From 00353bc0b970605ae092af594417a51a0cdf903f Mon Sep 17 00:00:00 2001
From: letouzey
Date: Tue, 28 Jun 2011 23:30:21 +0000
Subject: Deletion of useless Zlog_def

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14246 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/Numbers/Integer/BigZ/ZMake.v           |  4 ++--
 theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v |  4 ++--
 theories/Numbers/Natural/BigN/NMake.v           |  2 +-
 theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v |  6 ++---
 theories/ZArith/ZArith.v                        |  3 +--
 theories/ZArith/Zlog_def.v                      | 13 -----------
 theories/ZArith/Zlogarithm.v                    | 31 ++++++++++++++-----------
 theories/ZArith/vo.itarget                      |  1 -
 8 files changed, 26 insertions(+), 38 deletions(-)
 delete mode 100644 theories/ZArith/Zlog_def.v

diff --git a/theories/Numbers/Integer/BigZ/ZMake.v b/theories/Numbers/Integer/BigZ/ZMake.v
index 0bcf22e328..cb16e1291e 100644
--- a/theories/Numbers/Integer/BigZ/ZMake.v
+++ b/theories/Numbers/Integer/BigZ/ZMake.v
@@ -368,12 +368,12 @@ Module Make (N:NType) <: ZType.
   | Neg nx => zero
   end.
 
- Theorem spec_log2: forall x, to_Z (log2 x) = Zlog2 (to_Z x).
+ Theorem spec_log2: forall x, to_Z (log2 x) = Z.log2 (to_Z x).
  Proof.
   intros. destruct x as [p|p]; simpl. apply N.spec_log2.
   rewrite N.spec_0.
   destruct (Z_le_lt_eq_dec _ _ (N.spec_pos p)) as [LT|EQ].
-  rewrite Zlog2_nonpos; auto with zarith.
+  rewrite Z.log2_nonpos; auto with zarith.
   now rewrite <- EQ.
  Qed.
 
diff --git a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
index dd83b65da1..f409285669 100644
--- a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
+++ b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
@@ -324,12 +324,12 @@ Qed.
 Lemma log2_spec : forall n, 0<n ->
  2^(log2 n) <= n /\ n < 2^(succ (log2 n)).
 Proof.
- intros n. zify. apply Zlog2_spec.
+ intros n. zify. apply Z.log2_spec.
 Qed.
 
 Lemma log2_nonpos : forall n, n<=0 -> log2 n == 0.
 Proof.
- intros n. zify. apply Zlog2_nonpos.
+ intros n. zify. apply Z.log2_nonpos.
 Qed.
 
 (** Even / Odd *)
diff --git a/theories/Numbers/Natural/BigN/NMake.v b/theories/Numbers/Natural/BigN/NMake.v
index 66b39aca9b..64b8ec844d 100644
--- a/theories/Numbers/Natural/BigN/NMake.v
+++ b/theories/Numbers/Natural/BigN/NMake.v
@@ -1244,7 +1244,7 @@ Module Make (W0:CyclicType) <: NType.
  apply ZnZ.spec_head0; auto with zarith.
  Qed.
 
- Lemma spec_log2 : forall x, [log2 x] = Zlog2 [x].
+ Lemma spec_log2 : forall x, [log2 x] = Z.log2 [x].
  Proof.
   intros. destruct (Z_lt_ge_dec 0 [x]).
   symmetry. apply Z.log2_unique. apply spec_pos.
diff --git a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
index 9bed794f29..225c0853ec 100644
--- a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
+++ b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
@@ -277,13 +277,13 @@ Qed.
 Lemma log2_spec : forall n, 0<n ->
  2^(log2 n) <= n /\ n < 2^(succ (log2 n)).
 Proof.
- intros n. zify. change (Zlog2 [n]+1)%Z with (Zsucc (Zlog2 [n])).
- apply Zlog2_spec.
+ intros n. zify. change (Z.log2 [n]+1)%Z with (Z.succ (Z.log2 [n])).
+ apply Z.log2_spec.
 Qed.
 
 Lemma log2_nonpos : forall n, n<=0 -> log2 n == 0.
 Proof.
- intros n. zify. apply Zlog2_nonpos.
+ intros n. zify. apply Z.log2_nonpos.
 Qed.
 
 (** Even / Odd *)
diff --git a/theories/ZArith/ZArith.v b/theories/ZArith/ZArith.v
index 5a927fe6b8..abd735de5a 100644
--- a/theories/ZArith/ZArith.v
+++ b/theories/ZArith/ZArith.v
@@ -12,8 +12,7 @@ Require Export ZArith_base.
 
 (** Extra definitions *)
 
-Require Export
- Zpow_def Zlog_def Zdigits_def.
+Require Export Zpow_def Zdigits_def.
 
