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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

$$P = (P \lor Q) \land (P \lor \neg Q)$$

tree_traversal
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1 Answers1

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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 $Q$

Bram28
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  • This answers my question. Writing to let you know I will accept your answer but I have to wait 8 minutes to do so. Would upvote but can't do that either. Thanks for the help! – tree_traversal Feb 01 '19 at 14:46
  • @tree_traversal Don't worry about it. In fact, I shouldn't be gaining rep on a clarification on my own Answer! :) – Bram28 Feb 01 '19 at 14:51