*To*: Lawrence Paulson <lp15 at cam.ac.uk>*Subject*: Re: [isabelle] system of representatives of an equivalence relation*From*: Christian Sternagel <c.sternagel at gmail.com>*Date*: Fri, 11 Apr 2014 14:35:22 +0200*Cc*: "isabelle-users at cl.cam.ac.uk" <isabelle-users at cl.cam.ac.uk>, Dmitriy Traytel <traytel at in.tum.de>*In-reply-to*: <A0A31016-BEB3-451B-9D02-B98A8899971B@cam.ac.uk>*References*: <53479EA6.9030208@gmail.com> <5347A2BF.8010602@in.tum.de> <5347A4DE.4080606@gmail.com> <A0A31016-BEB3-451B-9D02-B98A8899971B@cam.ac.uk>*User-agent*: Mozilla/5.0 (X11; Linux x86_64; rv:24.0) Gecko/20100101 Thunderbird/24.4.0

Dear Larry, at least I'm under the impression that the representatives are needed ;).

cheers chris On 04/11/2014 01:41 PM, Lawrence Paulson wrote:

Are specific representatives actually needed? It might be better to use the equivalence classes themselves. That is the point of this construction. --lcpOn 11 Apr 2014, at 09:16, Christian Sternagel <c.sternagel at gmail.com> wrote: Thanks Dimitriy, That looks similar to the construction I'm currently using ;), i.e., "repsys A R = {(SOME x. x ∈ X) | X. X ∈ A // R}" I was hoping that some properties are already proved about it. E.g., that two non-equal elements of "repsys A R" are not in relation w.r.t. "R", "repsys A R" is a subset of "A", ... But it should be easy to do anyway. Would this be interesting for anybody else? cheers chris btw: I could not find the constant "proj" in Equiv_Relations.On 04/11/2014 10:07 AM, Dmitriy Traytel wrote: Hi Chris, Am 11.04.2014 09:49, schrieb Christian Sternagel:Dear fellow Isabellers, I am wondering whether there is already a way in the Isabelle/HOL library (or the AFP, for that matter) to obtain a system of representatives (I'm not sure whether this is the correct term, in German it is called "Repräsentantensystem") for a given equivalence relation, i.e., a set containing one representative of each equivalence class?Something like this: "(λX. SOME x. x ∈ X) ` Equiv_Relations.proj r ` Field r" The function Equiv_Relations.proj gives you the (non-empty) equivalence class of an element. Dmitriy

**Follow-Ups**:**Re: [isabelle] system of representatives of an equivalence relation***From:*Lawrence Paulson

**References**:**[isabelle] system of representatives of an equivalence relation***From:*Christian Sternagel

**Re: [isabelle] system of representatives of an equivalence relation***From:*Dmitriy Traytel

**Re: [isabelle] system of representatives of an equivalence relation***From:*Christian Sternagel

**Re: [isabelle] system of representatives of an equivalence relation***From:*Lawrence Paulson

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