ZArith + other : favor the use of modern names instead of compat notations

 - For instance, refl_equal --> eq_refl
 - Npos, Zpos, Zneg now admit more uniform qualified aliases
   N.pos, Z.pos, Z.neg.
 - A new module BinInt.Pos2Z with results about injections from
   positive to Z
 - A result about Z.pow pushed in the generic layer
 - Zmult_le_compat_{r,l} --> Z.mul_le_mono_nonneg_{r,l}
 - Using tactic Z.le_elim instead of Zle_lt_or_eq
 - Some cleanup in ring, field, micromega
   (use of "Equivalence", "Proper" ...)
 - Some adaptions in QArith (for instance changed Qpower.Qpower_decomp)
 - In ZMake and ZMake, functor parameters are now named NN and ZZ
   instead of N and Z for avoiding confusions

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15515 85f007b7-540e-0410-9357-904b9bb8a0f7

2 files changed, 14 insertions, 14 deletions

diff --git a/test-suite/micromega/example.v b/test-suite/micromega/example.v
index f5a953566..4a1231b35 100644
--- a/test-suite/micromega/example.v
+++ b/test-suite/micromega/example.v
@@ -77,13 +77,13 @@ Definition rbound2 (C:Z -> Z -> Z) : Prop :=
 
 Lemma bounded_drift : forall s t p q C D, s <= t /\ correct p t  /\ correct q t /\
   rbound1 C /\ rbound2 C /\ rbound1 D /\ rbound2 D  ->
-  Zabs (C p t - D q t) <= Zabs (C p s - D q s) + 2 * rho * (t- s).
+  Z.abs (C p t - D q t) <= Z.abs (C p s - D q s) + 2 * rho * (t- s).
 Proof.
   intros.
-  generalize (Zabs_eq (C p t - D q t)).
-  generalize (Zabs_non_eq (C p t - D q t)).
-  generalize (Zabs_eq (C p s -D q s)).
-  generalize (Zabs_non_eq (C p s - D q s)).
+  generalize (Z.abs_eq (C p t - D q t)).
+  generalize (Z.abs_neq (C p t - D q t)).
+  generalize (Z.abs_eq (C p s -D q s)).
+  generalize (Z.abs_neq (C p s - D q s)).
   unfold rbound2 in H.
   unfold rbound1 in H.
   intuition.
diff --git a/test-suite/micromega/square.v b/test-suite/micromega/square.v
index 4c00ffe4a..6fa547358 100644
--- a/test-suite/micromega/square.v
+++ b/test-suite/micromega/square.v
@@ -9,17 +9,17 @@
 Require Import ZArith Zwf Psatz QArith.
 Open Scope Z_scope.
 
-Lemma Zabs_square : forall x,  (Zabs  x)^2 = x^2.
+Lemma Z.abs_square : forall x,  (Z.abs  x)^2 = x^2.
 Proof.
  intros ; case (Zabs_dec x) ; intros ; psatz Z 2.
 Qed.
-Hint Resolve Zabs_pos Zabs_square.
+Hint Resolve Z.abs_nonneg Z.abs_square.
 
 Lemma integer_statement :  ~exists n, exists p, n^2 = 2*p^2 /\ n <> 0.
 Proof.
-intros [n [p [Heq Hnz]]]; pose (n' := Zabs n); pose (p':=Zabs p).
-assert (facts : 0 <= Zabs n /\ 0 <= Zabs p /\ Zabs n^2=n^2
-         /\ Zabs p^2 = p^2) by auto.
+intros [n [p [Heq Hnz]]]; pose (n' := Z.abs n); pose (p':=Z.abs p).
+assert (facts : 0 <= Z.abs n /\ 0 <= Z.abs p /\ Z.abs n^2=n^2
+         /\ Z.abs p^2 = p^2) by auto.
 assert (H : (0 < n' /\ 0 <= p' /\ n' ^2 = 2* p' ^2)) by
   (destruct facts as [Hf1 [Hf2 [Hf3 Hf4]]]; unfold n', p' ; psatz Z 2).
 generalize p' H; elim n' using (well_founded_ind (Zwf_well_founded 0)); clear.
@@ -35,7 +35,7 @@ Lemma QnumZpower : forall x : Q, Qnum (x ^ 2)%Q = ((Qnum x) ^ 2) %Z.
 Proof.
   intros.
   destruct x.
-  cbv beta  iota zeta delta - [Zmult].
+  cbv beta  iota zeta delta - [Z.mul].
   ring.
 Qed.
 
@@ -45,15 +45,15 @@ Proof.
   intros.
   destruct x.
   simpl.
-  unfold Zpower_pos.
+  unfold Z.pow_pos.
   simpl.
-  rewrite Pmult_1_r.
+  rewrite Pos.mul_1_r.
   reflexivity.
 Qed.
 
 Theorem sqrt2_not_rational : ~exists x:Q, x^2==2#1.
 Proof.
- unfold Qeq; intros [x]; simpl (Qden (2#1)); rewrite Zmult_1_r.
+ unfold Qeq; intros [x]; simpl (Qden (2#1)); rewrite Z.mul_1_r.
  intros HQeq.
  assert (Heq : (Qnum x ^ 2 = 2 * ' Qden x ^ 2%Q)%Z) by
    (rewrite QnumZpower in HQeq ; rewrite QdenZpower in HQeq ; auto).