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/plugins/setoid_ring/RealField.v b/plugins/setoid_ring/RealField.v
index 56473adb9c..14c4270f9a 100644
--- a/plugins/setoid_ring/RealField.v
+++ b/plugins/setoid_ring/RealField.v
@@ -111,19 +111,19 @@ Proof.
   intros n0 H' m; rewrite H'; auto with real.
 Qed.
 
-Lemma R_power_theory : power_theory 1%R Rmult (eq (A:=R))  nat_of_N pow.
+Lemma R_power_theory : power_theory 1%R Rmult (@eq R) N.to_nat pow.
 Proof.
  constructor. destruct n. reflexivity.
- simpl. induction p;simpl.
- rewrite ZL6. rewrite Rdef_pow_add;rewrite IHp. reflexivity.
- unfold nat_of_P;simpl;rewrite ZL6;rewrite Rdef_pow_add;rewrite IHp;trivial.
- rewrite Rmult_comm;apply Rmult_1_l.
+ simpl. induction p.
+ - rewrite Pos2Nat.inj_xI. simpl. now rewrite plus_0_r, Rdef_pow_add, IHp.
+ - rewrite Pos2Nat.inj_xO. simpl. now rewrite plus_0_r, Rdef_pow_add, IHp.
+ - simpl. rewrite Rmult_comm;apply Rmult_1_l.
 Qed.
 
 Ltac Rpow_tac t :=
   match isnatcst t with
   | false => constr:(InitialRing.NotConstant)
-  | _ => constr:(N_of_nat t)
+  | _ => constr:(N.of_nat t)
   end.
 
 Add Field RField : Rfield