Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
authornipkow
Wed, 19 Jan 1994 17:35:01 +0100
changeset 243 c22b85994e17
parent 242 8fe3e66abf0c
child 244 929fc2c63bd0
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF in HOL.
src/HOLCF/Cfun1.ML
src/HOLCF/Cfun1.thy
src/HOLCF/Cfun2.ML
src/HOLCF/Cfun2.thy
src/HOLCF/Cfun3.ML
src/HOLCF/Cfun3.thy
src/HOLCF/Cont.ML
src/HOLCF/Cont.thy
src/HOLCF/Cprod1.ML
src/HOLCF/Cprod1.thy
src/HOLCF/Cprod2.ML
src/HOLCF/Cprod2.thy
src/HOLCF/Cprod3.ML
src/HOLCF/Cprod3.thy
src/HOLCF/Dnat.ML
src/HOLCF/Dnat.thy
src/HOLCF/Dnat2.ML
src/HOLCF/Dnat2.thy
src/HOLCF/Fix.ML
src/HOLCF/Fix.thy
src/HOLCF/Fun1.ML
src/HOLCF/Fun1.thy
src/HOLCF/Fun2.ML
src/HOLCF/Fun2.thy
src/HOLCF/Fun3.ML
src/HOLCF/Fun3.thy
src/HOLCF/HOLCF.ML
src/HOLCF/HOLCF.thy
src/HOLCF/Holcfb.ML
src/HOLCF/Holcfb.thy
src/HOLCF/Lift1.ML
src/HOLCF/Lift1.thy
src/HOLCF/Lift2.ML
src/HOLCF/Lift2.thy
src/HOLCF/Lift3.ML
src/HOLCF/Lift3.thy
src/HOLCF/Makefile
src/HOLCF/One.ML
src/HOLCF/One.thy
src/HOLCF/Pcpo.ML
src/HOLCF/Pcpo.thy
src/HOLCF/Porder.ML
src/HOLCF/Porder.thy
src/HOLCF/ROOT.ML
src/HOLCF/Sprod0.ML
src/HOLCF/Sprod0.thy
src/HOLCF/Sprod1.ML
src/HOLCF/Sprod1.thy
src/HOLCF/Sprod2.ML
src/HOLCF/Sprod2.thy
src/HOLCF/Sprod3.ML
src/HOLCF/Sprod3.thy
src/HOLCF/Ssum0.ML
src/HOLCF/Ssum0.thy
src/HOLCF/Ssum1.ML
src/HOLCF/Ssum1.thy
src/HOLCF/Ssum2.ML
src/HOLCF/Ssum2.thy
src/HOLCF/Ssum3.ML
src/HOLCF/Ssum3.thy
src/HOLCF/Stream.ML
src/HOLCF/Stream.thy
src/HOLCF/Stream2.ML
src/HOLCF/Stream2.thy
src/HOLCF/Tr1.ML
src/HOLCF/Tr1.thy
src/HOLCF/Tr2.ML
src/HOLCF/Tr2.thy
src/HOLCF/Void.ML
src/HOLCF/Void.thy
src/HOLCF/ccc1.ML
src/HOLCF/ccc1.thy
src/HOLCF/cfun1.ML
src/HOLCF/cfun1.thy
src/HOLCF/cfun2.ML
src/HOLCF/cfun2.thy
src/HOLCF/cfun3.ML
src/HOLCF/cfun3.thy
src/HOLCF/cinfix.ML
src/HOLCF/cont.ML
src/HOLCF/cont.thy
src/HOLCF/cprod1.ML
src/HOLCF/cprod1.thy
src/HOLCF/cprod2.ML
src/HOLCF/cprod2.thy
src/HOLCF/cprod3.ML
src/HOLCF/cprod3.thy
src/HOLCF/dnat.ML
src/HOLCF/dnat.thy
src/HOLCF/dnat2.ML
src/HOLCF/dnat2.thy
src/HOLCF/fix.ML
src/HOLCF/fix.thy
src/HOLCF/fun1.ML
src/HOLCF/fun1.thy
src/HOLCF/fun2.ML
src/HOLCF/fun2.thy
src/HOLCF/fun3.ML
src/HOLCF/fun3.thy
src/HOLCF/holcf.ML
src/HOLCF/holcf.thy
src/HOLCF/holcfb.ML
src/HOLCF/holcfb.thy
src/HOLCF/lift1.ML
src/HOLCF/lift1.thy
src/HOLCF/lift2.ML
src/HOLCF/lift2.thy
src/HOLCF/lift3.ML
src/HOLCF/lift3.thy
src/HOLCF/one.ML
src/HOLCF/one.thy
src/HOLCF/pcpo.ML
src/HOLCF/pcpo.thy
src/HOLCF/porder.ML
src/HOLCF/porder.thy
src/HOLCF/sprod0.ML
src/HOLCF/sprod0.thy
src/HOLCF/sprod1.ML
src/HOLCF/sprod1.thy
src/HOLCF/sprod2.ML
src/HOLCF/sprod2.thy
src/HOLCF/sprod3.ML
src/HOLCF/sprod3.thy
src/HOLCF/ssum0.ML
src/HOLCF/ssum0.thy
src/HOLCF/ssum1.ML
src/HOLCF/ssum1.thy
src/HOLCF/ssum2.ML
src/HOLCF/ssum2.thy
src/HOLCF/ssum3.ML
src/HOLCF/ssum3.thy
src/HOLCF/stream.ML
src/HOLCF/stream.thy
src/HOLCF/stream2.ML
src/HOLCF/stream2.thy
src/HOLCF/test
src/HOLCF/tr1.ML
src/HOLCF/tr1.thy
src/HOLCF/tr2.ML
src/HOLCF/tr2.thy
src/HOLCF/void.ML
src/HOLCF/void.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cfun1.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,129 @@
+(*  Title: 	HOLCF/cfun1.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for cfun1.thy 
+*)
+
+open Cfun1;
+
+(* ------------------------------------------------------------------------ *)
+(* A non-emptyness result for Cfun                                          *)
+(* ------------------------------------------------------------------------ *)
+
+val CfunI = prove_goalw Cfun1.thy [Cfun_def] "(% x.x):Cfun"
+ (fn prems =>
+	[
+	(rtac (mem_Collect_eq RS ssubst) 1),
+	(rtac contX_id 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* less_cfun is a partial order on type 'a -> 'b                            *)
+(* ------------------------------------------------------------------------ *)
+
+val refl_less_cfun = prove_goalw Cfun1.thy [less_cfun_def] "less_cfun(f,f)"
+(fn prems =>
+	[
+	(rtac refl_less 1)
+	]);
+
+val antisym_less_cfun = prove_goalw Cfun1.thy [less_cfun_def] 
+	"[|less_cfun(f1,f2); less_cfun(f2,f1)|] ==> f1 = f2"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac injD 1),
+	(rtac antisym_less 2),
