--- a/src/HOL/Gfp.ML Mon Jul 24 23:51:11 2000 +0200
+++ b/src/HOL/Gfp.ML Mon Jul 24 23:51:46 2000 +0200
@@ -1,4 +1,4 @@
-(* Title: HOL/gfp
+(* Title: HOL/Gfp.ML
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
@@ -6,8 +6,6 @@
The Knaster-Tarski Theorem for greatest fixed points.
*)
-open Gfp;
-
(*** Proof of Knaster-Tarski Theorem using gfp ***)
(* gfp(f) is the least upper bound of {u. u <= f(u)} *)
@@ -16,7 +14,7 @@
by (etac (CollectI RS Union_upper) 1);
qed "gfp_upperbound";
-val prems = goalw Gfp.thy [gfp_def]
+val prems = goalw (the_context ()) [gfp_def]
"[| !!u. u <= f(u) ==> u<=X |] ==> gfp(f) <= X";
by (REPEAT (ares_tac ([Union_least]@prems) 1));
by (etac CollectD 1);
@@ -44,7 +42,7 @@
by Auto_tac;
qed "weak_coinduct";
-val [prem,mono] = goal Gfp.thy
+val [prem,mono] = goal (the_context ())
"[| X <= f(X Un gfp(f)); mono(f) |] ==> \
\ X Un gfp(f) <= f(X Un gfp(f))";
by (rtac (prem RS Un_least) 1);
@@ -59,7 +57,7 @@
by (REPEAT (ares_tac [UnI1, Un_least] 1));
qed "coinduct";
-val [mono,prem] = goal Gfp.thy
+val [mono,prem] = goal (the_context ())
"[| mono(f); a: gfp(f) |] ==> a: f(X Un gfp(f))";
by (rtac (mono RS mono_Un RS subsetD) 1);
by (rtac (mono RS gfp_lemma2 RS subsetD RS UnI2) 1);
@@ -74,7 +72,7 @@
by (REPEAT (ares_tac [subset_refl, monoI, Un_mono] 1 ORELSE etac monoD 1));
qed "coinduct3_mono_lemma";
-val [prem,mono] = goal Gfp.thy
+val [prem,mono] = goal (the_context ())
"[| X <= f(lfp(%x. f(x) Un X Un gfp(f))); mono(f) |] ==> \
\ lfp(%x. f(x) Un X Un gfp(f)) <= f(lfp(%x. f(x) Un X Un gfp(f)))";
by (rtac subset_trans 1);
@@ -98,12 +96,12 @@
(** Definition forms of gfp_Tarski and coinduct, to control unfolding **)
-val [rew,mono] = goal Gfp.thy "[| A==gfp(f); mono(f) |] ==> A = f(A)";
+val [rew,mono] = goal (the_context ()) "[| A==gfp(f); mono(f) |] ==> A = f(A)";
by (rewtac rew);
by (rtac (mono RS gfp_Tarski) 1);
qed "def_gfp_Tarski";
-val rew::prems = goal Gfp.thy
+val rew::prems = goal (the_context ())
"[| A==gfp(f); mono(f); a:X; X <= f(X Un A) |] ==> a: A";
by (rewtac rew);
by (REPEAT (ares_tac (map (rewrite_rule [rew]) prems @ [coinduct]) 1));
@@ -118,7 +116,7 @@
by (REPEAT (ares_tac (prems @ [subsetI,CollectI]) 1));
qed "def_Collect_coinduct";
-val rew::prems = goal Gfp.thy
+val rew::prems = goal (the_context ())
"[| A==gfp(f); mono(f); a:X; X <= f(lfp(%x. f(x) Un X Un A)) |] ==> a: A";
by (rewtac rew);
by (REPEAT (ares_tac (map (rewrite_rule [rew]) prems @ [coinduct3]) 1));