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