proposition: Lemma path_to_interval_inv_le alpha beta i j : path_to beta (interval i j) alpha -> (i <= j)%nat.
proof: Proof. destruct (le_lt_dec i j). auto. rewrite empty_interval. intro H; apply path_to_not_nil in H; now destruct H. auto. Qed.
imports: hydras(DecPreOrder Canon MoreLists First_toggle OrdNotations) Coq(Lia)