theorem Th37:
  X \ (Y \ Z) = (X \ Y) "\/" (X "/\" Z)
proof
  X \ (Y \ Z) = X "/\" (Y`"\/" Z``) by LATTICES:23
    .= X "/\" (Y`"\/" Z)
    .= (X "/\" Y`) "\/" (X "/\" Z) by LATTICES:def 11;
  hence thesis;
end;
