proposition: Lemma gacent_ract B : 'C_(|ract_groupAction)(B) = 'C_(|to)(A :&: B).
proof: Proof. by rewrite /gacent afix_ract setIA (setIidPr sAD). Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)