(* similar remark apply here… *)

Lemma max_arity_fapply_app f (l1 l2: list term): (* => Syntax.v ? *)
max_arity_term (fapply f (l1++l2)) =
max (length (l1++l2))
(max (maxl (map (@max_arity_term _ _ _) l1))
(maxl (map (@max_arity_term _ _ _) l2))).