Category:Proof by Cases

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This category contains pages concerning Proof by Cases:


Proof by cases is a valid argument in types of logic dealing with disjunctions $\lor$.

This includes propositional logic and predicate logic, and in particular natural deduction.


Proof Rule

If we can conclude $\phi \lor \psi$, and:
$(1): \quad$ By making the assumption $\phi$, we can conclude $\chi$
$(2): \quad$ By making the assumption $\psi$, we can conclude $\chi$
then we may infer $\chi$.


Sequent Form

Proof by Cases can be symbolised by the sequent:

$p \lor q, \paren {p \vdash r}, \paren {q \vdash r} \vdash r$