*To*: Dmitriy Traytel <traytel at in.tum.de>, "isabelle-users at cl.cam.ac.uk" <isabelle-users at cl.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 10:16:30 +0200*In-reply-to*: <5347A2BF.8010602@in.tum.de>*References*: <53479EA6.9030208@gmail.com> <5347A2BF.8010602@in.tum.de>*User-agent*: Mozilla/5.0 (X11; Linux x86_64; rv:24.0) Gecko/20100101 Thunderbird/24.4.0

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}"

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:*Dmitriy Traytel

**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

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