proposition: Lemma ti_size_spec_add: forall h sp i (Hs: 0 <= i < MAX_SPACES), total_space sp = nth_gen_size (Z.to_nat i) -> ti_size_spec h -> ti_size_spec (add_new_space h sp i Hs).
proof: Proof. intros. unfold ti_size_spec in *. rewrite Forall_forall in *. intros. specialize (H0 _ H1). unfold nth_gen_size_spec in *. destruct (Nat.eq_dec x (Z.to_nat i)); unfold gen_size. - subst x. rewrite !ans_nth_new. if_tac; auto. - rewrite !ans_nth_old; assumption. 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