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, 4 insertions, 4 deletions

diff --git a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
index 2c7884ac4..ce92f44d9 100644
--- a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
+++ b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
@@ -318,7 +318,7 @@ Program Instance mod_wd : Proper (eq==>eq==>eq) modulo.
 
 Theorem div_mod : forall a b, ~b==0 -> a == b*(div a b) + (modulo a b).
 Proof.
-intros a b. zify. intros. apply Z_div_mod_eq_full; auto.
+intros a b. zify. intros. apply Z.div_mod; auto.
 Qed.
 
 Theorem mod_bound_pos : forall a b, 0<=a -> 0<b ->
@@ -444,7 +444,7 @@ Qed.
 (** Recursion *)
 
 Definition recursion (A : Type) (a : A) (f : NN.t -> A -> A) (n : NN.t) :=
-  Nrect (fun _ => A) a (fun n a => f (NN.of_N n) a) (NN.to_N n).
+  N.peano_rect (fun _ => A) a (fun n a => f (NN.of_N n) a) (NN.to_N n).
 Arguments recursion [A] a f n.
 
 Instance recursion_wd (A : Type) (Aeq : relation A) :
@@ -457,7 +457,7 @@ unfold NN.to_N.
 rewrite <- Exx'; clear x' Exx'.
 induction (Z.to_N [x]) using N.peano_ind.
 simpl; auto.
-rewrite 2 Nrect_step. now apply Eff'.
+rewrite 2 N.peano_rect_succ. now apply Eff'.
 Qed.
 
 Theorem recursion_0 :
@@ -474,7 +474,7 @@ Proof.
 unfold eq, recursion; intros A Aeq a f EAaa f_wd n.
 replace (to_N (succ n)) with (N.succ (to_N n)) by
  (zify; now rewrite <- Z2N.inj_succ by apply spec_pos).
-rewrite Nrect_step.
+rewrite N.peano_rect_succ.
 apply f_wd; auto.
 zify. now rewrite Z2N.id by apply spec_pos.
 fold (recursion a f n). apply recursion_wd; auto. red; auto.