proposition: Lemma const_pathS_inv_strong : forall n alpha beta, const_path (S n) alpha beta -> {beta = canon alpha (S n)} + {const_path (S n) (canon alpha (S n)) beta}.
proof: Proof. intros n alpha beta H; destruct (T1_eq_dec beta (canon alpha (S n))). - left;auto. - right; destruct (const_pathS_inv H). + contradiction. + trivial. Qed.
imports: hydras(DecPreOrder Canon MoreLists First_toggle OrdNotations) Coq(Lia)