reserve L for Lattice;
reserve X,Y,Z,V for Element of L;
reserve L for D_Lattice;
reserve X,Y,Z for Element of L;

theorem
  (X "/\" Y) "\/" (X "/\" Z) = X implies X [= Y "\/" Z
proof
  assume (X "/\" Y) "\/" (X "/\" Z) = X;
  then X "/\" (Y "\/" Z) = X by LATTICES:def 11;
  hence thesis by LATTICES:4;
end;
