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

1 files changed, 12 insertions, 12 deletions

diff --git a/theories/Logic/Eqdep_dec.v b/theories/Logic/Eqdep_dec.v
index 59088aa75..2ed5d428c 100644
--- a/theories/Logic/Eqdep_dec.v
+++ b/theories/Logic/Eqdep_dec.v
@@ -9,7 +9,7 @@
 (* Created by Bruno Barras, Jan 1998 *)
 (* Made a module instance for EqdepFacts by Hugo Herbelin, Mar 2006 *)
 
-(** We prove that there is only one proof of [x=x], i.e [refl_equal x].
+(** We prove that there is only one proof of [x=x], i.e [eq_refl x].
     This holds if the equality upon the set of [x] is decidable.
     A corollary of this theorem is the equality of the right projections
     of two equal dependent pairs.
@@ -43,7 +43,7 @@ Section EqdepDec.
   Let comp (x y y':A) (eq1:x = y) (eq2:x = y') : y = y' :=
     eq_ind _ (fun a => a = y') eq2 _ eq1.
 
-  Remark trans_sym_eq : forall (x y:A) (u:x = y), comp u u = refl_equal y.
+  Remark trans_sym_eq : forall (x y:A) (u:x = y), comp u u = eq_refl y.
   Proof.
     intros.
     case u; trivial.
@@ -69,7 +69,7 @@ Section EqdepDec.
   Qed.
 
 
-  Let nu_inv (y:A) (v:x = y) : x = y := comp (nu (refl_equal x)) v.
+  Let nu_inv (y:A) (v:x = y) : x = y := comp (nu (eq_refl x)) v.
 
 
   Remark nu_left_inv : forall (y:A) (u:x = y), nu_inv (nu u) = u.
@@ -90,10 +90,10 @@ Section EqdepDec.
   Qed.
 
   Theorem K_dec :
-    forall P:x = x -> Prop, P (refl_equal x) -> forall p:x = x, P p.
+    forall P:x = x -> Prop, P (eq_refl x) -> forall p:x = x, P p.
   Proof.
     intros.
-    elim eq_proofs_unicity with x (refl_equal x) p.
+    elim eq_proofs_unicity with x (eq_refl x) p.
     trivial.
   Qed.
 
@@ -135,7 +135,7 @@ Require Import EqdepFacts.
 Theorem K_dec_type :
   forall A:Type,
     (forall x y:A, {x = y} + {x <> y}) ->
-    forall (x:A) (P:x = x -> Prop), P (refl_equal x) -> forall p:x = x, P p.
+    forall (x:A) (P:x = x -> Prop), P (eq_refl x) -> forall p:x = x, P p.
 Proof.
   intros A eq_dec x P H p.
   elim p using K_dec; intros.
@@ -146,7 +146,7 @@ Qed.
 Theorem K_dec_set :
   forall A:Set,
     (forall x y:A, {x = y} + {x <> y}) ->
-    forall (x:A) (P:x = x -> Prop), P (refl_equal x) -> forall p:x = x, P p.
+    forall (x:A) (P:x = x -> Prop), P (eq_refl x) -> forall p:x = x, P p.
 Proof fun A => K_dec_type (A:=A).
 
 (** We deduce the [eq_rect_eq] axiom for (decidable) types *)
@@ -212,13 +212,13 @@ Module DecidableEqDep (M:DecidableType).
 
   (** Uniqueness of Reflexive Identity Proofs *)
 
-  Lemma UIP_refl : forall (x:U) (p:x = x), p = refl_equal x.
+  Lemma UIP_refl : forall (x:U) (p:x = x), p = eq_refl x.
   Proof (UIP__UIP_refl U UIP).
 
   (** Streicher's axiom K *)
 
   Lemma Streicher_K :
-    forall (x:U) (P:x = x -> Prop), P (refl_equal x) -> forall p:x = x, P p.
+    forall (x:U) (P:x = x -> Prop), P (eq_refl x) -> forall p:x = x, P p.
   Proof (K_dec_type eq_dec).
 
   (** Injectivity of equality on dependent pairs in [Type] *)
@@ -281,13 +281,13 @@ Module DecidableEqDepSet (M:DecidableSet).
 
   (** Uniqueness of Reflexive Identity Proofs *)
 
-  Lemma UIP_refl : forall (x:U) (p:x = x), p = refl_equal x.
+  Lemma UIP_refl : forall (x:U) (p:x = x), p = eq_refl x.
   Proof N.UIP_refl.
 
   (** Streicher's axiom K *)
 
   Lemma Streicher_K :
-    forall (x:U) (P:x = x -> Prop), P (refl_equal x) -> forall p:x = x, P p.
+    forall (x:U) (P:x = x -> Prop), P (eq_refl x) -> forall p:x = x, P p.
   Proof N.Streicher_K.
 
   (** Proof-irrelevance on subsets of decidable sets *)
@@ -301,7 +301,7 @@ Module DecidableEqDepSet (M:DecidableSet).
 
   Lemma inj_pair2 :
     forall (P:U -> Type) (p:U) (x y:P p),
-      existS P p x = existS P p y -> x = y.
+      existT P p x = existT P p y -> x = y.
   Proof eq_dep_eq__inj_pair2 U N.eq_dep_eq.
 
   (** Injectivity of equality on dependent pairs with second component