proposition: Lemma vertex_valid_reset: forall g gen, vertex_valid g -> vertex_valid (reset_graph gen g).
proof: Proof. intros. unfold vertex_valid in *. intros. simpl. rewrite graph_has_v_reset. unfold remove_nth_gen_ve. rewrite fold_left_lrvae_vvalid. rewrite H. intuition; destruct H2. - destruct v as [vgen vidx]. simpl in *. subst vgen. change (gen, vidx) with ((fun idx : nat => (gen, idx)) vidx). apply in_map. rewrite nat_inc_list_In_iff. destruct H1. now red in H1. - apply list_in_map_inv in H0. destruct H0 as [? [? _]]; now subst v. Qed.
imports: Coq.ZArith.ZArith Coq.Program.Basics 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 CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext CertiGraph.lib.List_ext CertiGraph.graph.graph_model CertiGraph.graph.graph_gen CertiGraph.graph.path_lemmas CertiGraph.graph.subgraph2 CertiGraph.graph.graph_relation CertiGraph.graph.graph_isomorphism CertiGraph.graph.reachable_ind CertiGraph.CertiGC.GCGraph