proposition: Lemma lg_vgen_stable: forall (g: Graph) (x: V) (d: DV), (predicate_partial_labeledgraph g (Complement V (eq x))) ~=~ (predicate_partial_labeledgraph (labeledgraph_vgen g x d) (Complement V (eq x)))%LabeledGraph.
proof: Proof. intros. split; [| split]. + simpl. reflexivity. + intros; simpl. unfold update_vlabel. if_tac; auto. destruct H. exfalso; apply H2, H1. + intros; simpl. reflexivity. Qed.
imports: Coq.Logic.ProofIrrelevance Coq.Sets.Ensembles Coq.Sets.Finite_sets Coq.Classes.Morphisms CertiGraph.lib.Coqlib CertiGraph.lib.Ensembles_ext CertiGraph.lib.relation_list CertiGraph.lib.List_ext CertiGraph.lib.Equivalence_ext CertiGraph.lib.EquivDec_ext VST.msl.Coqlib2 Coq.Lists.List CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.reachable_ind