proposition: Lemma orbit_actr G a x y : a \in G -> (to y a \in orbit to G x) = (y \in orbit to G x).
proof: Proof. by move/mem_orbit/orbit_transl; apply. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)