prove that a language is context free given a regular language
Let $\phi(R) \subseteq 0^*$ result from $R$ by substituting $0$ for $1$. Alternatively, $\phi(R) = \{ 0^{|w|} : w \in R \}$. The previous description makes it clear that $\phi(R)$ is also regular. Now
$$
\operatorname{Sub}(R) = \phi(R) \{ 0^j 1^j \},
$$
the concatenation of the regular language $\phi(R)$ and the context-free language $\{0^j 1^j\}$.