proposition: Lemma standard_path_toS_zero : forall j beta i alpha, standard_path_toS j beta i alpha -> alpha <> zero.
proof: Proof. induction 1. - intro; now subst. - intro; subst; apply IHstandard_path_toS; auto. Qed.
imports: hydras(DecPreOrder Canon MoreLists First_toggle OrdNotations) Coq(Lia)