proposition: Lemma atransP2 G S : [transitive G, on S | to] -> {in S &, forall x y, exists2 a, a \in G & y = to x a}.
proof: Proof. by move=> GtrS x y /(atransP GtrS) <- /imsetP. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)