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Jun 8, 2011 at 17:55 comment added Henry Towsner If we're talking about proofs in formal systems of nonstandard analysis, there are general methods for extracting the standard proof from it. For instance, "Weak theories of nonstandard arithmetic and analysis" by Jeremy Avigad.
Jun 8, 2011 at 16:28 comment added Gerald Edgar One can go from nonstandard proof to standard proof using ultrapowers. It is just that such a proof may not be as "elegant".
Jun 8, 2011 at 16:19 history answered Noah CC BY-SA 3.0