Definition qif (f : function) args := match f with
  | main => 2*(suml args)
  | plus => suml args
  | errF => suml args
  end.

(* Specifications: *)
Lemma qif_subterm : subterm qif.
Lemma qif_monotonic : monotonicity_qif qif.
Lemma qi_is_compatible : compatible_QI qic qif.