diff options
Diffstat (limited to 'theories/ZArith/Zeven.v')
| -rw-r--r-- | theories/ZArith/Zeven.v | 22 |
1 files changed, 11 insertions, 11 deletions
diff --git a/theories/ZArith/Zeven.v b/theories/ZArith/Zeven.v index f4d702b2..dd48e84f 100644 --- a/theories/ZArith/Zeven.v +++ b/theories/ZArith/Zeven.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -58,8 +58,8 @@ Proof (Zodd_equiv n). (** Boolean tests of parity (now in BinInt.Z) *) -Notation Zeven_bool := Z.even (only parsing). -Notation Zodd_bool := Z.odd (only parsing). +Notation Zeven_bool := Z.even (compat "8.3"). +Notation Zodd_bool := Z.odd (compat "8.3"). Lemma Zeven_bool_iff n : Z.even n = true <-> Zeven n. Proof. @@ -130,17 +130,17 @@ Qed. Hint Unfold Zeven Zodd: zarith. -Notation Zeven_bool_succ := Z.even_succ (only parsing). -Notation Zeven_bool_pred := Z.even_pred (only parsing). -Notation Zodd_bool_succ := Z.odd_succ (only parsing). -Notation Zodd_bool_pred := Z.odd_pred (only parsing). +Notation Zeven_bool_succ := Z.even_succ (compat "8.3"). +Notation Zeven_bool_pred := Z.even_pred (compat "8.3"). +Notation Zodd_bool_succ := Z.odd_succ (compat "8.3"). +Notation Zodd_bool_pred := Z.odd_pred (compat "8.3"). (******************************************************************) -(** * Definition of [Zquot2], [Zdiv2] and properties wrt [Zeven] +(** * Definition of [Z.quot2], [Z.div2] and properties wrt [Zeven] and [Zodd] *) -Notation Zdiv2 := Z.div2 (only parsing). -Notation Zquot2 := Z.quot2 (only parsing). +Notation Zdiv2 := Z.div2 (compat "8.3"). +Notation Zquot2 := Z.quot2 (compat "8.3"). (** Properties of [Z.div2] *) @@ -223,7 +223,7 @@ Lemma Zsplit2 n : {p : Z * Z | let (x1, x2) := p in n = x1 + x2 /\ (x1 = x2 \/ x2 = x1 + 1)}. Proof. destruct (Z_modulo_2 n) as [(y,Hy)|(y,Hy)]; - rewrite Z.mul_comm, <- Zplus_diag_eq_mult_2 in Hy. + rewrite <- Z.add_diag in Hy. - exists (y, y). split. assumption. now left. - exists (y, y + 1). split. now rewrite Z.add_assoc. now right. Qed. |