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, 8 insertions, 8 deletions

diff --git a/theories/MSets/MSetEqProperties.v b/theories/MSets/MSetEqProperties.v
index 2e7da404e..4f0d93fb9 100644
--- a/theories/MSets/MSetEqProperties.v
+++ b/theories/MSets/MSetEqProperties.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 (eq_refl None)); 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 (eq_refl None))) in H; auto; discriminate.
 Qed.
 
 Lemma partition_filter_1:
@@ -879,8 +879,8 @@ 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 (eq_refl true) (MP.Add_add s0 x))); auto.
+rewrite <- (MP.Equal_cardinal (H3 (eq_refl false) (MP.Add_add s0 x))); auto.
 intros; rewrite fold_empty;auto.
 rewrite MP.cardinal_1; auto.
 unfold Empty; intros.
diff --git a/theories/MSets/MSetPositive.v b/theories/MSets/MSetPositive.v
index e83ac27d6..e500602fd 100644
--- a/theories/MSets/MSetPositive.v
+++ b/theories/MSets/MSetPositive.v
@@ -36,8 +36,8 @@ Local Unset Boolean Equality Schemes.
 Module PositiveOrderedTypeBits <: UsualOrderedType.
   Definition t:=positive.
   Include HasUsualEq <+ UsualIsEq.
-  Definition eqb := Peqb.
-  Definition eqb_eq := Peqb_eq.
+  Definition eqb := Pos.eqb.
+  Definition eqb_eq := Pos.eqb_eq.
   Include HasEqBool2Dec.
 
   Fixpoint bits_lt (p q:positive) : Prop :=
diff --git a/theories/MSets/MSetProperties.v b/theories/MSets/MSetProperties.v
index 0f24d76a9..396067b57 100644
--- a/theories/MSets/MSetProperties.v
+++ b/theories/MSets/MSetProperties.v
@@ -831,7 +831,7 @@ Module WPropertiesOn (Import E : DecidableType)(M : WSetsOn 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 (eq_refl _) x).
   set_iff; auto.
   intros _.
   change (0 + cardinal s < S n + cardinal s).
diff --git a/theories/MSets/MSetRBT.v b/theories/MSets/MSetRBT.v
index b53c03920..35d8245a7 100644
--- a/theories/MSets/MSetRBT.v
+++ b/theories/MSets/MSetRBT.v
@@ -282,7 +282,7 @@ Fixpoint treeify_aux (pred:bool)(n: positive) : treeify_t :=
 
 Fixpoint plength (l:list elt) := match l with
  | nil => 1%positive
- | _::l => Psucc (plength l)
+ | _::l => Pos.succ (plength l)
 end.
 
 Definition treeify (l:list elt) :=