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 Th42:
  X \ (Y "/\" Z) = (X \ Y) "\/" (X \ Z)
proof
  thus X \ (Y "/\" Z) = X "/\" (Y` "\/" Z`) by LATTICES:23
    .= (X \ Y) "\/" (X \ Z) by LATTICES:def 11;
end;
