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i do not have example, but i googled some people can use Isabelle to search lemma and discover new lemma with Isabelle

do not know where give hints to discover or search next lemma after current lemma proved automatically

can you give examples that how to discover lemmas?

Ho Yeung Lee
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  • This would be a good question to edit to try to improve your question score. Can you find a way to express it more clearly? To give some context? To give an example of a development where you would want such features, and why the tools you know about are insufficient? – dfeuer Oct 01 '15 at 16:13

2 Answers2

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For searching lemmas, find_theorems is usually what you would use, but that will only finds existing lemmas, either in your theory, or in the theories that you import, including the standard libraries.

Isabelle does not invent genuinely new lemmas for you.

Joachim Breitner
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Johansson et al. have recently presented a system for theory exploration, that is, coming up with lemmas based on your definitions. You can find their implementation on GitHub and the paper on arXiv. In the paper, you will also find a lot of examples. The only drawback is that, as far as I can tell, their implementation only works with Isabelle2013-2.

Johansson, Moa, et al. "Hipster: Integrating Theory Exploration in a Proof Assistant." Intelligent Computer Mathematics. Springer International Publishing, 2014. 108-122.

larsrh
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