The good/bad news is that no matter what you do, there is a super-exponential complexity result on proof-length for Presburger Artihmetic. So maybe, just let it be, or use reflection, i.e. the reflexifity theorem as any proof of Presburger :)

Best,
Amine.

Quoting Tobias Nipkow <[email protected]>:

All of the lemmas involved are either arihmetic or logical inference rules and make sense. Presburger is a generic and complex decision procedure. I am not surprised and would not want to optimize presburger to use fewer lemmas.

Tobias

Am 28/06/2011 00:08, schrieb Jasmin Blanchette:
Hi all,

Quick question: Josef Urban noticed that the proof terms for some lemmas proved directly by "presburger" can refer to lots of other lemmas; for example, the proof of "Parity.even_mult_two_ex" directly refers to 206 lemmas.

ML {* Thm.proof_body_of @{thm Parity.even_mult_two_ex} *}

(I've attached the list.) Is that normal? Does this have anything to do with "presburger"?

Jasmin




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