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* Adding sorting on tuples.
Co-authored-by: Cyril Cohen <CohenCyril@users.noreply.github.com>
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This change reduces
- use of numerical occurrence selectors (#436) and
- use of non ssreflect tactics such as `auto`,
and improves use of comparison predicates such as `posnP`, `leqP`, `ltnP`,
`ltngtP`, and `eqVneq`.
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- comparer -> compare (in order.v)
- eq constructor of compare goes last
- "x < y" is matched before "x > y"
- "x <= y" is matched before "x >= y"
- adding prod and lexi ordering on tuple
- adding missing CS
- edit CHANGELOG
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Use `{pred T}` systematically for generic _collective_ boolean
predicate.
Use `PredType` to construct `predType` instances.
Instrument core `ssreflect` files to replicate these and other new
features introduces by coq/coq#9555 (`nonPropType` interface,
`simpl_rel` that simplifies with `inE`).
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Related: coq/coq#9651
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Like injectivity lemmas, instances of cancellation lemmas (whose
conclusion is `cancel ? ?`, `{in ?, cancel ? ?}`, `pcancel`, or
`ocancel`) are passed to
generic lemmas such as `canRL` or `canLR_in`. Thus such lemmas should
not have trailing on-demand implicits _just before_ the `cancel`
conclusion, as these would be inconvenient to insert (requiring
essentially an explicit eta-expansion).
We therefore use `Arguments` or `Prenex Implicits` directives to make
all such arguments maximally inserted implicits. We don’t, however make
other arguments implicit, so as not to spoil direct instantiation of
the lemmas (in, e.g., `rewrite -[y](invmK injf)`).
We have also tried to do this with lemmas whose statement matches a
`cancel`, i.e., ending in `forall x, g (E[x]) = x` (where pattern
unification will pick up `f = fun x => E[x]`).
We also adjusted implicits of a few stray injectivity
lemmas, and defined constants.
We provide a shorthand for reindexing a bigop with a permutation.
Finally we used the new implicit signatures to simplify proofs that
use injectivity or cancellation lemmas.
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See the discussion here:
https://github.com/math-comp/math-comp/pull/242#discussion_r233778114
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Remove some unused canonical mixins.
Change simplification behavior of concrete comparison functions to allow for
better simplification using unfolding and sebsequent folding back e.g. with
`rewrite !eqE /= -!eqE`.
A bit of cleanup for `Prenex Implicits` declarations.
Document some explanations by G. Gonthier.
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