proposition: Lemma backward_edge_prop_app_comm: forall r1 r2 g from to, backward_edge_prop g (r1++r2) from to <-> backward_edge_prop g (r2++r1) from to.
proof: Proof. unfold backward_edge_prop; intros. apply forall_iff; intro e. apply forall_iff; intros ?H. apply forall_iff; intros ?H. apply forall_iff; intros ?H. rewrite ! @filter_sum_right_app. unfold reachable_through_set. split; intros [s [? ?]]; exists s; split; auto; (rewrite in_app in H2|-*; tauto). 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