Re: [isabelle] HOL/List.thy lemma suggestions



They are too complicated for a library.

Tobias

On 18/05/2018 17:12, Jørgen Villadsen wrote:
Hi Tobias,

Thanks for the investigations. Any chance that the original lemma suggestions could be added?

lemma sublist_map_fst_zip: obtains zs where "(map fst (zip xs ys)) @ zs = xs"
   by (induct xs ys rule:list_induct2') simp_all

lemma sublist_map_snd_zip: obtains zs where "(map snd (zip xs ys)) @ zs = ys"
   by (induct xs ys rule:list_induct2') simp_all

At least we found them useful... :-)

Best regards, Jørgen

-----Original Message-----
From: cl-isabelle-users-bounces at lists.cam.ac.uk [mailto:cl-isabelle-users-bounces at lists.cam.ac.uk] On Behalf Of Tobias Nipkow
Sent: 18. maj 2018 16:42
To: cl-isabelle-users at lists.cam.ac.uk
Subject: Re: [isabelle] HOL/List.thy lemma suggestions

Hi Lukas,

Your lemmas look natural but replacing the existing simp-rules with them broke a
number of proofs and didn't help any. Thus I have left things as they are. I
didn't add them as ordinary lemmas because my impression is that in most cases
one zips lists of the same length.

But thanks for the suggestion.

Tobias

On 17/05/2018 15:25, Lukas Bulwahn wrote:
Hi Jørgen,

I would propose the following lemma as alternative:

lemma map_fst_zip:
    "map fst (zip xs ys) = take (min (length xs) (length ys)) xs"
by (induct xs ys rule: list_induct2') simp_all

The advantage is that it is a refinement of the existing map_fst_zip;
so I would expect that all previous proofs with map_fst_zip would
still complete with this new one (but I have not tried it).

In your proof, you can then simply replace, obtaining some zs, by
naming the witness. zs is `drop (min (length xs) (length ys)) xs`.
Then, in your proof:
(map fst (zip xs ys)) @ drop (min (length xs) (length ys)) xs
= take (min (length xs) (length ys)) xs @ drop (min (length xs) (length ys)) xs
= xs

This reasoning can be automatically found with (simp add: map_fst_zip).

For map_snd_zip, it is analogous.

I hope this helps.

Best regards,

Lukas



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