% setops.ax Version 0.5
hof(set_member,definition,
    ! [A] : (member @ A) = (lambda [X:A, S:A->$o] : S @ X)).
hof(empty_set,definition,
    empty_set = (lambda [A] : lambda [X:A] : ($false))).
hof(set_union,definition,
    union = (lambda [A] : lambda [X:A->$o, Y:A->$o] : lambda [Z] :
        ((member @ A @ Z @ X) | (member @ A @ Z @ Y)) ) ).
hof(set_intersection,definition,
    inter = (lambda [A] : lambda [X:A->$o, Y:A->$o] : lambda [Z] :
        ((X @ Z) & (Y @ Z)) ) ).