proposition: Lemma subgraph_node_prop: forall n (g1 g2: PreGraph V E) p1 p2, (predicate_subgraph g1 p1) ~=~ (predicate_subgraph g2 p2) -> Included p1 (vvalid g1) -> Included p2 (vvalid g2) -> (p1 n <-> p2 n).
proof: Proof. intros. destruct H as [? _]. specialize (H n). specialize (H0 n). specialize (H1 n). simpl in *. unfold Ensembles.In in *. unfold predicate_vvalid in H. 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