Definition dummies (n m : nat)(e : Cobham) : Cobham :=
  Comp (n+m) e (map (Proj (n+m)) (seq 0 n)).

(* Specifications: *)
Lemma arity_dummies e n n' : arity e = ok_arity n' -> arity (dummies n' n e) = ok_arity (n + n').
Lemma rec_bounded_dummies : forall e n m, rec_bounded' e -> rec_bounded' (dummies n m e).
Lemma dummies_correct e n m l: n <= length l -> Sem (dummies n m e) l = Sem e (firstn n l).