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
  L is 1_Lattice implies {Top L} is Filter of L
proof
  assume L is 1_Lattice;
  then reconsider K = L as 1_Lattice;
  now
    let p,q be Element of K;
A1: p in {Top K} iff p = Top K by TARSKI:def 1;
    hence p in {Top K} & q in {Top K} implies p"/\"q in {Top K};
    assume p"/\"q in {Top K};
    then
A2: p"/\"q = Top K by TARSKI:def 1;
    p"/\"q [= p & q"/\" p [= q by LATTICES:6;
    hence p in {Top K} & q in {Top K} by A1,A2;
  end;
  hence thesis by Th8;
end;
