proposition: Lemma copied_vertex_reachable_inv: forall (g: LGraph) (r v: VType) to, sound_gc_graph g -> copied_vertex_prop g (vgeneration r) to -> raw_mark (vlabel g r) = true -> vgeneration v = vgeneration r -> vgeneration r <> to -> no_dangling_dst g -> graph_has_v g r -> reachable g (copied_vertex (vlabel g r)) v -> reachable g r v.
proof: Proof. intros. remember (vgeneration r) as from. clear Heqfrom. unfold reachable, reachable_by in H6. destruct H6 as [[cr' p] ?]. pose proof H6. apply reachable_by_path_head in H7. simpl in H7. subst cr'. eapply copied_vertex_reachable_by_path_inv in H6; eauto. destruct H6 as [p' [? ?]]. now exists (r, p'). 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