Rule of Addition/Proof Rule/Tableau Form

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Proof Rule

Let $\phi$ and $\psi$ be two propositional formulas.

The Rule of Addition is invoked in a tableau proof for $\phi$ or $\psi$ in either of the two forms:


Form 1

Let $\phi$ be a propositional formula in a tableau proof.

Pool:    The pooled assumptions of $\phi$             
Formula:    $\phi \lor \psi$             
Description:    Rule of Addition             
Depends on:    The line containing $\phi$             
Abbreviation:    $\operatorname {Add}_1$ or $\lor \mathcal I_1$             


Form 2

Let $\psi$ be a propositional formula in a tableau proof.

Pool:    The pooled assumptions of $\psi$             
Formula:    $\phi \lor \psi$             
Description:    Rule of Addition             
Depends on:    The line containing $\psi$             
Abbreviation:    $\operatorname {Add}_2$ or $\lor \mathcal I_2$