
diff -r 000000000000 -r a5a9c433f639 src/ZF/ex/equiv.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/ex/equiv.thy	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,28 @@
+(*  Title: 	ZF/ex/equiv.thy
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1993  University of Cambridge
+
+Equivalence relations in Zermelo-Fraenkel Set Theory 
+*)
+
+Equiv = Trancl +
+consts
+    refl,equiv 	::      "[i,i]=>o"
+    sym         ::      "i=>o"
+    "'/"        ::      "[i,i]=>i"  (infixl 90)  (*set of equiv classes*)
+    congruent	::	"[i,i=>i]=>o"
+    congruent2  ::      "[i,[i,i]=>i]=>o"
+
+rules
+    refl_def      "refl(A,r) == r <= (A*A) & (ALL x: A. <x,x> : r)"
+    sym_def       "sym(r) == ALL x y. <x,y>: r --> <y,x>: r"
+    equiv_def     "equiv(A,r) == refl(A,r) & sym(r) & trans(r)"
+    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




