proposition: Lemma vertex_update_mark1: forall (g: Graph) x lx, label_marked lx -> mark1 x g (labeledgraph_vgen g x lx).
proof: Proof. intros. split; [| split; [| split]]. + reflexivity. + simpl. unfold update_vlabel. destruct_eq_dec x x; [auto | congruence]. + simpl; intros. unfold update_vlabel. destruct_eq_dec x n'; [tauto | auto]. + simpl; intros. unfold update_vlabel in H1. destruct_eq_dec x n'; [tauto | auto]. Qed.
imports: Coq.Logic.ProofIrrelevance Coq.Classes.Morphisms VST.msl.Coqlib2 CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext CertiGraph.lib.Relation_ext CertiGraph.lib.relation_list CertiGraph.lib.EnumEnsembles CertiGraph.lib.List_ext CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.reachable_computable CertiGraph.graph.reachable_ind CertiGraph.graph.graph_gen CertiGraph.graph.subgraph2 CertiGraph.graph.dual_graph