theorem
  C is 1_Lattice & Top C = "\/"(the carrier of C, C)
proof
  set j = "\/"(the carrier of C, C);
A1: now
    let a;
A2: j [= j"\/"a by LATTICES:5;
A3: j"\/"a [= j by Th38;
    hence j"\/"a = j by A2,LATTICES:8;
    thus a"\/"j = j by A2,A3,LATTICES:8;
  end;
  then C is upper-bounded;
  hence thesis by A1,LATTICES:def 17;
end;
