proposition: Lemma mulGS A B : (G * A \subset G * B) = (A \subset G * B).
proof: Proof. apply/idP/idP; first exact: subset_trans (mulG_subr A). by move/(mulgS G); rewrite mulgA mulGid. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)