Tableau Confutation is Finished
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Theorem
Let $T$ be a tableau confutation.
Then $T$ is a finished tableau.
Proof
By definition of tableau confutation, every branch of $T$ is contradictory.
The result follows by definition of finished propositional tableau.
$\blacksquare$
Sources
- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.10$: Completeness