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 Th17:
  L is 0_Lattice implies <.L.) = <.Bottom L.)
proof
  assume L is 0_Lattice;
  then reconsider L9 = L as 0_Lattice;
  thus <.L.) c= <.Bottom L.)
  proof
    let x be object;
    assume x in <.L.);
    then reconsider x as Element of L9;
    Bottom L in <.Bottom L.) & x "/\" Bottom L9 = Bottom L9;
    hence thesis by Th8;
  end;
  thus thesis;
end;
