proposition: Lemma orbit_eq_mem G x y : (orbit to G x == orbit to G y) = (x \in orbit to G y).
proof: Proof. exact: sameP eqP (orbit_eqP G x y). Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)