Rule of Assumption/Proof Rule/Tableau Form
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Proof Rule
Let $\phi$ be a propositional formula.
The Rule of Assumption is invoked for $\phi$ in a tableau proof in the following manner:
Pool: | The line on which the Rule of Assumption is invoked | ||||||||
Formula: | $\phi$ | ||||||||
Description: | Assumption or Premise | ||||||||
Depends on: | (None) | ||||||||
Abbreviation: | $\mathrm A$ or $\mathrm P$ accordingly |
Note that the Description: field of the Rule of Assumption is populated with either:
or:
- $(2): \quad$ Assumption if it is to be discharged later in the proof.
On completion of the proof, only those lines annotated Premise are to remain in the pool of assumptions of the conclusion.
Also defined as
Some sources introduce the formula line as:
- Show $\phi$
Sources
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $2$ Conditionals and Negation