Right inverses for partial differential operators on spaces of Whitney functions

For v is an element of R-n let K be a compact set in R-n containing a suitable smooth surface and such that the intersection {tv + x : t is an element of R} boolean AND K is a closed interval or a single point for all x is an element of K. We prove that every linear first order differential operator with constant coefficients in direction v on space of Whitney functions epsilon(K) admits a continuous linear right inverse.