Category:Proof by Cases
Jump to navigation
Jump to search
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:
- $p \lor q, \paren {p \vdash r}, \paren {q \vdash r} \vdash r$
Pages in category "Proof by Cases"
The following 21 pages are in this category, out of 21 total.
P
- Proof by Cases
- Proof by Cases with Contradiction
- Proof by Cases/Also known as
- Proof by Cases/Explanation
- Proof by Cases/Formulation 1
- Proof by Cases/Formulation 1/Forward Implication
- Proof by Cases/Formulation 1/Forward Implication/Proof 1
- Proof by Cases/Formulation 1/Forward Implication/Proof 2
- Proof by Cases/Formulation 1/Proof
- Proof by Cases/Formulation 1/Reverse Implication
- Proof by Cases/Formulation 2
- Proof by Cases/Formulation 2/Forward Implication
- Proof by Cases/Formulation 2/Forward Implication/Proof 1
- Proof by Cases/Formulation 2/Forward Implication/Proof by Truth Table
- Proof by Cases/Formulation 2/Proof
- Proof by Cases/Formulation 2/Reverse Implication
- Proof by Cases/Formulation 3
- Proof by Cases/Proof Rule
- Proof by Cases/Sequent Form
- Proof by Cases/Sequent Form/Proof 1
- Proof by Cases/Sequent Form/Proof 2