You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
30 lines
980 B
30 lines
980 B
\begin{logicproof}{2}
|
|
p \implies q & \prem \\
|
|
(p \land r) \lor q & \prem \\
|
|
\begin{subproof}
|
|
q \implies p & \assum \\
|
|
\begin{subproof}
|
|
p \land r & \assum \\
|
|
r & $\ande{2} 4$ \\
|
|
r \lor q & $\ori{1} 5$
|
|
\end{subproof}
|
|
\begin{subproof}
|
|
q & \assum \\
|
|
r \lor q & $\ori{2} 7$
|
|
\end{subproof}
|
|
r \lor q & $\ore 2,4-6,7-8$ \\
|
|
\begin{subproof}
|
|
p \land r & \assum \\
|
|
p & $\ande{1} 10 $\\
|
|
q & $\impe 1,11$ \\
|
|
(s \land t) \lor q & $\ori{2} 12$
|
|
\end{subproof}
|
|
\begin{subproof}
|
|
q & \assum \\
|
|
(s \land t) \lor q & $\ori{2} 14$
|
|
\end{subproof}
|
|
(s \land t) \lor q & $\ore 2,10-13,14-15 $\\
|
|
((s \land t) \lor q) \land (r \lor q) & $\andi 16,9$
|
|
\end{subproof}
|
|
(q \implies p) \implies ((s \land t) \lor q) \land (r \lor q) & $\impi 3-17$
|
|
\end{logicproof}
|