proposition: Lemma svwl_roots_graph_compatible: forall from to roots l g1 g2, from <> to -> graph_has_gen g1 to -> copy_compatible g1 -> gen_unmarked g1 to -> roots_graph_compatible roots g1 -> scan_vertex_while_loop from to l g1 g2 -> roots_graph_compatible roots g2.
proof: Proof. intros until l. induction l; intros; inversion H4; subst; clear H4; try easy. 1: eapply IHl; eauto. pose proof H9. eapply svfl_roots_graph_compatible in H9; eauto. - apply (IHl g3); auto. + rewrite <- svfl_graph_has_gen; eauto. + eapply svfl_copy_compatible; eauto. + eapply svfl_gen_unmarked; eauto. - split; auto. - unfold no_scan in H8; lia. - intros. rewrite nat_inc_list_In_iff in H5. 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