reserve x,y,Y,Z for set,
  L for LATTICE,
  l for Element of L;

theorem Th31:
  for L being RelStr, X being Subset of L holds chi(X, the carrier
  of L) is Function of L, BoolePoset {{}}
proof
  let L be RelStr, X be Subset of L;
  the carrier of BoolePoset {{}} = the carrier of InclPoset bool {{}} by
YELLOW_1:4
    .= bool {{}} by YELLOW_1:1
    .= {0,1} by CARD_1:49,ZFMISC_1:24;
  hence thesis;
end;
