End ImfsetTh.
Section PowerSetTheory.
Variable (K : choiceType).
Fact fpowerset_key : unit. Proof. exact: tt. Qed.
Definition fpowerset (A : {fset K}) : {fset {fset K}} :=
[fset[fpowerset_key] [fsetval y in Y : {set A}] | Y in powerset [set: A]].

(* Specifications: *)
Lemma fpowersetE A B : (B \in fpowerset A) = (B `<=` A).
Lemma fpowersetCE (X A B : {fset K}) :
(A \in fpowerset (X `\` B)) = (A `<=` X) && [disjoint A & B]%fset.
Lemma fpowerset0 : fpowerset fset0 = [fset fset0].
End PowerSetTheory.