:- op(200, xfy, elt).
:- op(200, xfy, subset).
:- op(200, xfy, equal_set).
:- op(150,xfx,inter).
definition(A subset B <=> ! [X]:(X elt A => X elt B)).
definition(A equal_set B <=> A subset B & B subset A).
definition((X elt powerset(A))<=> X subset A).
definition(X elt  A inter B  <=>  X elt A  &  X elt B).