proposition: Lemma comparable_ge_min : (min x y <= z) = (x <= z) || (y <= z).
proof: Proof. case: comparableP cmp_xy => // [||<-//]; rewrite ?orbb//; last rewrite orbC; by move=> xy _; apply/idP/idP => [->|/orP[]]//; apply/le_trans/ltW. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)