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]].

Lemma fpowersetE A B : (B \in fpowerset A) = (B `<=` A).