  In this work we present a general theorem concerning chain rules for linear
openness of set-valued mappings acting between metric spaces. As particular
cases, we obtain classical and also some new results in this field of research,
including the celebrated Lyusternik-Graves Theorem. The applications deal with
the study of the well-posedness of the solution mappings associated to
parametric variational systems. Sharp estimates for the involved regularity
moduli are given.
