Section SetSubsetOrder.
Definition type (disp : unit) (T : finType) := {set T}.
Definition type_of (disp : unit) (T : finType) of phant T := type disp T.
Identity Coercion type_of_type_of : type_of >-> type.
Context {disp : unit} {T : finType}.
Local Notation "{ 'subset' T }" := (type_of disp (Phant T)).
Implicit Type (A B C : {subset T}).

Lemma le_def A B : A \subset B = (A :&: B == A).