diff options
| author |  Enrico Tassi <gareuselesinge@debian.org> | 2015-01-25 14:42:51 +0100 |
|---|---|---|
| committer | Enrico Tassi <gareuselesinge@debian.org> | 2015-01-25 14:42:51 +0100 |
| commit | 7cfc4e5146be5666419451bdd516f1f3f264d24a (patch) | |
| tree | e4197645da03dc3c7cc84e434cc31d0a0cca7056 /theories/ZArith/Wf_Z.v | |
| parent | 420f78b2caeaaddc6fe484565b2d0e49c66888e5 (diff) | |
Imported Upstream version 8.5~beta1+dfsg
Diffstat (limited to 'theories/ZArith/Wf_Z.v')
| -rw-r--r-- | theories/ZArith/Wf_Z.v | 10 |
1 files changed, 4 insertions, 6 deletions
diff --git a/theories/ZArith/Wf_Z.v b/theories/ZArith/Wf_Z.v index 5350f86d..09909bdb 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 1999-2014 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -151,9 +151,7 @@ Section Efficient_Rec. forall P:Z -> Prop, (forall x:Z, (forall y:Z, 0 <= y < x -> P y) -> 0 <= x -> P x) -> forall x:Z, 0 <= x -> P x. - Proof. - exact Zlt_0_rec. - Qed. + Proof. intros; now apply Zlt_0_rec. Qed. (** Obsolete version of [Z.lt] induction principle on non-negative numbers *) @@ -170,7 +168,7 @@ Section Efficient_Rec. (forall x:Z, (forall y:Z, 0 <= y < x -> P y) -> P x) -> forall x:Z, 0 <= x -> P x. Proof. - exact Z_lt_rec. + intros; now apply Z_lt_rec. Qed. (** An even more general induction principle using [Z.lt]. *) @@ -196,7 +194,7 @@ Section Efficient_Rec. (forall x:Z, (forall y:Z, z <= y < x -> P y) -> z <= x -> P x) -> forall x:Z, z <= x -> P x. Proof. - exact Zlt_lower_bound_rec. + intros; now apply Zlt_lower_bound_rec with z. Qed. End Efficient_Rec. |