diff options
Diffstat (limited to 'theories/Logic/Classical_Pred_Type.v')
| -rw-r--r-- | theories/Logic/Classical_Pred_Type.v | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/Logic/Classical_Pred_Type.v b/theories/Logic/Classical_Pred_Type.v index 9d57fe88..7e1a4096 100644 --- a/theories/Logic/Classical_Pred_Type.v +++ b/theories/Logic/Classical_Pred_Type.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 *) @@ -42,7 +42,7 @@ Qed. Lemma not_ex_all_not : forall P:U -> Prop, ~ (exists n : U, P n) -> forall n:U, ~ P n. Proof. (* Intuitionistic *) -unfold not in |- *; intros P notex n abs. +unfold not; intros P notex n abs. apply notex. exists n; trivial. Qed. @@ -52,20 +52,20 @@ Lemma not_ex_not_all : Proof. intros P H n. apply NNPP. -red in |- *; intro K; apply H; exists n; trivial. +red; intro K; apply H; exists n; trivial. Qed. Lemma ex_not_not_all : forall P:U -> Prop, (exists n : U, ~ P n) -> ~ (forall n:U, P n). Proof. (* Intuitionistic *) -unfold not in |- *; intros P exnot allP. +unfold not; intros P exnot allP. elim exnot; auto. Qed. Lemma all_not_not_ex : forall P:U -> Prop, (forall n:U, ~ P n) -> ~ (exists n : U, P n). Proof. (* Intuitionistic *) -unfold not in |- *; intros P allnot exP; elim exP; intros n p. +unfold not; intros P allnot exP; elim exP; intros n p. apply allnot with n; auto. Qed. |