theorem
  C is 0_Lattice & Bottom C = "\/"({},C)
proof
A1: now
    let a;
    {} is_less_than ("\/"({},C))"/\"a;
    then
A2: "\/"({},C) [= ("\/"({},C))"/\"a by Def21;
A3: ("\/"({},C))"/\"a [= "\/"({},C ) by LATTICES:6;
    hence ("\/"({},C))"/\"a = "\/"({},C) by A2,LATTICES:8;
    thus a"/\"("\/"({},C)) = "\/"({},C) by A2,A3,LATTICES:8;
  end;
  then C is lower-bounded;
  hence thesis by A1,LATTICES:def 16;
end;
