2.4.10: Derivability and the Propositional Connectives
- \(A \lor B, \lnot A, \lnot B\) is inconsistent.
- Both \(A \Proves A \lor B\) and \(B \Proves A \lor B\) .
Proof.
-
We give a derivation of the sequent
\(A \lor B, \lnot A, \lnot B \Sequent\)
:
(Recall that double inference lines indicate several weakening, contraction, and exchange inferences.)
-
Both sequents
\(A \Sequent A \lor B\)
and
\(B \Sequent A \lor B\)
have derivations:
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