Can someone explain (or give a reference) why the Galois representation attached to a pdivisible group over the ring of integers of a padic ring is Crystalline?

This is shown in §6 of Fontaine's paper "Sur certains types de représentations padiques du groupe de Galois d'un corps local; construction d'un anneau de BarsottiTate", see the point i) after Theorem 6.2. The paper is available on jstor: http://www.jstor.org/pss/2007012 

