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Oct 30 '14 at 4:20 comment added cookie monster I marked your answer for providing more details however I'm not familiar with some of the rules you used so I followed your answer as a guide to come up with similar solution. I end up opening a new one here to avoid complicating this thread. Please take a look at it and confirm if my steps are valid. I am having problems discharging an assumption, so your help will be appreciated.
Oct 29 '14 at 20:26 history edited Mauro ALLEGRANZA CC BY-SA 3.0
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Oct 29 '14 at 18:03 comment added cookie monster I think you also made a mistake with step 13, you got it with -I not →I
Oct 29 '14 at 16:35 comment added Mauro ALLEGRANZA @cookiemonster - in 12 the symbol ⊥ stay for a contradiction : step 4) ¬ C and step 11) C ; thus, having derived a contradiction, we negate the assumption 5) A & B, getting 13) ¬ (A & B). This can be done with the abbreviation ¬ P := P → ⊥; in this way, deriving a contradiction from ¬ C, C is nothing else than apply →E to C → ⊥, C in order to derive ⊥. Then, having (A & B) ⊢ ⊥, we derive (A & B) → ⊥, i.e. ¬ (A & B) by →I.
Oct 29 '14 at 16:34 comment added cookie monster please can you go over your answer again and correct the rest!
Oct 29 '14 at 16:28 comment added Mauro ALLEGRANZA @cookiemonster - right, tanks ! coorected the typo into steps 6 and 8. For step 7, it is correct : A ⊢ B → A, for every A, because A → (B → A) is valid (it is a tautology).
Oct 29 '14 at 16:28 comment added cookie monster Also you can't really get step 10 unless you have (A → B) ^ (B → A). I don't understand what you mean by step 12. Step 13 is not clear as well. I'm not sure if I can understand this well, it seems like you are using the symbols in a different way.
Oct 29 '14 at 16:26 history edited Mauro ALLEGRANZA CC BY-SA 3.0
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Oct 29 '14 at 16:10 comment added cookie monster Isn't step 6 from ^ E on line 5? Also step 7 doesn't seem correct.You don't even have B yet? In addition on step 8, shouldn't that be ^ E on line 5?
Oct 29 '14 at 14:37 history edited Mauro ALLEGRANZA CC BY-SA 3.0
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Oct 29 '14 at 11:24 history edited Mauro ALLEGRANZA CC BY-SA 3.0
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Oct 29 '14 at 9:02 history edited Mauro ALLEGRANZA CC BY-SA 3.0
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Oct 29 '14 at 8:44 history answered Mauro ALLEGRANZA CC BY-SA 3.0