Rule of Addition/Sequent Form/Proof 1
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Theorem
The Rule of Addition can be symbolised by the sequents:
- $(1): \quad p \vdash p \lor q$
- $(2): \quad q \vdash p \lor q$
Proof
Form 1
By the tableau method of natural deduction:
Line | Pool | Formula | Rule | Depends upon | Notes | |
---|---|---|---|---|---|---|
1 | 1 | $p$ | Premise | (None) | ||
2 | 1 | $p \lor q$ | Rule of Addition: $\lor \II_1$ | 1 |
$\blacksquare$
Form 2
By the tableau method of natural deduction:
Line | Pool | Formula | Rule | Depends upon | Notes | |
---|---|---|---|---|---|---|
1 | 1 | $q$ | Premise | (None) | ||
2 | 1 | $p \lor q$ | Rule of Addition: $\lor \II_2$ | 1 |
$\blacksquare$