
diff -r 5f9d7ed4ea0c -r 12943ab62cc5 Integ/Equiv.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Integ/Equiv.thy	Mon Feb 27 16:36:17 1995 +0100
@@ -0,0 +1,28 @@
+(*  Title: 	Equiv.thy
+    ID:         $Id$
+    Authors: 	Riccardo Mattolini, Dip. Sistemi e Informatica
+        	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1994 Universita' di Firenze
+    Copyright   1993  University of Cambridge
+
+Equivalence relations in Higher-Order Set Theory 
+*)
+
+Equiv = Relation +
+consts
+    refl,equiv 	::      "['a set,('a*'a) set]=>bool"
+    sym         ::      "('a*'a) set=>bool"
+    "'/"        ::      "['a set,('a*'a) set]=>'a set set"  (infixl 90) 
+                        (*set of equiv classes*)
+    congruent	::	"[('a*'a) set,'a=>'b]=>bool"
+    congruent2  ::      "[('a*'a) set,['a,'a]=>'b]=>bool"
+
+defs
+    refl_def      "refl(A,r) == r <= Sigma(A,%x.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 == UN x:A. {r^^{x}}"  
+    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




