With $\varepsilon\equiv1$, every $t\notin\{0,2^j\}$ extends $(0,2^j)$ safely using at most one auxiliary letter $2t-2^j$

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With $\varepsilon\equiv1$, every $t\notin\{0,2^j\}$ extends $(0,2^j)$ safely using at most one auxiliary letter $2t-2^j$ · Prove2Me