src/CCL/Lfp.ML

-(*  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]);
 qed "induct";
 
 (** 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)";
 by (EVERY1 [rtac induct,        (*backtracking to force correct induction*)
             REPEAT1 o (ares_tac (map (rewrite_rule [rew]) prems))]);
 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);
 by (resolve_tac prems 1);
 by (rtac lfp_lemma2 1);
 by (resolve_tac prems 1);
 qed "lfp_mono";
-