src/ZF/ex/Equiv.thy
author lcp
Tue Aug 16 18:58:42 1994 +0200 (1994-08-16)
changeset 532 851df239ac8b
parent 434 89d45187f04d
permissions -rw-r--r--
ZF/Makefile,ROOT.ML, ZF/ex/Integ.thy: updated for EquivClass
     1 (*  Title: 	ZF/ex/Equiv.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 Equiv = 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 rules
    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