /(.≡ₚ /g;
s/ ≡ₚ)/ ≡ₚ.)/g;
s/(≢ₚ /(.≢ₚ /g;
s/ ≢ₚ)/ ≢ₚ.)/g;
s/(::: /(.::: /g;
s/ :::)/ :::.)/g;
s/(+++ /(.+++ /g;
s/ +++)/ +++.)/g;
' -i $(find -name "*.v")
```

Use Open/Close Scope without Local (i.e., export the scope opening)
only when the scope corresponds to the main purpose of the module.