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;

theorem
  p [= r implies p [= q"\/"r
proof
  assume p [= r;
  then
A1: p"\/"q [= r"\/"q by Th1;
  p [= p"\/"q by LATTICES:5;
  hence thesis by A1,LATTICES:7;
end;
