  The classical Juzvinski\u{i} Addition Theorem states that the entropy of an
automorphism of a compact group decomposes along invariant subgroups. Thomas
generalized the theorem to a skew-product setting. Using L. Bowen's f-invariant
we prove the addition theorem for actions of finitely generated free groups on
skew-products with compact totally disconnected groups or compact Lie groups
(correcting an error from [Bo10c]) and discuss examples.
