  A cardinal kappa is countably closed if mu^omega < kappa whenever mu < kappa.
  Assume that there is no inner model with a Woodin cardinal and that every set
has a sharp. Let K be the core model. Assume that kappa is a countably closed
cardinal and that alpha is a successor cardinal of K with kappa < alpha <
kappa^+. Then cf( alpha ) = kappa. In particular, K computes successors of
countably closed singular cardinals correctly.
  (The hypothesis of countable closure is not required; see "Weak covering
without countable closure", W. J. Mitchell and E. Schimmerling, Math. Res.
Lett., Vol. 2, No. 5, Sept. 1995.)
