User:Lord Farin/Tableau Proof Rules/Or-Elimination

Proof by Cases
Given $p \lor q$, $p \vdash r$ and $q \vdash r$, we have also $r$.


 * align="right" | $l$ ||
 * align="right" | $I,J,K,$ but excluding $i,j$
 * $r$
 * Proof by Cases: $\text{PBC}$
 * $i .. i', j .. j', k$
 * $i .. i', j .. j', k$