proposition: Lemma astabQ H Abar : 'C(Abar |'Q) = coset H @*^-1 'C(Abar).
proof: Proof. apply/setP=> x; rewrite inE /= dom_qactJ morphpreE in_setI /=. apply: andb_id2l => Nx; rewrite !inE -sub1set centsC cent_set1. apply: eq_subset_r => {Abar} Hy; rewrite inE qactJ Nx (sameP eqP conjg_fixP). by rewrite (sameP cent1P eqP) (sameP commgP eqP). Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)