*To*: Christian Sternagel <c.sternagel at gmail.com>*Subject*: Re: [isabelle] system of representatives of an equivalence relation*From*: Lawrence Paulson <lp15 at cam.ac.uk>*Date*: Fri, 11 Apr 2014 12:41:33 +0100*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*: <5347A4DE.4080606@gmail.com>*References*: <53479EA6.9030208@gmail.com> <5347A2BF.8010602@in.tum.de> <5347A4DE.4080606@gmail.com>

Are specific representatives actually needed? It might be better to use the equivalence classes themselves. That is the point of this construction. --lcp > On 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 >

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

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

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