  Unbroken continuous translational invariance is often taken as a basic
assumption in discussions of spontaneous symmetry breaking (SSB), which singles
out SSB of translational invariance itself as an exceptional case. We present a
framework which allows us to treat translational invariance on the same footing
as other symmetries. It is shown that existing theorems on SSB can be
straightforwardly extended to this general case. As a concrete application, we
analyze the Nambu-Goldstone modes in a (ferromagnetic) supersolid. We prove on
the ground of the general theorems that the Bogoliubov mode stemming from a
spontaneously broken internal U(1) symmetry and the longitudinal phonon due to
a crystalline order are distinct physical modes.
