Subsystem entropy for ℤd sofic shifts

We prove that any ℤd shift of finite type with positive topological entropy has a family of subsystems of finite type whose entropies are dense in the interval from zero to the entropy of the original shift. We show a similar result for ℤd sofic shifts, and also show every ℤd sofic shift can be covered by a ℤd shift of finite type arbitrarily close in entropy.