Lemma HORec_nonexpansive {A} `{ageable A} : forall B (F : pred A -> (B -> pred A) -> B -> pred A) (HF1 : forall X, HOcontractive (F X)) (HF2 : forall R a, nonexpansive (fun X => F X R a)), forall a, nonexpansive (fun X => HORec (F X) a).