# Finished Branch Lemma/Corollary

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## Corollary to Finished Branch Lemma

Let $\Gamma$ be a finished branch of a propositional tableau $\left({T, \mathbf H, \Phi}\right)$.

Then $\Phi \left[{\Gamma}\right]$, the image of $\Gamma$ under $\Phi$, is satisfiable for boolean interpretations.

## Proof

This needs considerable tedious hard slog to complete it.In particular: Branch not contradictory. See Finished Set LemmaTo discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Finish}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |