# HG changeset patch
# User lcp
# Date 793899998 -3600
# Node ID b6c0407f203e716e48cf78a9481b76ffdf420c3e
# Parent  12943ab62cc55d655e582e62d6f0ede83c9bbf13
Installation of Integ (ported from ZF by Mattolini)

diff -r 12943ab62cc5 -r b6c0407f203e Integ/Integ.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Integ/Integ.thy	Mon Feb 27 16:46:38 1995 +0100
@@ -0,0 +1,80 @@
+(*  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"		("quotient_def")
+
+arities int :: ord
+        int :: plus
+        int :: times
+        int :: 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
diff -r 12943ab62cc5 -r b6c0407f203e Integ/ROOT.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Integ/ROOT.ML	Mon Feb 27 16:46:38 1995 +0100
@@ -0,0 +1,12 @@
+(*  Title:  	HOL/Integ/ROOT
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1995  University of Cambridge
+
+The Integers in HOL (ported from ZF by Riccardo Mattolini)
+*)
+
+HOL_build_completed;    (*Cause examples to fail if HOL did*)
+
+loadpath := ["Integ"];
+time_use_thy "Integ" handle _ => exit 1;
diff -r 12943ab62cc5 -r b6c0407f203e Integ/Relation.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Integ/Relation.ML	Mon Feb 27 16:46:38 1995 +0100
@@ -0,0 +1,98 @@
+(*  Title: 	Relation.ML
+    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
+
+Functions represented as relations in HOL Set Theory 
+*)
+
+val RSLIST = curry (op MRS);
+
+open Relation;
+
+goalw Relation.thy [converse_def] "!!a b r. <a,b>:r ==> <b,a>:converse(r)";
+by (simp_tac prod_ss 1);
+by (fast_tac set_cs 1);
+qed "converseI";
+
+goalw Relation.thy [converse_def] "!!a b r. <a,b> : converse(r) ==> <b,a> : r";
+by (fast_tac comp_cs 1);
+qed "converseD";
+
+qed_goalw "converseE" Relation.thy [converse_def]
+    "[| yx : converse(r);  \
+\       !!x y. [| yx=<y,x>;  <x,y>:r |] ==> P \
+\    |] ==> P"
+ (fn [major,minor]=>
+  [ (rtac (major RS CollectE) 1),
+    (REPEAT (eresolve_tac [bexE,exE, conjE, minor] 1)),
+    (hyp_subst_tac 1),
+    (assume_tac 1) ]);
+
+val converse_cs = comp_cs addSIs [converseI] 
+			  addSEs [converseD,converseE];
+
+qed_goalw "Domain_iff" Relation.thy [Domain_def]
+    "a: Domain(r) = (EX y. <a,y>: r)"
+ (fn _=> [ (fast_tac comp_cs 1) ]);
+
+qed_goal "DomainI" Relation.thy "!!a b r. <a,b>: r ==> a: Domain(r)"
+ (fn _ => [ (etac (exI RS (Domain_iff RS iffD2)) 1) ]);
+
+qed_goal "DomainE" Relation.thy
+    "[| a : Domain(r);  !!y. <a,y>: r ==> P |] ==> P"
+ (fn prems=>
+  [ (rtac (Domain_iff RS iffD1 RS exE) 1),
+    (REPEAT (ares_tac prems 1)) ]);
+
+qed_goalw "RangeI" Relation.thy [Range_def] "!!a b r.<a,b>: r ==> b : Range(r)"
+ (fn _ => [ (etac (converseI RS DomainI) 1) ]);
+
+qed_goalw "RangeE" Relation.thy [Range_def]
+    "[| b : Range(r);  !!x. <x,b>: r ==> P |] ==> P"
+ (fn major::prems=>
+  [ (rtac (major RS DomainE) 1),
+    (resolve_tac prems 1),
+    (etac converseD 1) ]);
+
+(*** Image of a set under a function/relation ***)
+
+qed_goalw "Image_iff" Relation.thy [Image_def]
+    "b : r^^A = (? x:A. <x,b>:r)"
+ (fn _ => [ fast_tac (comp_cs addIs [RangeI]) 1 ]);
+
+qed_goal "Image_singleton_iff" Relation.thy
+    "(b : r^^{a}) = (<a,b>:r)"
+ (fn _ => [ rtac (Image_iff RS trans) 1,
+	    fast_tac comp_cs 1 ]);
+
+qed_goalw "ImageI" Relation.thy [Image_def]
+    "!!a b r. [| <a,b>: r;  a:A |] ==> b : r^^A"
+ (fn _ => [ (REPEAT (ares_tac [CollectI,RangeI,bexI] 1)),
+            (resolve_tac [conjI ] 1),
+            (resolve_tac [RangeI] 1),
+            (REPEAT (fast_tac set_cs 1))]);
+
+qed_goalw "ImageE" Relation.thy [Image_def]
+    "[| b: r^^A;  !!x.[| <x,b>: r;  x:A |] ==> P |] ==> P"
+ (fn major::prems=>
+  [ (rtac (major RS CollectE) 1),
+    (safe_tac set_cs),
+    (etac RangeE 1),
+    (rtac (hd prems) 1),
+    (REPEAT (etac bexE 1 ORELSE ares_tac prems 1)) ]);
+
+qed_goal "Image_subset" Relation.thy
+    "!!A B r. r <= Sigma(A,%x.B) ==> r^^C <= B"
+ (fn _ =>
+  [ (rtac subsetI 1),
+    (REPEAT (eresolve_tac [asm_rl, ImageE, subsetD RS SigmaD2] 1)) ]);
+
+val rel_cs = converse_cs addSIs [converseI] 
+                         addIs  [ImageI, DomainI, RangeI]
+                         addSEs [ImageE, DomainE, RangeE];
+
+val rel_eq_cs = rel_cs addSIs [equalityI];
+
diff -r 12943ab62cc5 -r b6c0407f203e Integ/Relation.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Integ/Relation.thy	Mon Feb 27 16:46:38 1995 +0100
@@ -0,0 +1,24 @@
+(*  Title: 	Relation.thy
+    ID:         $Id$
+    Author: 	Riccardo Mattolini, Dip. Sistemi e Informatica
+        and	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1994 Universita' di Firenze
+    Copyright   1993  University of Cambridge
+
+Functions represented as relations in Higher-Order Set Theory 
+*)
+
+Relation = Trancl +
+consts
+    converse    ::      "('a*'a) set => ('a*'a) set"
+    "^^"        ::      "[('a*'a) set,'a set] => 'a set" (infixl 90)
+    Domain      ::      "('a*'a) set => 'a set"
+    Range       ::      "('a*'a) set => 'a set"
+
+defs
+    converse_def  "converse(r) == {z. (? w:r. ? x y. w=<x,y> & z=<y,x>)}"
+    Domain_def    "Domain(r) == {z. ! x. (z=x --> (? y. <x,y>:r))}"
+    Range_def     "Range(r) == Domain(converse(r))"
+    Image_def     "r ^^ s == {y. y:Range(r) &  (? x:s. <x,y>:r)}"
+
+end