(**************************************************************************)
-(* ___ *)
+(* ___ *)
(* ||M|| *)
(* ||A|| A project by Andrea Asperti *)
(* ||T|| *)
(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/nat/nat".
-
include "higher_order_defs/functions.ma".
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
| (S p) \Rightarrow p ].
theorem pred_Sn : \forall n:nat.n=(pred (S n)).
- intros. reflexivity.
+ intros. simplify. reflexivity.
qed.
theorem injective_S : injective nat nat S.