proposition: Lemma label_node_not_in_nids: forall p h s l, (step_star (init p) h s /\ In l h) -> not (label_node l = init_nid).
proof: Proof. intros. intro. apply label_node_in_nids in H. rewrite H0 in H. clear H0. apply init_not_in_nids in H. assumption. Qed.
imports: Coq(FunctionalExtensionality Arith Lia) Coq(Arith.Peano_dec Arith.Compare_dec) Coq(Relations.Relation_Operators) Coq(List) Chapar(Predefs)