 (** Extra modules using [Omega] or [Ring]. *)
 
diff --git a/theories/ZArith/Zlog_def.v b/theories/ZArith/Zlog_def.v
deleted file mode 100644
index 8326cb13c4..0000000000
--- a/theories/ZArith/Zlog_def.v
+++ /dev/null
@@ -1,13 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010     *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-Require Import BinInt Zorder Zpow_def.
-
-Notation Zlog2 := Z.log2 (only parsing).
-Notation Zlog2_spec := Z.log2_spec (only parsing).
-Notation Zlog2_nonpos := Z.log2_nonpos (only parsing).
diff --git a/theories/ZArith/Zlogarithm.v b/theories/ZArith/Zlogarithm.v
index b80e96c2ab..30948ca7a3 100644
--- a/theories/ZArith/Zlogarithm.v
+++ b/theories/ZArith/Zlogarithm.v
@@ -8,11 +8,14 @@
 
 (**********************************************************************)
 
-(** The integer logarithms with base 2.
+(** The integer logarithms with base 2. *)
 
-    NOTA: This file is deprecated, please use Zlog2 defined in Zlog_def.
+(** THIS FILE IS DEPRECATED.
+    Please rather use [Z.log2] (or [Z.log2_up]), which
+    are defined in [BinIntDef], and whose properties can
+    be found in [BinInt.Z]. *)
 
-    There are three logarithms defined here,
+(*  There are three logarithms defined here,
     depending on the rounding of the real 2-based logarithm:
     - [Log_inf]: [y = (Log_inf x) iff 2^y <= x < 2^(y+1)]
       i.e. [Log_inf x] is the biggest integer that is smaller than [Log x]
@@ -21,7 +24,7 @@
     - [Log_nearest]: [y= (Log_nearest x) iff 2^(y-1/2) < x <= 2^(y+1/2)]
       i.e. [Log_nearest x] is the integer nearest from [Log x] *)
 
-Require Import ZArith_base Omega Zcomplements Zlog_def Zpower.
+Require Import ZArith_base Omega Zcomplements Zpower.
 Local Open Scope Z_scope.
 
 Section Log_pos. (* Log of positive integers *)
@@ -44,25 +47,25 @@ Section Log_pos. (* Log of positive integers *)
 
   Hint Unfold log_inf log_sup.
 
-  Lemma Psize_log_inf : forall p, Zpos (Psize_pos p) = Zsucc (log_inf p).
+  Lemma Psize_log_inf : forall p, Zpos (Pos.size p) = Z.succ (log_inf p).
   Proof.
-   induction p; simpl; now rewrite ?Zpos_succ_morphism, ?IHp.
+   induction p; simpl; now rewrite <- ?Z.succ_Zpos, ?IHp.
   Qed.
 
-  Lemma Zlog2_log_inf : forall p, Zlog2 (Zpos p) = log_inf p.
+  Lemma Zlog2_log_inf : forall p, Z.log2 (Zpos p) = log_inf p.
   Proof.
-   unfold Zlog2. destruct p; simpl; trivial; apply Psize_log_inf.
+   unfold Z.log2. destruct p; simpl; trivial; apply Psize_log_inf.
   Qed.
 
   Lemma Zlog2_up_log_sup : forall p, Z.log2_up (Zpos p) = log_sup p.
   Proof.
    induction p; simpl.
-   change (Zpos p~1) with (2*(Zpos p)+1).
-   rewrite Z.log2_up_succ_double, Zlog2_log_inf; try easy.
-   unfold Zsucc. now rewrite !(Zplus_comm _ 1), Zplus_assoc.
-   change (Zpos p~0) with (2*Zpos p).
-   now rewrite Z.log2_up_double, IHp.
-   reflexivity.
+   - change (Zpos p~1) with (2*(Zpos p)+1).
+     rewrite Z.log2_up_succ_double, Zlog2_log_inf; try easy.
+     unfold Z.succ. now rewrite !(Z.add_comm _ 1), Z.add_assoc.
+   - change (Zpos p~0) with (2*Zpos p).
+     now rewrite Z.log2_up_double, IHp.
+   - reflexivity.
   Qed.
 
   (** Then we give the specifications of [log_inf] and [log_sup]
diff --git a/theories/ZArith/vo.itarget b/theories/ZArith/vo.itarget
index 9605735dcd..767ba4f1b4 100644
--- a/theories/ZArith/vo.itarget
+++ b/theories/ZArith/vo.itarget
@@ -29,6 +29,5 @@ Zpower.vo
 Zpow_facts.vo
 Zsqrt_compat.vo
 Zwf.vo
-Zlog_def.vo
 Zeuclid.vo
 Zdigits_def.vo
\ No newline at end of file
-- 
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