reserve a for set;
reserve L for lower-bounded sup-Semilattice;
reserve x for Element of L;

theorem
  Rel2Map L is isomorphic
proof
  ex g being Function of MonSet L, InclPoset Aux L st
  g = (Rel2Map L)" & g is monotone
  proof
    reconsider g = Map2Rel L as Function of MonSet L, InclPoset Aux L;
    take g;
    thus thesis by Th32;
  end;
  hence thesis by WAYBEL_0:def 38;
end;
