proposition: Lemma make_header_tag_prep64: forall z, 0 <= z < two_p (8 * 8) -> Int64.and (Int64.repr z) (Int64.repr 255) = Int64.sub (Int64.repr z) (Int64.mul (Int64.repr (z / two_p 8)) (Int64.repr (two_p 8))).
proof: Proof. intros. replace (Int64.repr 255) with (Int64.sub (Int64.repr 256) Int64.one) by now vm_compute. rewrite <- (Int64.modu_and _ _ (Int64.repr 8)) by now vm_compute. rewrite Int64.modu_divu by (vm_compute; intro S; inversion S). rewrite (Int64.divu_pow2 _ _ (Int64.repr 8)) by now vm_compute. rewrite (Int64.mul_pow2 _ _ (Int64.repr 8)) by now vm_compute. rewrite Int64.shru_div_two_p, !Int64.unsigned_repr; [| rep_lia | ]. - rewrite Int64.shl_mul_two_p, Int64.unsigned_repr by rep_lia. easy. - simpl Z.mul in H. unfold Int64.max_unsigned, Int64.modulus. unfold Int64.wordsize, Wordsize_64.wordsize. rewrite two_power_nat_two_p. simpl Z.of_nat. lia. 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