diff options
Diffstat (limited to 'theories/Logic/Classical_Prop.v')
| -rw-r--r-- | theories/Logic/Classical_Prop.v | 11 |
1 files changed, 10 insertions, 1 deletions
diff --git a/theories/Logic/Classical_Prop.v b/theories/Logic/Classical_Prop.v index f8b0e65b..ce3e84a7 100644 --- a/theories/Logic/Classical_Prop.v +++ b/theories/Logic/Classical_Prop.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Classical_Prop.v 8642 2006-03-17 10:09:02Z notin $ i*) +(*i $Id: Classical_Prop.v 8892 2006-06-04 17:59:53Z herbelin $ i*) (** Classical Propositional Logic *) @@ -22,6 +22,15 @@ unfold not in |- *; intros; elim (classic p); auto. intro NP; elim (H NP). Qed. +(** Peirce's law states [forall P Q:Prop, ((P -> Q) -> P) -> P]. + Thanks to [forall P, False -> P], it is equivalent to the + following form *) + +Lemma Peirce : forall P:Prop, ((P -> False) -> P) -> P. +Proof. +intros P H; destruct (classic P); auto. +Qed. + Lemma not_imply_elim : forall P Q:Prop, ~ (P -> Q) -> P. Proof. intros; apply NNPP; red in |- *. |