proposition: Lemma atrans_acts G S : [transitive G, on S | to] -> [acts G, on S | to].
proof: Proof. move=> GtrS; apply/subsetP=> a Ga; rewrite !inE. by apply/subsetP=> x /(atransP GtrS) <-; rewrite inE imset_f. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)