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