proposition: Lemma class_subG x A : x \in G -> A \subset G -> x ^: A \subset G.
proof: Proof. move=> Gx sAG; apply/subsetP=> _ /imsetP[y Ay ->]. by rewrite groupJ // (subsetP sAG). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)