*To*: Lawrence Paulson <lp15 at cam.ac.uk>*Subject*: [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, 01 Nov 2012 01:20:19 +0000*Cc*: isabelle-users at cl.cam.ac.uk*In-reply-to*: <B342CF2B-EEC3-4932-A98D-193702F57A14@cam.ac.uk>*Organization*: University of Birmingham*References*: <50916DB3.4030707@cs.bham.ac.uk> <B342CF2B-EEC3-4932-A98D-193702F57A14@cam.ac.uk>*User-agent*: Mozilla/5.0 (X11; Linux x86_64; rv:16.0) Gecko/20121029 Thunderbird/16.0.1

2012-10-31 20:09 Lawrence Paulson:

On 31 Oct 2012, at 18:28, Christoph LANGE <c.lange at cs.bham.ac.uk> wrote:* In statements such as "!x. p x --> q x" it is tedious (and always the same) to break their structure down to a level where the actually interesting work starts.It is almost never necessary or helpful to state a theorem in that format.

Thanks for your advice! However simply changing my statements to …

I suggest lemma "p x ==> q x" for a straightforward proof, or lemma assumes "p x" shows "q x" for a more complicated structured proof.

lemma skip_index_keeps_non_negativity : fixes n::nat and v::real_vector assumes non_empty: "n > 0" and non_negative: "non_negative_real_vector n v"

proof fix i::nat

proof assume "in_range n i" ... show "non_negative_real_vector (n-(1::nat)) (skip_index v i)" sorry qed qed

Cheers, and thanks, 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:*Christian Sternagel

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

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