proposition: Lemma astabsP S a : reflect (forall x, (to x a \in S) = (x \in S)) (a \in 'N(S | to)).
proof: Proof. apply: (iffP idP) => [nSa x|nSa]; first exact: astabs_act. by rewrite !inE; apply/subsetP=> x; rewrite inE nSa. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)