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