I am going through the accepted proof in this thread. There is a section of the proof that uses Adjacency to transform (¬∨)∧(¬∨)∧(¬∨) into (¬∨∨)∧(¬∨∨¬)∧(¬∨)∧(¬∨).
It is not obvious to me how this was done.
Can someone show the complete steps of how this is achieved?
Adjacency
$$P = (P \lor Q) \land (P \lor \neg Q)$$
The $\neg P \lor R$ gets transformed into $(\neg P \lor R \lor Q) \land (\neg P \lor R \lor \neg Q)$:
$$\neg P \lor R \overset{Adjacency}{=}$$
$$((\neg P \lor R) \lor Q) \land ((\neg P \lor R) \lor \neg Q) \overset{Association}{=}$$
$$((\neg P \lor R) \lor Q) \land ((\neg P \lor R) \lor \neg Q)$$
So in terms of Pattern Matching:
The '$P$' is $\neg P \lor R$, while the '$Q$' is $Q$