src/ZF/EquivClass.thy
changeset 535 9d62c7e08699
child 753 ec86863e87c8
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/ZF/EquivClass.thy	Tue Aug 16 19:06:14 1994 +0200
     1.3 @@ -0,0 +1,23 @@
     1.4 +(*  Title: 	ZF/EquivClass.thy
     1.5 +    ID:         $Id$
     1.6 +    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
     1.7 +    Copyright   1994  University of Cambridge
     1.8 +
     1.9 +Equivalence relations in Zermelo-Fraenkel Set Theory 
    1.10 +*)
    1.11 +
    1.12 +EquivClass = Rel + Perm + 
    1.13 +consts
    1.14 +    "'/"        ::      "[i,i]=>i"  (infixl 90)  (*set of equiv classes*)
    1.15 +    congruent	::	"[i,i=>i]=>o"
    1.16 +    congruent2  ::      "[i,[i,i]=>i]=>o"
    1.17 +
    1.18 +rules
    1.19 +    quotient_def  "A/r == {r``{x} . x:A}"
    1.20 +    congruent_def "congruent(r,b) == ALL y z. <y,z>:r --> b(y)=b(z)"
    1.21 +
    1.22 +    congruent2_def
    1.23 +       "congruent2(r,b) == ALL y1 z1 y2 z2. \
    1.24 +\           <y1,z1>:r --> <y2,z2>:r --> b(y1,y2) = b(z1,z2)"
    1.25 +
    1.26 +end