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