Hypothesis (F_mono : {homo F : X Y / X `<=` Y}) (F_bound : {homo F : X / X `<=` U}).
Notation Fsub := (sub_fun F).
Notation iterF := (fun i => iter i F fset0).

Lemma Fsub_mono : {homo Fsub : X Y / X \subset Y}.
Hint Resolve Fsub_mono.