New version of the library, a bit more structured.

[helm.git] / helm / matita / library / datatypes / bool.ma

diff --git a/helm/matita/library/datatypes/bool.ma b/helm/matita/library/datatypes/bool.ma
new file mode 100644 (file)
index 0000000..fdb376c
--- /dev/null
+++ b/helm/matita/library/datatypes/bool.ma
@@ -0,0 +1,45 @@
+(**************************************************************************)
+(*       ___                                                               *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
+(*      ||A||       E.Tassi, S.Zacchiroli                                 *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU Lesser General Public License Version 2.1         *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/bool/".
+
+inductive bool : Set \def 
+  | true : bool
+  | false : bool.
+
+definition notb : bool \to bool \def
+\lambda b:bool. 
+ match b with 
+ [ true \Rightarrow false
+ | false \Rightarrow true ].
+
+definition andb : bool \to bool \to bool\def
+\lambda b1,b2:bool. 
+ match b1 with 
+ [ true \Rightarrow 
+       match b2 with [true \Rightarrow true | false \Rightarrow false]
+ | false \Rightarrow false ].
+
+definition orb : bool \to bool \to bool\def
+\lambda b1,b2:bool. 
+ match b1 with 
+ [ true \Rightarrow 
+       match b2 with [true \Rightarrow true | false \Rightarrow false]
+ | false \Rightarrow false ].
+
+definition if_then_else : bool \to Prop \to Prop \to Prop \def 
+\lambda b:bool.\lambda P,Q:Prop.
+match b with
+[ true \Rightarrow P
+| false  \Rightarrow Q].