proposition: Lemma contra_orbit G x y : x \notin orbit to G y -> x != y.
proof: Proof. by apply: contraNneq => ->; apply: orbit_refl. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)