*To*: Lawrence Paulson <lp15 at cam.ac.uk>*Subject*: Re: [isabelle] Simpler theorem statements, and proofs for them [Re: Started auction theory toolbox; announcement, next steps, and questions]*From*: Christoph LANGE <c.lange at cs.bham.ac.uk>*Date*: Thu, 22 Nov 2012 14:13:40 +0000*Cc*: isabelle-users at cl.cam.ac.uk*In-reply-to*: <C76381F2-5127-48DF-B198-DE2B3AABEAB1@cam.ac.uk>*Organization*: University of Birmingham*References*: <50916DB3.4030707@cs.bham.ac.uk> <B342CF2B-EEC3-4932-A98D-193702F57A14@cam.ac.uk> <5091CE53.6020006@cs.bham.ac.uk> <C76381F2-5127-48DF-B198-DE2B3AABEAB1@cam.ac.uk>*User-agent*: Mozilla/5.0 (X11; Linux x86_64; rv:16.0) Gecko/20121029 Thunderbird/16.0.1

Dear Larry, dear all, I'm now back at our auction formalisation and catching up with emails.

shows "!i . p x --> q x" to fixes ... and i assumes "p x" shows "q x"

... by (induct i arbitrary: xs) (case_tac xs, simp_all)+

2012-11-01 12:03 Lawrence Paulson:

You should look at the documentation on the induct/induction proof methods.

lemma maximum_sufficient : fixes n::nat and ... assumes assm1: "p n" and assm2: "q n" and assm3: "r n" shows "s n" using assms (* <-- now this became necessary, otherwise even "case 0" would fail, but why? *) proof (induct n) case 0 then show ?case by simp next case (Suc n) (* and now I have to explicitly restate all assumptions: *) assume assm1: "p (Suc n)" assume assm2: "q (Suc n)" assume assm3: "r (Suc n)" ... show "s (Suc n)" ... qed Cheers, and thanks for any help, Christoph -- Christoph Lange, School of Computer Science, University of Birmingham http://cs.bham.ac.uk/~langec/, Skype duke4701 → Enabling Domain Experts to use Formalised Reasoning @ AISB 2013 2–5 April 2013, Exeter, UK. Deadlines 10 Dec (stage 1), 14 Jan (st. 2) http://cs.bham.ac.uk/research/projects/formare/events/aisb2013/

**Follow-Ups**:**Re: [isabelle] Simpler theorem statements, and proofs for them [Re: Started auction theory toolbox; announcement, next steps, and questions]***From:*Tobias Nipkow

**Re: [isabelle] Simpler theorem statements, and proofs for them [Re: Started auction theory toolbox; announcement, next steps, and questions]***From:*Lars Noschinski

**Re: [isabelle] Simpler theorem statements, and proofs for them [Re: Started auction theory toolbox; announcement, next steps, and questions]***From:*Makarius

**References**:**[isabelle] Simpler theorem statements, and proofs for them [Re: Started auction theory toolbox; announcement, next steps, and questions]***From:*Christoph LANGE

*From:*Lawrence Paulson

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