proposition: Lemma frr_no_dangling_dst: forall from to roots g roots' g', graph_has_gen g to -> copy_compatible g -> from <> to -> roots_graph_compatible roots g -> forward_roots_relation from to roots g roots' g' -> no_dangling_dst g -> no_dangling_dst g'.
proof: Proof. intros. induction H3; auto. apply IHforward_roots_relation; clear IHforward_roots_relation. - rewrite <- fr_graph_has_gen; eauto. - eapply fr_copy_compatible; eauto. - pose proof fr_roots_graph_compatible 0 from to (inl 0%Z) g1 g2 (r::roots1). simpl in H6. rewrite upd_Znth0, Znth_0_cons in H6. spec H6; auto. spec H6; [list_solve| ]. repeat (spec H6;[ auto |]). apply Forall_filter_sum_right_cons_e in H6; auto. - apply (fr_O_no_dangling_dst from to (inl 0%Z) g1 g2 (r::roots1)); auto; simpl; try list_solve. Qed.
imports: Coq.ZArith.ZArith Coq.Program.Basics Coq.micromega.Lia 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 VST.zlist.list_solver CertiGraph.lib.EquivDec_ext CertiGraph.lib.List_ext CertiGraph.graph.graph_model CertiGraph.graph.graph_gen