  We study horizontal semistable and horizontal de Rham representations of the
absolute Galois group of a certain smooth affinoid over a p-adic field. In
particular, we prove that a horizontal de Rham representation becomes
horizontal semistable after a finite extension of the base field. As an
application, we show that every de Rham local system on a smooth rigid analytic
variety becomes horizontal semistable etale locally around every classical
point. We also discuss potentially crystalline loci of de Rham local systems
and cohomologically potentially good reduction loci of smooth proper morphisms.
