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

4 files changed, 9 insertions, 11 deletions

diff --git a/theories/FSets/FSetBridge.v b/theories/FSets/FSetBridge.v
index 25ce5577e..f0a588379 100644
--- a/theories/FSets/FSetBridge.v
+++ b/theories/FSets/FSetBridge.v
@@ -165,7 +165,7 @@ Module DepOfNodep (Import M: S) <: Sdep with Module E := M.E.
     case (for_all (fdec Pdec) s); unfold For_all in |- *; [ left | right ];
      intros.
     assert (compat_bool E.eq (fdec Pdec)); auto.
-    generalize (H0 H3 (refl_equal _) _ H2).
+    generalize (H0 H3 Logic.eq_refl _ H2).
     unfold fdec in |- *.
     case (Pdec x); intuition.
     inversion H4.
@@ -230,7 +230,7 @@ Module DepOfNodep (Import M: S) <: Sdep with Module E := M.E.
     unfold fdec in |- *; case (Pdec x); intuition.
       change ((fun x => negb (fdec Pdec x)) x = true) in |- *.
       apply (filter_2 (s:=s) (x:=x)); auto.
-    set (b := fdec Pdec x) in *; generalize (refl_equal b);
+    set (b := fdec Pdec x) in *; generalize (Logic.eq_refl b);
      pattern b at -1 in |- *; case b; unfold b in |- *;
      [ left | right ].
     elim (H4 x); intros _ B; apply B; auto with set.
diff --git a/theories/FSets/FSetEqProperties.v b/theories/FSets/FSetEqProperties.v
index 755bc7dd0..ac495c040 100644
--- a/theories/FSets/FSetEqProperties.v
+++ b/theories/FSets/FSetEqProperties.v
@@ -206,7 +206,7 @@ intros.
 generalize (@choose_1 s) (@choose_2 s).
 destruct (choose s);intros.
 exists e;auto with set.
-generalize (H1 (refl_equal None)); clear H1.
+generalize (H1 Logic.eq_refl); clear H1.
 intros; rewrite (is_empty_1 H1) in H; discriminate.
 Qed.
 
@@ -631,7 +631,7 @@ destruct (choose (filter f s)).
 intros H0 _; apply exists_1; auto.
 exists e; generalize (H0 e); rewrite filter_iff; auto.
 intros _ H0.
-rewrite (is_empty_1 (H0 (refl_equal None))) in H; auto; discriminate.
+rewrite (is_empty_1 (H0 Logic.eq_refl)) in H; auto; discriminate.
 Qed.
 
 Lemma partition_filter_1:
@@ -881,8 +881,8 @@ generalize (@add_filter_1 f Hf s0 (add x s0) x) (@add_filter_2 f Hf s0 (add x s0
 assert (~ In x (filter f s0)).
  intro H1; rewrite (mem_1 (filter_1 Hf H1)) in H; discriminate H.
 case (f x); simpl; intros.
-rewrite (MP.cardinal_2 H1 (H2 (refl_equal true) (MP.Add_add s0 x))); auto.
-rewrite <- (MP.Equal_cardinal (H3 (refl_equal false) (MP.Add_add s0 x))); auto.
+rewrite (MP.cardinal_2 H1 (H2 Logic.eq_refl (MP.Add_add s0 x))); auto.
+rewrite <- (MP.Equal_cardinal (H3 Logic.eq_refl (MP.Add_add s0 x))); auto.
 intros; rewrite fold_empty;auto.
 rewrite MP.cardinal_1; auto.
 unfold Empty; intros.
diff --git a/theories/FSets/FSetFacts.v b/theories/FSets/FSetFacts.v
index f473b3342..b240ede4d 100644
--- a/theories/FSets/FSetFacts.v
+++ b/theories/FSets/FSetFacts.v
@@ -315,11 +315,11 @@ symmetry.
 rewrite <- H1; intros a Ha.
 rewrite <- (H a) in Ha.
 destruct H0 as (_,H0).
-exact (H0 (refl_equal true) _ Ha).
+exact (H0 Logic.eq_refl _ Ha).
 rewrite <- H0; intros a Ha.
 rewrite (H a) in Ha.
 destruct H1 as (_,H1).
-exact (H1 (refl_equal true) _ Ha).
+exact (H1 Logic.eq_refl _ Ha).
 Qed.
 
 Instance Empty_m : Proper (Equal ==> iff) Empty.
@@ -489,5 +489,3 @@ End WFacts_fun.
 
 Module WFacts (M:WS) := WFacts_fun M.E M.
 Module Facts := WFacts.
-
-
diff --git a/theories/FSets/FSetProperties.v b/theories/FSets/FSetProperties.v
index 8651a96f7..25b042ca9 100644
--- a/theories/FSets/FSetProperties.v
+++ b/theories/FSets/FSetProperties.v
@@ -823,7 +823,7 @@ Module WProperties_fun (Import E : DecidableType)(M : WSfun E).
   rewrite (inter_subset_equal H).
   generalize (@cardinal_inv_1 (diff s' s)).
   destruct (cardinal (diff s' s)).
-  intro H2; destruct (H2 (refl_equal _) x).
+  intro H2; destruct (H2 Logic.eq_refl x).
   set_iff; auto.
   intros _.
   change (0 + cardinal s < S n + cardinal s).