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) \ Z = (X \ (Y "\/" Z)) "\/" (Y \ (X "\/" Z))
proof
  thus (X \+\ Y) \ Z = (X \ Y \ Z) "\/" (Y \ X \ Z) by LATTICES:def 11
    .= (X \ (Y "\/" Z)) "\/" (Y \ X \ Z) by Th45
    .= (X \ (Y "\/" Z)) "\/" (Y \ (X "\/" Z)) by Th45;
end;
