Definition Pred : Cobham :=
Rec Zero (Proj 2 0) (Proj 2 0) (Proj 1 0).
(* Eval vm_compute in (arity pred'). *)
Definition move_arg (n i j:nat) (e:Cobham) : Cobham :=
Comp n e (move_forward i j
(map (Proj n) (seq 0 n)) (Proj n 0)).
Definition dummies (n m : nat)(e : Cobham) : Cobham :=
Comp (n+m) e (map (Proj (n+m)) (seq 0 n)).

Lemma arity_dummies e n n' :
arity e = ok_arity n' ->
arity (dummies n' n e) = ok_arity (n + n').