proposition: Lemma comparable_le_min : (z <= min x y) = (z <= x) && (z <= y).
proof: Proof. case: comparableP cmp_xy => // [||<-//]; rewrite ?andbb//; last rewrite andbC; by case: (comparableP z) => // [/lt_trans xlt/xlt|->] /ltW. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)