(**************************************************************************)
-(* ___ *)
+(* ___ *)
(* ||M|| *)
(* ||A|| A project by Andrea Asperti *)
(* ||T|| *)
(* *)
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-set "baseuri" "cic:/matita/nat/nat".
-
include "higher_order_defs/functions.ma".
-theorem esempio: \forall A,B,C:Prop.(A \to B \to C) \to (A \to B)
-\to A \to C.
-
-
-
inductive nat : Set \def
| O : nat
| S : nat \to nat.
+interpretation "Natural numbers" 'N = nat.
+
+default "natural numbers" cic:/matita/nat/nat/nat.ind.
+
+alias num (instance 0) = "natural number".
+
definition pred: nat \to nat \def
\lambda n:nat. match n with
[ O \Rightarrow O