proposition: Lemma mem_mulg A B x y : x \in A -> y \in B -> x * y \in A * B.
proof: Proof. by move=> Ax By; apply/mulsgP; exists x y. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)