Move Z definitions out of Integers and into Zbits

The module Integers.Make contained lots of definitions and theorems
about Z integers that were independent of the word size.  These
definitions and theorems are useful outside Integers.Make, but
it felt unnatural to fetch them from modules Int or Int64.

This commit moves the word-size-independent definitions and theorems
to a new module, lib/Zbits.v, and fixes their uses in the code base.

2 files changed, 10 insertions, 9 deletions

diff --git a/powerpc/Asmgenproof1.v b/powerpc/Asmgenproof1.v
index c18757b2..afbba882 100644
--- a/powerpc/Asmgenproof1.v
+++ b/powerpc/Asmgenproof1.v
@@ -16,6 +16,7 @@ Require Import Coqlib.
 Require Import Errors.
 Require Import Maps.
 Require Import AST.
+Require Import Zbits.
 Require Import Integers.
 Require Import Floats.
 Require Import Values.
@@ -80,13 +81,13 @@ Proof.
     unfold Int.modu, Int.zero. decEq.
     change 0 with (0 mod 65536).
     change (Int.unsigned (Int.repr 65536)) with 65536.
-    apply Int.eqmod_mod_eq. omega.
-    unfold x, low_s. eapply Int.eqmod_trans.
-    apply Int.eqmod_divides with Int.modulus.
+    apply eqmod_mod_eq. omega.
+    unfold x, low_s. eapply eqmod_trans.
+    apply  eqmod_divides with Int.modulus.
     unfold Int.sub. apply Int.eqm_unsigned_repr_l. apply Int.eqm_refl.
     exists 65536. compute; auto.
     replace 0 with (Int.unsigned n - Int.unsigned n) by omega.
-    apply Int.eqmod_sub. apply Int.eqmod_refl. apply Int.eqmod_sign_ext'.
+    apply eqmod_sub. apply eqmod_refl. apply Int.eqmod_sign_ext'.
     compute; auto.
   rewrite H0 in H. rewrite Int.add_zero in H.
   rewrite <- H. unfold x. rewrite Int.sub_add_opp. rewrite Int.add_assoc.
diff --git a/powerpc/SelectLongproof.v b/powerpc/SelectLongproof.v
index a214d131..f16c967e 100644
--- a/powerpc/SelectLongproof.v
+++ b/powerpc/SelectLongproof.v
@@ -12,7 +12,7 @@
 
 (** Correctness of instruction selection for 64-bit integer operations *)
 
-Require Import String Coqlib Maps Integers Floats Errors.
+Require Import String Coqlib Maps Zbits Integers Floats Errors.
 Require Archi.
 Require Import AST Values Memory Globalenvs Events.
 Require Import Cminor Op CminorSel.
@@ -221,11 +221,11 @@ Proof.
   change (Int64.unsigned Int64.iwordsize) with 64.
   f_equal.
   rewrite Int.unsigned_repr. 
-  apply Int.eqmod_mod_eq. omega. 
-  apply Int.eqmod_trans with a.
-  apply Int.eqmod_divides with Int.modulus. apply Int.eqm_sym. apply Int.eqm_unsigned_repr.
+  apply eqmod_mod_eq. omega. 
+  apply eqmod_trans with a.
+  apply eqmod_divides with Int.modulus. apply Int.eqm_sym. apply Int.eqm_unsigned_repr.
   exists (two_p (32-6)); auto.
-  apply Int.eqmod_divides with Int64.modulus. apply Int64.eqm_unsigned_repr.
+  apply eqmod_divides with Int64.modulus. apply Int64.eqm_unsigned_repr.
   exists (two_p (64-6)); auto.
   assert (0 <= Int.unsigned (Int.repr a) mod 64 < 64) by (apply Z_mod_lt; omega).
   assert (64 < Int.max_unsigned) by (compute; auto).