This should ensure that `coqchk` no longer reports axioms.

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).