proposition: Lemma atransP G S : [transitive G, on S | to] -> forall x, x \in S -> orbit to G x = S.
proof: Proof. by case/imsetP=> x _ -> y; apply/orbit_eqP. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)