proposition: Lemma leR_max z : max x y <= z <-> x <= z /\ y <= z.
proof: Proof. split=> [lemz | [lexz leyz]]; first by split; apply: leR_trans lemz. by case: (max x y) / IFR_cases => _ [] [_ ->]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div order) mathcomp(ssralg ssrnum ssrint rat intdiv) Coq(Morphisms Setoid) fourcolor(real realsyntax)