  Invariance properties of classes in the variational sequence suggested to
Krupka et al. the idea that there should exist a close correspondence between
the notions of variationality of a differential form and invariance of its
exterior derivative. It was shown by them that the invariance of a closed
Helmholtz form of a dynamical form is equivalent with local variationality of
the Lie derivative of the dynamical form, so that the latter is locally the
Euler--Lagrange form of a Lagrangian. We show that the corresponding local
system of Euler--Lagrange forms is variationally equivalent to a global
Euler--Lagrange form.
