[isabelle] Simpler theorem statements, and proofs for them [Re: Started auction theory toolbox; announcement, next steps, and questions]
- 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
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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 …
lemma "p x ==> q x"
for a straightforward proof, or
lemma assumes "p x" shows "q x"
for a more complicated structured proof.
… such a structure doesn't always work; I think the proofs will also
need some adaptation.
The following lemma (reduced to the structural outline) has a
(anti-)pattern that is typical for my formalisation:
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"
shows "\<forall>i::nat . in_range n i \<longrightarrow>
non_negative_real_vector (n-(1::nat)) (skip_index v i)"
show "in_range n i \<longrightarrow> non_negative_real_vector
(n-(1::nat)) (skip_index v i)"
assume "in_range n i"
show "non_negative_real_vector (n-(1::nat)) (skip_index v i)" sorry
How would I have to adapt the proof when rephrasing the statement as
shows "in_range n i \<Longrightarrow> ..." ?
(I'll be happy to accept "RTFM" as an answer, if you could give me a
Cheers, and thanks,
Christoph Lange, School of Computer Science, University of Birmingham
http://cs.bham.ac.uk/~langec, Skype duke4701
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