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 $\lor \II_1$      


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 $\lor \II_2$