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;
reserve L for 0_Lattice;
reserve X,Y,Z for Element of L;
reserve L for B_Lattice;
reserve X,Y,Z,V for Element of L;

theorem
  (X "\/" Y) \ Y = X \ Y
proof
  (X "\/" Y) \ Y = (X "/\" Y`) "\/" (Y "/\" Y`) by LATTICES:def 11
    .= (X "/\" Y`) "\/" Bottom L by LATTICES:20
    .= X "/\" Y`;
  hence thesis;
end;
