--- 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