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920 B

\setlength\subproofhorizspace{1.7em}
\begin{logicproof}{2}
\forall x \; P(x) \lor \forall x \; Q(x) & prem.\\
\begin{subproof}
\forall x \; P(x) & ass.\\
\begin{subproof}
\llap{$t\enspace \;$} P(t) & $\forall \mathrm{e}$ 2\\
P(t) \lor Q(t) & $\lor \mathrm{i}_1$ 3
\end{subproof}
\forall y \; (P(y) \lor Q(y)) & $\forall \mathrm{i}$ 3-4
\end{subproof}
\begin{subproof}
\forall x \; Q(x) & ass.\\
\begin{subproof}
\llap{$s\enspace \;$} Q(s) & $\forall \mathrm{e}$ 6\\
P(s) \lor Q(s) & $\lor \mathrm{i}_2$ 7
\end{subproof}
\forall y \; (P(y) \lor Q(y)) & $\forall \mathrm{i}$ 7-8
\end{subproof}
\forall y \; (P(y) \lor Q(y)) & $\lor \mathrm{e}$ 1,2-5,6-9
\end{logicproof}