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 Th15:
  q in <.p.) iff p [= q
proof
  q in <.p.) iff ex r st q = r & p [= r;
  hence thesis;
end;
