proposition: Lemma backward_edge_prop_incl: forall r1 r2 g from to, (forall x, In x r1 -> In x r2) -> backward_edge_prop g r1 from to -> backward_edge_prop g r2 from to.
proof: Proof. unfold backward_edge_prop; intros. specialize (H0 e H1 H2 H3); clear - H H0. destruct H0 as [s [? ?]]; exists s; split; auto. clear H1. apply filter_sum_right_In_iff in H0. apply filter_sum_right_In_iff. auto. Qed.
imports: Coq.ZArith.ZArith Coq.Program.Basics compcert.lib.Integers compcert.common.Values VST.veric.base VST.veric.Clight_lemmas VST.veric.val_lemmas VST.veric.shares VST.msl.seplog VST.msl.shares VST.zlist.sublist VST.floyd.coqlib3 VST.floyd.functional_base VST.floyd.data_at_rec_lemmas CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext CertiGraph.lib.List_ext CertiGraph.graph.graph_model CertiGraph.graph.graph_gen CertiGraph.graph.path_lemmas CertiGraph.graph.subgraph2 CertiGraph.graph.graph_relation CertiGraph.graph.graph_isomorphism CertiGraph.graph.reachable_ind CertiGraph.CertiGC.GCGraph