proposition: Lemma orbit_stabilizer : orbit to G x = [set to x (repr Ca) | Ca in rcosets 'C_G[x | to] G].
proof: Proof. rewrite -amove_orbit -imset_comp /=; apply/setP=> z. by apply/idP/imsetP=> [xGz | [y xGy ->]]; first exists z; rewrite /= ?amoveK. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)