proposition: Lemma path_to_tail alpha s beta : path_to beta s alpha -> forall gamma n, nf (T1.cons gamma n alpha) -> path_to (T1.cons gamma n beta) s (T1.cons gamma n alpha).
proof: Proof. intros H gamma n Hnf; assert (H1:= path_to_not_In_zero H). rewrite path_to_path_toS_iff; auto. apply path_toS_tail; auto. now rewrite <- path_to_path_toS_iff. Qed.
imports: hydras(DecPreOrder Canon MoreLists First_toggle OrdNotations) Coq(Lia)