
diff -r 000000000000 -r a5a9c433f639 src/ZF/ex/integ.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/ex/integ.thy	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,54 @@
+(*  Title: 	ZF/ex/integ.thy
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1993  University of Cambridge
+
+The integers as equivalence classes over nat*nat.
+*)
+
+Integ = Equiv + Arith +
+consts
+    intrel,integ::      "i"
+    znat	::	"i=>i"		("$# _" [80] 80)
+    zminus	::	"i=>i"		("$~ _" [80] 80)
+    znegative	::	"i=>o"
+    zmagnitude	::	"i=>i"
+    "$*"        ::      "[i,i]=>i"      (infixl 70)
+    "$'/"       ::      "[i,i]=>i"      (infixl 70) 
+    "$'/'/"     ::      "[i,i]=>i"      (infixl 70)
+    "$+"	::      "[i,i]=>i"      (infixl 65)
+    "$-"        ::      "[i,i]=>i"      (infixl 65)
+    "$<"	:: 	"[i,i]=>o"  	(infixl 50)
+
+rules
+
+    intrel_def
+     "intrel == {p:(nat*nat)*(nat*nat). 		\
+\        EX x1 y1 x2 y2. p=<<x1,y1>,<x2,y2>> & x1#+y2 = x2#+y1}"
+
+    integ_def   "integ == (nat*nat)/intrel"
+    
+    znat_def	"$# m == intrel `` {<m,0>}"
+    
+    zminus_def	"$~ Z == UN p:Z. split(%x y. intrel``{<y,x>}, p)"
+    
+    znegative_def
+	"znegative(Z) == EX x y. x:y & y:nat & <x,y>:Z"
+    
+    zmagnitude_def
+	"zmagnitude(Z) == UN p:Z. split(%x y. (y#-x) #+ (x#-y), p)"
+    
+    zadd_def
+     "Z1 $+ Z2 == \
+\       UN p1:Z1. UN p2:Z2. split(%x1 y1. split(%x2 y2. 		\
+\                                         intrel``{<x1#+x2, y1#+y2>}, p2), p1)"
+    
+    zdiff_def   "Z1 $- Z2 == Z1 $+ zminus(Z2)"
+    zless_def	"Z1 $< Z2 == znegative(Z1 $- Z2)"
+    
+    zmult_def
+     "Z1 $* Z2 == \
+\       UN p1:Z1. UN p2:Z2.  split(%x1 y1. split(%x2 y2. 	\
+\                   intrel``{<x1#*x2 #+ y1#*y2, x1#*y2 #+ y1#*x2>}, p2), p1)"
+    
+ end




