(* similar remark apply here… *)

Lemma max_arity_make_rec n s g h0 h1 f:
max_arity_prog (rules g) ≤ maxar g →
max_arity_prog (rules h0) ≤ maxar h0 →
max_arity_prog (rules h1) ≤ maxar h1 →
max_arity_prog (rules (make_rec (S n) s g h0 h1 f)) ≤
maxar (make_rec (S n) s g h0 h1 f).