proposition: Lemma orbitE : orbit x = rot (index x p) p.
proof: Proof. set i := index _ _; rewrite /orbit order_cycle -(size_rot i) rot_index// -/i. set q := _ ++ _; suffices /fpathP[j ->]: fpath f x q by rewrite /= size_traject. by move: f_p; rewrite -(rot_cycle i) rot_index// (cycle_path x); case/andP. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat) mathcomp(seq path fintype)