proposition: Lemma comparable_lt_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. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)