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, 6 insertions, 6 deletions

diff --git a/theories/Reals/R_Ifp.v b/theories/Reals/R_Ifp.v
index 9e04a7daf..c089b648d 100644
--- a/theories/Reals/R_Ifp.v
+++ b/theories/Reals/R_Ifp.v
@@ -58,7 +58,7 @@ Proof.
       intros a b; rewrite b; clear a b; rewrite <- Z_R_minus;
         cut (up 0 = 1%Z).
   intro; rewrite H1;
-    rewrite (Rminus_diag_eq (IZR 1) (IZR 1) (refl_equal (IZR 1)));
+    rewrite (Rminus_diag_eq (IZR 1) (IZR 1) (eq_refl (IZR 1)));
       apply Ropp_0.
   elim (archimed 0); intros; clear H2; unfold Rgt in H1;
     rewrite (Rminus_0_r (IZR (up 0))) in H0; generalize (lt_O_IZR (up 0) H1);
@@ -130,16 +130,16 @@ Proof.
 Qed.
 
 (**********)
-Lemma Int_part_INR : forall n:nat, Int_part (INR n) = Z_of_nat n.
+Lemma Int_part_INR : forall n:nat, Int_part (INR n) = Z.of_nat n.
 Proof.
   intros n; unfold Int_part in |- *.
-  cut (up (INR n) = (Z_of_nat n + Z_of_nat 1)%Z).
+  cut (up (INR n) = (Z.of_nat n + Z.of_nat 1)%Z).
   intros H'; rewrite H'; simpl in |- *; ring.
-  apply sym_equal; apply tech_up; auto.
-  replace (Z_of_nat n + Z_of_nat 1)%Z with (Z_of_nat (S n)).
+  symmetry; apply tech_up; auto.
+  replace (Z.of_nat n + Z.of_nat 1)%Z with (Z.of_nat (S n)).
   repeat rewrite <- INR_IZR_INZ.
   apply lt_INR; auto.
-  rewrite Zplus_comm; rewrite <- Znat.inj_plus; simpl in |- *; auto.
+  rewrite Z.add_comm; rewrite <- Znat.Nat2Z.inj_add; simpl in |- *; auto.
   rewrite plus_IZR; simpl in |- *; auto with real.
   repeat rewrite <- INR_IZR_INZ; auto with real.
 Qed.