  It is shown that a strong system of vector fields on a fiber bundle in the
sense of [Modugno, M. Systems of connections and invariant lagrangians. In:
Differential geometric methods in theoretical physics, Proc. 15th Int. Conf.,
DGM, Clausthal/FRG 1986, 518-534 World Scientific Publishing Co. (1987)] is
induced from a principal fiber bundle if and only if each vertical vector field
of the system is complete.
