  We prove some theorems about self-avoiding walks attached to an impenetrable
surface (i.e. positive walks) and subject to a force. Specifically we show the
force dependence of the free energy is identical when the force is applied at
the last vertex or at the top (confining) plane. We discuss the relevance of
this result to numerical results and to a recent result about convergence rates
when the walk is being pushed towards the surface.
