Definition:Gentzen Proof System/Instance 1/Beta-Rule/Notation
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Definition
Let $\mathscr G$ be instance 1 of a Gentzen proof system.
Let $\mathbf B$ be a $\beta$-formula, with $\mathbf B_1, \mathbf B_2$ as in the table of $\beta$-formulas.
In a tableau proof, the $\beta$-rule can be used as follows:
Pool: | Empty. | ||||||||
Formula: | $U_1 \cup \set {\mathbf B}$. | ||||||||
Description: | $\beta$-Rule. | ||||||||
Depends on: | The line containing $U_1 \cup \set {\mathbf B_1, \mathbf B_2}$. | ||||||||
Abbreviation: | $\beta \circ$, where $\circ$ is the binary logical connective such that $\mathbf B = \mathbf B_1 \circ \mathbf B_2$ or $\mathbf B = \neg \paren {\mathbf B_1 \circ \mathbf B_2}$. |