proposition: Lemma card_orbit_in G x : G \subset D -> #|orbit to G x| = #|G : 'C_G[x | to]|.
proof: Proof. move=> sGD; rewrite orbit_stabilizer 1?card_in_imset //. exact: can_in_inj (act_reprK _). Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)