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\begin{logicproof}{2}
\lnot q \lor p & \prem \\
\begin{subproof}
q & \assum \\
\begin{subproof}
\lnot q & \assum \\
\false & $\nege 2,3$ \\
p \lor r & $\bote 4$
\end{subproof}
\begin{subproof}
p & \assum \\
p \lor r & $\ori{1} 6$
\end{subproof}
p \lor r & $\ore 1,3-5,6-7$
\end{subproof}
q \implies (p \lor r) & $\impi 2-8$
\end{logicproof}