proposition: Lemma mem_setact S a x : x \in S -> to x a \in to^* S a.
proof: Proof. exact: imset_f. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)