Definition Zero_e (n:nat) : Cobham :=
Comp n Zero nil.
Definition One_e (n:nat) : Cobham :=
Comp n (Comp 0 (Succ true) [Zero]) nil.
(** Def 12 of (Rose) *)
Definition App_e : Cobham :=
Rec (Proj 1 0)
(Comp 3 (Succ false) [Proj 3 1])
(Comp 3 (Succ true) [Proj 3 1])
(Comp 2 Smash [Comp 2 (Succ true) [Proj 2 0]; Comp 2 (Succ true) [Proj 2 1] ]).

Lemma arity_App : arity App_e = ok_arity 2.