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 Th10:
  p in H implies p"\/"q in H & q"\/"p in H
proof
  p [= p"\/"q by LATTICES:5;
  hence thesis by Th9;
end;
