src/ZF/EquivClass.thy
author clasohm
Tue Feb 06 12:27:17 1996 +0100 (1996-02-06)
changeset 1478 2b8c2a7547ab
parent 1401 0c439768f45c
permissions -rw-r--r--
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     1 (*  Title:      ZF/EquivClass.thy
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1994  University of Cambridge
     5 
     6 Equivalence relations in Zermelo-Fraenkel Set Theory 
     7 *)
     8 
     9 EquivClass = Rel + Perm + 
    10 consts
    11     "'/"        ::      [i,i]=>i  (infixl 90)  (*set of equiv classes*)
    12     congruent   ::      [i,i=>i]=>o
    13     congruent2  ::      [i,[i,i]=>i]=>o
    14 
    15 defs
    16     quotient_def  "A/r == {r``{x} . x:A}"
    17     congruent_def "congruent(r,b) == ALL y z. <y,z>:r --> b(y)=b(z)"
    18 
    19     congruent2_def
    20        "congruent2(r,b) == ALL y1 z1 y2 z2. 
    21            <y1,z1>:r --> <y2,z2>:r --> b(y1,y2) = b(z1,z2)"
    22 
    23 end