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Dec 11, 2016 at 19:38 comment added gowrath Is there any way to prove this in PA without having proven associativity of addition? I tried doing this with just commutativity of addition and the axioms but unfortunately got stuck at the point in your proof where you invoke associativity of addition. I get the that I can just prove this as a lemma but was just curious if it were possible without it. Thank you!
Feb 17, 2013 at 4:23 history answered Joel David Hamkins CC BY-SA 3.0