  Let (N,F) be an F-isocrystal, with associated Newton vector \nu in (Q^n)_+.
To any lattice M in N (an F-crystal) is associated its Hodge vector \mu(M) in
(Z^n)_+. By Mazur's inequality we have \mu(M)>= \nu. We show that, conversely,
for any \mu in (Z^n)_+ with \mu >= \nu, there exists a lattice M in N such that
\mu=\mu(M). We also give variants of this existence theorem for symplectic
  F-isocrystals, and for periodic lattice chains.
