reserve L for Lattice,
  p,p1,q,q1,r,r1 for Element of L;
reserve x,y,z,X,Y,Z,X1,X2 for set;
reserve H,F for Filter of L;

theorem
  {p} is Filter of L implies L is upper-bounded
proof
  assume {p} is Filter of L;
  then reconsider F = {p} as Filter of L;
  take p;
  let q;
  p in F by TARSKI:def 1;
  then p"\/"q in F by Th10;
  hence thesis by TARSKI:def 1;
end;
