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11 (*        v         GNU General Public License Version 2                  *)
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14
15 include "nat/nat.ma".
16
17 definition f :=
18  λs1,s2:nat.
19    let rec aux (s3:nat → nat) (x:nat) on x :=
20      match x with
21      [ O ⇒ s3 (S x)
22      | S m ⇒ aux2 s3 m] 
23     and aux2 (s3:nat → nat) (x:nat) on x :=
24      match x with
25      [ O ⇒ s3 x
26      | S m ⇒ aux s3 m]
27     in aux.
28     
29 definition g :=
30  λw.