Reference for one-sided subshifts

A well known result in Symbolic Dynamics asserts that every two-sided subshift on a finite alphabet necessarily consists of all doubly infinite words not containing any finite word from a given set of "forbidden" words (Proposition 1.3.4, D. Lind and B. Marcus, An introduction to symbolic dynamics and coding, Cambridge Univ. Press, 1999). This result is also true for one-sided subshifts (essentially the same proof works) but after researching a lot, I cannot find a direct reference to it, namely one that refers explicitly to one-sided subshifts. Can anyone help me find such a reference?

• Negative answers are OK, such as "I'm a dynamic systems specialist and I am pretty sure no one published this result". – Ruy Aug 24 '16 at 12:23

Theorem 3.16. A subset $X \subseteq \Sigma_\mathcal A$ is a shift space if and only if $X = X_\mathcal F$ for some subset $\mathcal F \subseteq \Sigma^{fin}_\mathcal A$.