It is shown that for pairs of electron densities (ρagr and TMPH1165math001) obtained from mixing orbital densities in a spin-compensated four-electron system, the kinetic energy functional of the non-interacting reference system (Ts[ρ]) satisfies the general inequality TMPH1165math002. This condition is discussed in the context of the gradient expansion approximation to Ts[ρ] and its possible use in variational orbital-free calculations. In particular, it is shown that the second-order term of the analytic form given by von Weizsaumlcker violates this inequality for the considered pairs.