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Unformatted text preview: S deﬁned in Question 1 with 2 applications of the rule ( r ). Solution: Required formal proof is a sequence A 1 ,A 2 ,A 3 , where A 1 = ( A ⇒ A ) (Axiom) A 2 = ( A ⇒ ( A ⇒ A )) Rule ( r ) application 1 for A = A, B = A . A 3 = (( A ⇒ A ) ⇒ ( A ⇒ ( A ⇒ A ))) Rule ( r ) application 2 for A = A,B = ( A ⇒ A ). 1 QUESTION 3 Prove, by constructing a formal proof that ‘ S (( ¬ A ⇒ B ) ⇒ ( A ⇒ ( ¬ A ⇒ B ))) . Solution: Required formal proof is a sequence A 1 ,A 2 , where A 1 = ( A ⇒ ( ¬ A ⇒ B )) Axiom A 2 = (( ¬ A ⇒ B ) ⇒ ( A ⇒ ( ¬ A ⇒ B ))) Rule ( r ) application for A = A,B = ( ¬ A ⇒ B ). 2...
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 Spring '08
 Bachmair,L
 Computer Science, Logic, formal proof, sequence a1

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