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 Th64:
  X \+\ Y = (X "\/" Y) \ (X "/\" Y)
proof
  thus X \+\ Y = (X \ X "/\" Y) "\/" (Y \ X) by Th33
    .= (X \ X "/\" Y) "\/" (Y \ X "/\" Y) by Th33
    .= (X "\/" Y) \ (X "/\" Y) by LATTICES:def 11;
end;
