From: Andrea Asperti <andrea.asperti@unibo.it>
Date: Fri, 12 Mar 2010 12:23:31 +0000 (+0000)
Subject: New definition of negation
X-Git-Tag: make_still_working~3011
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=ee1df68d10351f30ea591ccc2173197d99e307cc;p=helm.git

New definition of negation
---

diff --git a/helm/software/matita/nlibrary/Plogic/connectives.ma b/helm/software/matita/nlibrary/Plogic/connectives.ma
index d840143e3..84bd36454 100644
--- a/helm/software/matita/nlibrary/Plogic/connectives.ma
+++ b/helm/software/matita/nlibrary/Plogic/connectives.ma
@@ -23,18 +23,27 @@ ninductive False: Prop ≝ .
 
 default "false" cic:/matita/basics/connectives/False.ind.
 
+(*
 ndefinition Not: Prop → Prop ≝
-λA. A → False.
+λA. A → False. *)
+
+ninductive Not (A:Prop): Prop ≝
+nmk: (A → False) → Not A.
+
+ncheck Not_ind.
 
 interpretation "logical not" 'not x = (Not x).
 
+ntheorem absurd : ∀ A:Prop. A → ¬A → False.
+#A; #H; #Hn; nelim Hn;/2/; nqed.
+
+(*
 ntheorem absurd : ∀ A,C:Prop. A → ¬A → C.
 #A; #C; #H; #Hn; nelim (Hn H).
-nqed.
+nqed. *)
 
 ntheorem not_to_not : ∀A,B:Prop. (A → B) → ¬B →¬A.
-/3/.
-nqed.
+/4/; nqed.
 
 ninductive And (A,B:Prop) : Prop ≝
     conj : A → B → And A B.