src/ZF/Integ/EquivClass.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/Integ/EquivClass.thy	Tue Sep 22 13:49:22 1998 +0200
@@ -0,0 +1,23 @@
+(*  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