  We prove that if all roots of the discrete Wronskian with step 1 of a set of
quasi-exponentials with real bases are real, simple and differ by at least 1,
then the complex span of this set of quasi-exponentials has a basis consisting
of quasi-exponentials with real coefficients. This result generalizes the B.
and M.Shapiro conjecture about spaces of polynomials.
  The proof is based on the Bethe ansatz method for the XXX model.
