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/Rtrigo_def.v b/theories/Reals/Rtrigo_def.v
index c64931353..9b6edab68 100644
--- a/theories/Reals/Rtrigo_def.v
+++ b/theories/Reals/Rtrigo_def.v
@@ -130,17 +130,17 @@ Proof.
   intro; cut (0 <= up (/ eps))%Z.
   intro; assert (H2 := IZN _ H1); elim H2; intros; exists (max x 1).
   split.
-  cut (0 < IZR (Z_of_nat x)).
-  intro; rewrite INR_IZR_INZ; apply Rle_lt_trans with (/ IZR (Z_of_nat x)).
-  apply Rmult_le_reg_l with (IZR (Z_of_nat x)).
+  cut (0 < IZR (Z.of_nat x)).
+  intro; rewrite INR_IZR_INZ; apply Rle_lt_trans with (/ IZR (Z.of_nat x)).
+  apply Rmult_le_reg_l with (IZR (Z.of_nat x)).
   assumption.
   rewrite <- Rinv_r_sym;
     [ idtac | red in |- *; intro; rewrite H5 in H4; elim (Rlt_irrefl _ H4) ].
-  apply Rmult_le_reg_l with (IZR (Z_of_nat (max x 1))).
-  apply Rlt_le_trans with (IZR (Z_of_nat x)).
+  apply Rmult_le_reg_l with (IZR (Z.of_nat (max x 1))).
+  apply Rlt_le_trans with (IZR (Z.of_nat x)).
   assumption.
   repeat rewrite <- INR_IZR_INZ; apply le_INR; apply le_max_l.
-  rewrite Rmult_1_r; rewrite (Rmult_comm (IZR (Z_of_nat (max x 1))));
+  rewrite Rmult_1_r; rewrite (Rmult_comm (IZR (Z.of_nat (max x 1))));
     rewrite Rmult_assoc; rewrite <- Rinv_l_sym.
   rewrite Rmult_1_r; repeat rewrite <- INR_IZR_INZ; apply le_INR;
     apply le_max_l.