--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "nat/nat.ma".
+
+definition f :=
+ λs1,s2:nat.
+ let rec aux (s3:nat → nat) (x:nat) on x :=
+ match x with
+ [ O ⇒ s3 (S x)
+ | S m ⇒ aux2 s3 m]
+ and aux2 (s3:nat → nat) (x:nat) on x :=
+ match x with
+ [ O ⇒ s3 x
+ | S m ⇒ aux s3 m]
+ in aux.
+
+definition g :=
+ λw.
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