proposition: Lemma joing_sub A B C : A <*> B = C -> A \subset C /\ B \subset C.
proof: Proof. by move <-; apply/joing_subP. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)