proposition: Lemma sound1_inv4: sound1 edge_closed res_reachable_closed.
proof: Proof. intros. unfold sound1, edge_closed, res_reachable_closed. simpl. intros ? ? ?. apply closed_edge_closed_reachable; auto. Qed.
imports: Coq.Sets.Finite_sets Coq.Arith.Arith Coq.Logic.ProofIrrelevance Coq.Logic.FunctionalExtensionality Coq.Sorting.Permutation Coq.micromega.Lia CertiGraph.lib.Coqlib CertiGraph.lib.List_ext CertiGraph.lib.EquivDec_ext CertiGraph.lib.EnumEnsembles Coq.Lists.List VST.msl.Coqlib2 CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.reachable_ind CertiGraph.graph.subgraph2 CertiGraph.graph.graph_gen CertiGraph.graph.MathGraph CertiGraph.graph.FiniteGraph