src/ZF/Integ/EquivClass.thy

www;

(*  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 + 
consts
    "'/"        ::      [i,i]=>i  (infixl 90)  (*set of equiv classes*)
    congruent   ::      [i,i=>i]=>o
    congruent2  ::      [i,[i,i]=>i]=>o

defs
    quotient_def  "A/r == {r``{x} . x:A}"
    congruent_def "congruent(r,b) == ALL y z. <y,z>:r --> b(y)=b(z)"

    congruent2_def
       "congruent2(r,b) == ALL y1 z1 y2 z2. 
           <y1,z1>:r --> <y2,z2>:r --> b(y1,y2) = b(z1,z2)"

end