## 6.7.17 Peano arithmetic

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The Peano page defines Peano arithmetic thus:

Proofs in are tactic evaluated by . This tactic constantly needs and as premisses. It would take too much cpu time if the tactic should prove and each time they are needed. For that reason, the tactic generates sequent operators which prove in the beginning of the proof. That is trivial when working in itself, but requires a couple of sequent operations when working e.g. in .

There is only one difference between and . The latter starts out proving both and . The former only proves .

For completeness, here are the axioms of .

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Klaus Grue,
GRD-2010-01-05