proposition: Lemma partialgraph_edge_iff: forall (g: Graph) (p: V -> Prop) x y, (edge g x y /\ p x /\ p y) <-> edge (predicate_partialgraph g p) x y.
proof: Proof. intros. unfold edge. rewrite <- partialgraph_step_iff. simpl. unfold predicate_vvalid. tauto. 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