proposition: Lemma orbit_inv A x y : (y \in orbit to A^-1 x) = (x \in orbit to A y).
proof: Proof. by rewrite orbit_inv_in ?subsetT. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)