reserve X for set,
  x,y,z for Element of BooleLatt X,
  s for set;
reserve y for Element of BooleLatt X;

theorem Th3:
  BooleLatt X is lower-bounded & Bottom BooleLatt X = {}
proof {} c= X;
  then reconsider x = {} as Element of BooleLatt X by Def1;
A1: x"/\"y = x;
A2: y"/\"x = x;
  thus BooleLatt X is lower-bounded
  proof
    take x;
    thus thesis;
  end;
  hence thesis by A1,A2,LATTICES:def 16;
end;
