diff options
Diffstat (limited to 'theories/Logic/Classical_Prop.v')
| -rw-r--r-- | theories/Logic/Classical_Prop.v | 14 |
1 files changed, 8 insertions, 6 deletions
diff --git a/theories/Logic/Classical_Prop.v b/theories/Logic/Classical_Prop.v index c51050d5..1f6b05f5 100644 --- a/theories/Logic/Classical_Prop.v +++ b/theories/Logic/Classical_Prop.v @@ -1,12 +1,14 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011 *) +(* <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 *) (************************************************************************) -(*i $Id: Classical_Prop.v 14641 2011-11-06 11:59:10Z herbelin $ i*) +(* File created for Coq V5.10.14b, Oct 1995 *) +(* Classical tactics for proving disjunctions by Julien Narboux, Jul 2005 *) +(* Inferred proof-irrelevance and eq_rect_eq added by Hugo Herbelin, Mar 2006 *) (** Classical Propositional Logic *) @@ -18,7 +20,7 @@ Axiom classic : forall P:Prop, P \/ ~ P. Lemma NNPP : forall p:Prop, ~ ~ p -> p. Proof. -unfold not in |- *; intros; elim (classic p); auto. +unfold not; intros; elim (classic p); auto. intro NP; elim (H NP). Qed. @@ -33,7 +35,7 @@ Qed. Lemma not_imply_elim : forall P Q:Prop, ~ (P -> Q) -> P. Proof. -intros; apply NNPP; red in |- *. +intros; apply NNPP; red. intro; apply H; intro; absurd P; trivial. Qed. @@ -66,7 +68,7 @@ Qed. Lemma or_not_and : forall P Q:Prop, ~ P \/ ~ Q -> ~ (P /\ Q). Proof. -simple induction 1; red in |- *; simple induction 2; auto. +simple induction 1; red; simple induction 2; auto. Qed. Lemma not_or_and : forall P Q:Prop, ~ (P \/ Q) -> ~ P /\ ~ Q. @@ -110,7 +112,7 @@ Module Eq_rect_eq. Lemma eq_rect_eq : forall (U:Type) (p:U) (Q:U -> Type) (x:Q p) (h:p = p), x = eq_rect p Q x p h. Proof. -intros; rewrite proof_irrelevance with (p1:=h) (p2:=refl_equal p); reflexivity. +intros; rewrite proof_irrelevance with (p1:=h) (p2:=eq_refl p); reflexivity. Qed. End Eq_rect_eq. |