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Unformatted text preview: A ⇒ A ) (b) We know that ‘ H ( ¬ A ⇒ ( A ⇒ B )). Prove, that ¬ A,A ‘ H B . Problem 4 Here are consecutive steps B 1 ,...,B 5 in a proof of ( B ⇒ ¬¬ B ) in H 2 . The comments included are incomplete. Complete the comments by writing all details for each step of the proof. You have to write down the proper substitutions and formulas used at each step of the proof. B 1 = (( ¬¬¬ B ⇒ ¬ B ) ⇒ (( ¬¬¬ B ⇒ B ) ⇒ ¬¬ B )) Axiom A 3 B 2 = ( ¬¬¬ B ⇒ ¬ B ) Already proved fact: ‘ H 2 ( ¬¬ B ⇒ B ) B 3 = (( ¬¬¬ B ⇒ B ) ⇒ ¬¬ B ) (MP) B 4 = ( B ⇒ ( ¬¬¬ B ⇒ B )) Axiom A 1 B 5 = ( B ⇒ ¬¬ B ) Already proved fact: ( A ⇒ B ) , ( B ⇒ C ) ‘ H 2 ( A ⇒ C ) 2...
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 Spring '08
 Bachmair,L
 Computer Science, Logic, British B class submarine, Axiom A3 B2

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