Rule of Addition/Sequent Form/Proof 1

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:

$p \vdash p \lor q$
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:

$q \vdash p \lor q$
Line Pool Formula Rule Depends upon Notes
1 1 $q$ Premise (None)
2 1 $p \lor q$ Rule of Addition: $\lor \II_2$ 1

$\blacksquare$

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