proposition: Lemma lcosetS x A B : (x *: A \subset x *: B) = (A \subset B).
proof: Proof. apply/idP/idP=> sAB; last exact: mulgS. by rewrite -(lcosetK x A) -(lcosetK x B) mulgS. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)