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, 9 insertions, 9 deletions

diff --git a/theories/Init/Peano.v b/theories/Init/Peano.v
index c3716eaa6..cbb960ceb 100644
--- a/theories/Init/Peano.v
+++ b/theories/Init/Peano.v
@@ -115,8 +115,8 @@ Qed.
 
 (** Standard associated names *)
 
-Notation plus_0_r_reverse := plus_n_O (only parsing).
-Notation plus_succ_r_reverse := plus_n_Sm (only parsing).
+Notation plus_0_r_reverse := plus_n_O (compat "8.2").
+Notation plus_succ_r_reverse := plus_n_Sm (compat "8.2").
 
 (** Multiplication *)
 
@@ -132,22 +132,22 @@ Hint Resolve (f_equal2 mult): core.
 
 Lemma mult_n_O : forall n:nat, 0 = n * 0.
 Proof.
-  induction n; simpl in |- *; auto.
+  induction n; simpl; auto.
 Qed.
 Hint Resolve mult_n_O: core.
 
 Lemma mult_n_Sm : forall n m:nat, n * m + n = n * S m.
 Proof.
-  intros; induction n as [| p H]; simpl in |- *; auto.
-  destruct H; rewrite <- plus_n_Sm; apply (f_equal S).
-  pattern m at 1 3 in |- *; elim m; simpl in |- *; auto.
+  intros; induction n as [| p H]; simpl; auto.
+  destruct H; rewrite <- plus_n_Sm; apply eq_S.
+  pattern m at 1 3; elim m; simpl; auto.
 Qed.
 Hint Resolve mult_n_Sm: core.
 
 (** Standard associated names *)
 
-Notation mult_0_r_reverse := mult_n_O (only parsing).
-Notation mult_succ_r_reverse := mult_n_Sm (only parsing).
+Notation mult_0_r_reverse := mult_n_O (compat "8.2").
+Notation mult_succ_r_reverse := mult_n_Sm (compat "8.2").
 
 (** Truncated subtraction: [m-n] is [0] if [n>=m] *)
 
@@ -219,7 +219,7 @@ Theorem nat_double_ind :
    (forall n m:nat, R n m -> R (S n) (S m)) -> forall n m:nat, R n m.
 Proof.
   induction n; auto.
-  destruct m as [| n0]; auto.
+  destruct m; auto.
 Qed.
 
 (** Maximum and minimum : definitions and specifications *)