
diff -r f04b33ce250f -r a4dc62a46ee4 Integ/Integ.thy
--- a/Integ/Integ.thy	Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,79 +0,0 @@
-(*  Title: 	Integ.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
-
-The integers as equivalence classes over nat*nat.
-*)
-
-Integ = Equiv + Arith +
-consts
-  intrel      :: "((nat * nat) * (nat * nat)) set"
-
-defs
-  intrel_def
-   "intrel == {p. ? x1 y1 x2 y2. p=<<x1::nat,y1>,<x2,y2>> & x1+y2 = x2+y1}"
-
-subtype (Integ)
-  int = "{x::(nat*nat).True}/intrel"		(Equiv.quotient_def)
-
-instance
-  int :: {ord, plus, times, minus}
-
-consts
-  zNat        :: "nat set"
-  znat	      :: "nat => int"	   ("$# _" [80] 80)
-  zminus      :: "int => int"	   ("$~ _" [80] 80)
-  znegative   :: "int => bool"
-  zmagnitude  :: "int => int"
-  zdiv,zmod   :: "[int,int]=>int"  (infixl 70)
-  zpred,zsuc  :: "int=>int"
-
-defs
-  zNat_def    "zNat == {x::nat. True}"
-
-  znat_def    "$# m == Abs_Integ(intrel ^^ {<m,0>})"
-
-  zminus_def
-	"$~ Z == Abs_Integ(UN p:Rep_Integ(Z). split(%x y. intrel^^{<y,x>},p))"
-
-  znegative_def
-      "znegative(Z) == EX x y. x<y & <x,y::nat>:Rep_Integ(Z)"
-
-  zmagnitude_def
-      "zmagnitude(Z) == Abs_Integ(UN p:Rep_Integ(Z).split(%x y. intrel^^{<(y-x) + (x-y),0>},p))"
-
-  zadd_def
-   "Z1 + Z2 == 
-       Abs_Integ(UN p1:Rep_Integ(Z1). UN p2:Rep_Integ(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)"
-
-  zle_def   "Z1 <= (Z2::int) == ~(Z2 < Z1)"
-
-  zmult_def
-   "Z1 * Z2 == 
-       Abs_Integ(UN p1:Rep_Integ(Z1). UN p2:Rep_Integ(Z2). split(%x1 y1.   
-           split(%x2 y2. intrel^^{<x1*x2 + y1*y2, x1*y2 + y1*x2>},p2),p1))"
-
-  zdiv_def
-   "Z1 zdiv Z2 ==   
-       Abs_Integ(UN p1:Rep_Integ(Z1). UN p2:Rep_Integ(Z2). split(%x1 y1.   
-           split(%x2 y2. intrel^^{<(x1-y1)div(x2-y2)+(y1-x1)div(y2-x2),   
-           (x1-y1)div(y2-x2)+(y1-x1)div(x2-y2)>},p2),p1))"
-
-  zmod_def
-   "Z1 zmod Z2 ==   
-       Abs_Integ(UN p1:Rep_Integ(Z1).UN p2:Rep_Integ(Z2).split(%x1 y1.   
-           split(%x2 y2. intrel^^{<(x1-y1)mod((x2-y2)+(y2-x2)),   
-           (x1-y1)mod((x2-y2)+(x2-y2))>},p2),p1))"
-
-  zsuc_def     "zsuc(Z) == Z + $# Suc(0)"
-
-  zpred_def    "zpred(Z) == Z - $# Suc(0)"
-end




