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