proposition: Lemma frr_P_holds: forall from to r1 r2 g1 g2, P g1 -> graph_has_gen g1 to -> forward_roots_relation from to r1 g1 r2 g2 -> P g2.
proof: Proof. intros. revert H H0; induction H1; simpl; intros; auto. apply IHforward_roots_relation; auto. eapply fr_O_P_holds; eauto. rewrite <- fr_graph_has_gen; eauto. 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