# Talk:Subset is Compatible with Ordinal Successor

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## Proofs

Proof 1 needs to explain why "the last part is a contradiction".

I continue to believe that proofs 1 and 3 are fundamentally the same proof; the justifications based on AoF can very cleanly be pushed down to become alternative proofs of the lemmas Ordinal is not Element of Itself and Ordinal Membership is Asymmetric. The only other differences are that proof 3 expands explanation a bit and moves the invocation of trichotomy to the top to give a clearer picture of the proof structure from the start. I don't think it's perfect yet, but over all I believe it is an improvement and completion of Proof 1, rather than a truly different proof. --Dfeuer (talk) 18:11, 24 April 2013 (UTC)