proposition: Fact join_lel x y : join x y <= join y x.
proof: Proof. have:= le_refl (join y x); rewrite joinP => /andP [ylej xlej]. by rewrite joinP ylej xlej. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)