*To*: Peter Gammie <peteg42 at gmail.com>*Subject*: Re: [isabelle] conversions for symmetric/commutative operators*From*: Peter Lammich <lammich at in.tum.de>*Date*: Tue, 09 Nov 2021 14:28:23 +0100*Authentication-results*: cam.ac.uk; iprev=pass (mail-out2.in.tum.de) smtp.remote-ip=131.159.0.36; spf=pass smtp.mailfrom=in.tum.de; arc=none*Cc*: cl-isabelle-users <cl-isabelle-users at lists.cam.ac.uk>*Importance*: Normal*In-reply-to*: <7711F679-C145-4B57-9DB7-16D7FEBDDF0D@gmail.com>

I second Peter that having attributes that create more than one lemma as output may be a useful thing. I also often write things like [simp, THEN xxx, simp], to register two simp rules derived from the same lemma.

Peter

On 9 Nov 2021 13:34, Peter Gammie <peteg42 at gmail.com> wrote:

Hello,

I find myself with a sea of conversions of the form exhibited by `filter_empty_conv`. `HOL.List` is missing its obvious friend:

lemma empty_filter_conv:

shows "([] = filter P xs) = (\<forall>x\<in>set xs. \<not> P x)"

by (induct xs) simp_all

which could also be derived via a rule of the form:

(x = y) = z ==> (y = x) = z

(and so forth for other symmetric or commutative operators such as inf and sup).

One could imagine defining an attribute `symconv` like `symmetric` to handle this:

lemmas empty_filter_conv = filter_empty_conv[symconv]

But in my ideal world I wouldn’t need to type this out and make up another name, but would instead bind both theorems to the same name, e.g.

lemma empty_filter_conv[symconv]:

shows "([] = filter P xs) = (\<forall>x\<in>set xs. \<not> P x)”

…

thm empty_filter_conv

> ([] = filter P xs) = (\<forall>x\<in>set xs. \<not> P x)

> (filter P xs = []) = (\<forall>x\<in>set xs. \<not> P x)

However AIUI attributes map a single theorem to a single theorem, so this isn’t going to work.

All I can think of is to create another keyword like `lemma` that does a bit of post-processing before the binding is made. This feels a bit heavyweight.

Has anyone got a better solution? It might help to make these sorts of lemma pairs more systematic in the distribution.

cheers,

peter

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