(* similar remark apply here… *)

Lemma max_arity_make_comp n s h gN gS f:
max_arity_prog (rules h) ≤ maxar h →
(max_arity_prog (concat (map rules gN))) ≤ maxl (map maxar gN) →
(max_arity_prog (concat (map rules gS))) ≤ maxl (map maxar gS) →
max_arity_prog (rules (make_comp n s h gN gS f)) ≤ maxar (make_comp n s h gN gS f).