
theorem Th26:
  for X,x be set holds x is Element of BoolePoset X iff x c= X
proof
  let X,x be set;
  LattPOSet BooleLatt X = RelStr(#the carrier of BooleLatt X, LattRel (
    BooleLatt X)#) by LATTICE3:def 2;
  then
A1: the carrier of BoolePoset X = the carrier of BooleLatt X by YELLOW_1:def 2
    .= bool X by LATTICE3:def 1;
  hence x is Element of BoolePoset X implies x c= X;
  thus thesis by A1;
end;
