Extending $(0,1)$ by one even target $t\equiv 0 \pmod 4$ forces $\varepsilon_0=1$ and $2t-1$ before $t$

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Extending $(0,1)$ by one even target $t\equiv 0 \pmod 4$ forces $\varepsilon_0=1$ and $2t-1$ before $t$ · Prove2Me