proposition: Lemma astabM M N : M \subset R -> N \subset R -> 'C(M * N | to) = 'C(M | to) :&: 'C(N | to).
proof: Proof. move=> sMR sNR; rewrite -astabU -astab_gen ?mul_subG // genM_join. by rewrite astab_gen // subUset sMR. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)