src/ZF/Integ/EquivClass.thy

* Isar/Pure: emulation of instantiation tactics (rule_tac, cut_tac,
etc.) now consider the syntactic context of assumptions, giving a
better chance to get type-inference of the arguments right (this is
especially important for locales);
* system: refrain from any attempt at filtering input streams; no
longer support ``8bit'' encoding of old isabelle font, instead proper
iso-latin characters may now be used;

(*  Title:      ZF/EquivClass.thy
    ID:         $Id$
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1994  University of Cambridge

Equivalence relations in Zermelo-Fraenkel Set Theory 
*)

EquivClass = Rel + Perm + 

constdefs

  quotient    :: [i,i]=>i    (infixl "'/'/" 90)  (*set of equiv classes*)
      "A//r == {r``{x} . x:A}"

  congruent   :: [i,i=>i]=>o
      "congruent(r,b) == ALL y z. <y,z>:r --> b(y)=b(z)"

  congruent2  :: [i,[i,i]=>i]=>o
      "congruent2(r,b) == ALL y1 z1 y2 z2. 
           <y1,z1>:r --> <y2,z2>:r --> b(y1,y2) = b(z1,z2)"

end