X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Flibrary%2Fdatatypes%2Fbool.ma;h=3292e6789610f6114c590be58d18c729a3bf92fe;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=a4667da30249730b98bc4f39c522dd824a180019;hpb=69dc6031c9e0574fa7a74ced74deeb7f9ec5695b;p=helm.git

diff --git a/helm/matita/library/datatypes/bool.ma b/helm/matita/library/datatypes/bool.ma
index a4667da30..3292e6789 100644
--- a/helm/matita/library/datatypes/bool.ma
+++ b/helm/matita/library/datatypes/bool.ma
@@ -19,9 +19,20 @@ include "logic/equality.ma".
 inductive bool : Set \def 
   | true : bool
   | false : bool.
-  
+
+theorem bool_elim: \forall P:bool \to Prop. \forall b:bool.
+  (b = true \to P true)
+  \to (b = false \to P false)
+  \to P b.
+  intros 2 (P b).
+  elim b;
+  [ apply H; reflexivity
+  | apply H1; reflexivity
+  ]
+qed.
+
 theorem not_eq_true_false : true \neq false.
-simplify.intro.
+unfold Not.intro.
 change with 
 match true with
 [ true \Rightarrow False
@@ -51,15 +62,21 @@ definition andb : bool \to bool \to bool\def
  [ true \Rightarrow b2
  | false \Rightarrow false ].
 
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "boolean and" 'and x y = (cic:/matita/datatypes/bool/andb.con x y).
+
 theorem andb_elim: \forall b1,b2:bool. \forall P:bool \to Prop.
 match b1 with
 [ true \Rightarrow P b2
-| false \Rightarrow P false] \to P (andb b1 b2).
+| false \Rightarrow P false] \to P (b1 \land b2).
 intros 3.elim b1.exact H. exact H.
 qed.
 
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "boolean and" 'and x y = (cic:/matita/datatypes/bool/andb.con x y).
+theorem andb_true_true: \forall b1,b2. (b1 \land b2) = true \to b1 = true.
+intro. elim b1.
+reflexivity.
+assumption.
+qed.
 
 definition orb : bool \to bool \to bool\def
 \lambda b1,b2:bool.