proposition: Lemma in_tl_nat_inc_list: forall i n, In i (tl (nat_inc_list n)) -> 1 <= i.
proof: Proof. destruct n. inversion 1. induction n. inversion 1. intros. simpl in H. rewrite Zpos_P_of_succ_nat in H. rewrite tl_app in H. 2: { rewrite Zlength_app. replace (Zlength (Z.of_nat n :: nil)) with 1 by reflexivity. pose proof (Zlength_nonneg (nat_inc_list n)). lia. } apply in_app_or in H; destruct H. - apply IHn. simpl. assumption. - simpl in H. destruct H; lia. Qed.
imports: Coq.Lists.List Coq.micromega.Lia Coq.Sorting.Permutation Coq.ZArith.ZArith_base Coq.ZArith.Zcomplements Coq.Logic.FunctionalExtensionality CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext VST.zlist.sublist VST.zlist.list_solver