diff options
Diffstat (limited to 'theories/ZArith/Wf_Z.v')
| -rw-r--r-- | theories/ZArith/Wf_Z.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/ZArith/Wf_Z.v b/theories/ZArith/Wf_Z.v index bcccc126..3935e124 100644 --- a/theories/ZArith/Wf_Z.v +++ b/theories/ZArith/Wf_Z.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 *) @@ -39,7 +39,7 @@ Proof. Qed. Lemma Z_of_nat_complete_inf (x : Z) : - 0 <= x -> {n : nat | x = Z_of_nat n}. + 0 <= x -> {n : nat | x = Z.of_nat n}. Proof. intros H. exists (Z.to_nat x). symmetry. now apply Z2Nat.id. Qed. @@ -53,7 +53,7 @@ Qed. Lemma Z_of_nat_set : forall P:Z -> Set, - (forall n:nat, P (Z_of_nat n)) -> forall x:Z, 0 <= x -> P x. + (forall n:nat, P (Z.of_nat n)) -> forall x:Z, 0 <= x -> P x. Proof. intros P H x Hx. now destruct (Z_of_nat_complete_inf x Hx) as (n,->). Qed. @@ -129,7 +129,7 @@ Section Efficient_Rec. - now destruct Hz. Qed. - (** A more general induction principle on non-negative numbers using [Zlt]. *) + (** A more general induction principle on non-negative numbers using [Z.lt]. *) Lemma Zlt_0_rec : forall P:Z -> Type, @@ -155,7 +155,7 @@ Section Efficient_Rec. exact Zlt_0_rec. Qed. - (** Obsolete version of [Zlt] induction principle on non-negative numbers *) + (** Obsolete version of [Z.lt] induction principle on non-negative numbers *) Lemma Z_lt_rec : forall P:Z -> Type, @@ -173,7 +173,7 @@ Section Efficient_Rec. exact Z_lt_rec. Qed. - (** An even more general induction principle using [Zlt]. *) + (** An even more general induction principle using [Z.lt]. *) Lemma Zlt_lower_bound_rec : forall P:Z -> Type, forall z:Z, |