Section Fixpoints.
Variables (T : choiceType) (U : {fset T}).
Definition sub_fun (F : {fset T} -> {fset T}) (X : {set U}) : {set U} :=
fsub U (F [fsetval x in X]).
Variable (F : {fset T} -> {fset T}).
Hypothesis (F_mono : {homo F : X Y / X `<=` Y}).
Hypothesis (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}.