proposition: Lemma lcv_edge_valid: forall g v to, edge_valid g -> graph_has_gen g to -> edge_valid (lgraph_copy_v g v to).
proof: Proof. intros. unfold edge_valid in *. intros. unfold graph_has_e in *. simpl. rewrite pcv_evalid_iff, lcv_graph_has_v_iff, H; auto. split; intros. - destruct H1 as [[? ?] | ?]. + split; [now left|]. rewrite lcv_get_edges_old; auto. + assert (fst e = new_copied_v g to). { apply list_in_map_inv in H1; destruct H1 as [x [? ?]]; subst e; simpl; auto. } split; [now right|]. rewrite H2. now rewrite get_edges_map_map, lcv_lacv_get_edges, lacv_get_edges_new, map_map. - destruct H1. destruct H1; [left | right]. + split; auto. rewrite lcv_get_edges_old in H2; assumption. + rewrite H1 in H2. rewrite get_edges_map_map, lcv_lacv_get_edges, lacv_get_edges_new, map_map in H2. assumption. 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