use Proper and rewrite from stdlib for monotonicity #14
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This PR replaces the
monotonicpredicate withProper (le ==> le)from stdlib.Pros:
setoid_rewriteandsetoid_replacefor upper bounding expressions instead of using the custompoly_monotactic + existential variables.nat -> natfunctions can be shown by thesolve_propertactic from stdlib instead of using smpl which has been dropped from the depedencies of coq-library-undecidability (smpl is still needed for other things however).Pros?:
inOPolylemmas.smpl_inOis weaker and only provesinOPolyinstead of of bothmonotonicandinOPolywhich are often used together.Cons:
Proper (le ==> le)is more verbose and arguably harder to understand thanmonotonic.smpltactic.