--- a/src/CCL/Lfp.ML Sat Sep 17 14:02:31 2005 +0200
+++ b/src/CCL/Lfp.ML Sat Sep 17 17:35:26 2005 +0200
@@ -1,55 +1,46 @@
-(* Title: CCL/lfp
+(* Title: CCL/Lfp.ML
ID: $Id$
-
-Modified version of
- Title: HOL/lfp.ML
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1992 University of Cambridge
-
-For lfp.thy. The Knaster-Tarski Theorem
*)
-open Lfp;
-
(*** Proof of Knaster-Tarski Theorem ***)
(* lfp(f) is the greatest lower bound of {u. f(u) <= u} *)
-val prems = goalw Lfp.thy [lfp_def] "[| f(A) <= A |] ==> lfp(f) <= A";
+val prems = goalw (the_context ()) [lfp_def] "[| f(A) <= A |] ==> lfp(f) <= A";
by (rtac (CollectI RS Inter_lower) 1);
by (resolve_tac prems 1);
qed "lfp_lowerbound";
-val prems = goalw Lfp.thy [lfp_def]
+val prems = goalw (the_context ()) [lfp_def]
"[| !!u. f(u) <= u ==> A<=u |] ==> A <= lfp(f)";
by (REPEAT (ares_tac ([Inter_greatest]@prems) 1));
by (etac CollectD 1);
qed "lfp_greatest";
-val [mono] = goal Lfp.thy "mono(f) ==> f(lfp(f)) <= lfp(f)";
+val [mono] = goal (the_context ()) "mono(f) ==> f(lfp(f)) <= lfp(f)";
by (EVERY1 [rtac lfp_greatest, rtac subset_trans,
rtac (mono RS monoD), rtac lfp_lowerbound, atac, atac]);
qed "lfp_lemma2";
-val [mono] = goal Lfp.thy "mono(f) ==> lfp(f) <= f(lfp(f))";
-by (EVERY1 [rtac lfp_lowerbound, rtac (mono RS monoD),
+val [mono] = goal (the_context ()) "mono(f) ==> lfp(f) <= f(lfp(f))";
+by (EVERY1 [rtac lfp_lowerbound, rtac (mono RS monoD),
rtac lfp_lemma2, rtac mono]);
qed "lfp_lemma3";
-val [mono] = goal Lfp.thy "mono(f) ==> lfp(f) = f(lfp(f))";
+val [mono] = goal (the_context ()) "mono(f) ==> lfp(f) = f(lfp(f))";
by (REPEAT (resolve_tac [equalityI,lfp_lemma2,lfp_lemma3,mono] 1));
qed "lfp_Tarski";
(*** General induction rule for least fixed points ***)
-val [lfp,mono,indhyp] = goal Lfp.thy
+val [lfp,mono,indhyp] = goal (the_context ())
"[| a: lfp(f); mono(f); \
\ !!x. [| x: f(lfp(f) Int {x. P(x)}) |] ==> P(x) \
\ |] ==> P(a)";
by (res_inst_tac [("a","a")] (Int_lower2 RS subsetD RS CollectD) 1);
by (rtac (lfp RSN (2, lfp_lowerbound RS subsetD)) 1);
-by (EVERY1 [rtac Int_greatest, rtac subset_trans,
+by (EVERY1 [rtac Int_greatest, rtac subset_trans,
rtac (Int_lower1 RS (mono RS monoD)),
rtac (mono RS lfp_lemma2),
rtac (CollectI RS subsetI), rtac indhyp, atac]);
@@ -57,12 +48,12 @@
(** Definition forms of lfp_Tarski and induct, to control unfolding **)
-val [rew,mono] = goal Lfp.thy "[| h==lfp(f); mono(f) |] ==> h = f(h)";
+val [rew,mono] = goal (the_context ()) "[| h==lfp(f); mono(f) |] ==> h = f(h)";
by (rewtac rew);
by (rtac (mono RS lfp_Tarski) 1);
qed "def_lfp_Tarski";
-val rew::prems = goal Lfp.thy
+val rew::prems = goal (the_context ())
"[| A == lfp(f); a:A; mono(f); \
\ !!x. [| x: f(A Int {x. P(x)}) |] ==> P(x) \
\ |] ==> P(a)";
@@ -71,7 +62,7 @@
qed "def_induct";
(*Monotonicity of lfp!*)
-val prems = goal Lfp.thy
+val prems = goal (the_context ())
"[| mono(g); !!Z. f(Z)<=g(Z) |] ==> lfp(f) <= lfp(g)";
by (rtac lfp_lowerbound 1);
by (rtac subset_trans 1);
@@ -79,4 +70,3 @@
by (rtac lfp_lemma2 1);
by (resolve_tac prems 1);
qed "lfp_mono";
-