proposition: Lemma afix_gen_in A : A \subset D -> 'Fix_to(<<A>>) = 'Fix_to(A).
proof: Proof. move=> sAD; apply/eqP; rewrite eqEsubset afixS ?sub_gen //=. by rewrite -astabCin gen_subG ?astabCin. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)