proposition: Lemma np_roots_rel_cons: forall roots1 roots2 roots3 from i l, np_roots_rel from roots1 roots2 [i] -> np_roots_rel from roots2 roots3 l -> np_roots_rel from roots1 roots3 (i :: l).
proof: Proof. intros. unfold np_roots_rel in *. intros. simpl. specialize (H0 _ _ H1). destruct H0. split; intros. - destruct H3; auto. subst. destruct (in_dec Z.eq_dec j l); auto. destruct (H v j (H2 n)). apply H3. hnf; auto. - apply Decidable.not_or in H3. destruct H3. specialize (H2 H4). specialize (H _ _ H2). destruct H. apply H5. simpl. tauto. Qed.
imports: Coq.ZArith.ZArith Coq.Program.Basics Coq.micromega.Lia compcert.lib.Integers compcert.common.Values VST.veric.base VST.veric.Clight_lemmas VST.veric.val_lemmas VST.veric.shares VST.msl.seplog VST.msl.shares VST.zlist.sublist VST.floyd.coqlib3 VST.floyd.functional_base VST.floyd.data_at_rec_lemmas VST.zlist.list_solver CertiGraph.lib.EquivDec_ext CertiGraph.lib.List_ext CertiGraph.graph.graph_model CertiGraph.graph.graph_gen