+	(atac 3),
+	(atac 2),
+	(rtac inj_inverseI 1),
+	(rtac Rep_Cfun_inverse 1)
+	]);
+
+val trans_less_cfun = prove_goalw Cfun1.thy [less_cfun_def] 
+	"[|less_cfun(f1,f2); less_cfun(f2,f3)|] ==> less_cfun(f1,f3)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac trans_less 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* lemmas about application of continuous functions                         *)
+(* ------------------------------------------------------------------------ *)
+
+val cfun_cong = prove_goal Cfun1.thy 
+	 "[| f=g; x=y |] ==> f[x] = g[y]"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val cfun_fun_cong = prove_goal Cfun1.thy "f=g ==> f[x] = g[x]"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac cfun_cong 1),
+	(rtac refl 1)
+	]);
+
+val cfun_arg_cong = prove_goal Cfun1.thy "x=y ==> f[x] = f[y]"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac cfun_cong 1),
+	(rtac refl 1),
+	(atac 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* additional lemma about the isomorphism between -> and Cfun               *)
+(* ------------------------------------------------------------------------ *)
+
+val Abs_Cfun_inverse2 = prove_goal Cfun1.thy "contX(f) ==> fapp(fabs(f)) = f"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac Abs_Cfun_inverse 1),
+	(rewrite_goals_tac [Cfun_def]),
+	(etac (mem_Collect_eq RS ssubst) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* simplification of application                                            *)
+(* ------------------------------------------------------------------------ *)
+
+val Cfunapp2 = prove_goal Cfun1.thy 
+	"contX(f) ==> (fabs(f))[x] = f(x)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac (Abs_Cfun_inverse2 RS fun_cong) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* beta - equality for continuous functions                                 *)
+(* ------------------------------------------------------------------------ *)
+
+val beta_cfun = prove_goal Cfun1.thy 
+	"contX(c1) ==> (LAM x .c1(x))[u] = c1(u)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac Cfunapp2 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* load ML file cinfix.ML                                                   *)
+(* ------------------------------------------------------------------------ *)
+
+
+ writeln "Reading file  cinfix.ML"; 
+use "cinfix.ML";
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cfun1.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,45 @@
+(*  Title: 	HOLCF/cfun1.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Definition of the type ->  of continuous functions
+
+*)
+
+Cfun1 = Cont +
+
+
+(* new type of continuous functions *)
+
+types "->" 2        (infixr 5)
+
+arities "->" :: (pcpo,pcpo)term		(* No properties for ->'s range *)
+
+consts  
+	Cfun	:: "('a => 'b)set"
+	fapp	:: "('a -> 'b)=>('a => 'b)"	("(_[_])" [11,0] 1000)
+						(* usually Rep_Cfun *)
+						(* application      *)
+
+	fabs	:: "('a => 'b)=>('a -> 'b)"	(binder "LAM " 10)
+						(* usually Abs_Cfun *)
+						(* abstraction      *)
+
+	less_cfun :: "[('a -> 'b),('a -> 'b)]=>bool"
+
+rules 
+
+  Cfun_def	"Cfun == {f. contX(f)}"
+
+  (*faking a type definition... *)
+  (* -> is isomorphic to Cfun   *)
+
+  Rep_Cfun		"fapp(fo):Cfun"
+  Rep_Cfun_inverse	"fabs(fapp(fo)) = fo"
+  Abs_Cfun_inverse	"f:Cfun ==> fapp(fabs(f))=f"
+
+  (*defining the abstract constants*)
+  less_cfun_def		"less_cfun(fo1,fo2) == ( fapp(fo1) << fapp(fo2) )"
+
+end
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cfun2.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,276 @@
+(*  Title: 	HOLCF/cfun2.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for cfun2.thy 
+*)
+
+open Cfun2;
+
+(* ------------------------------------------------------------------------ *)
+(* access to less_cfun in class po                                          *)
+(* ------------------------------------------------------------------------ *)
+
+val less_cfun = prove_goal Cfun2.thy "( f1 << f2 ) = (fapp(f1) << fapp(f2))"
+(fn prems =>
+	[
+	(rtac (inst_cfun_po RS ssubst) 1),
+	(fold_goals_tac [less_cfun_def]),
+	(rtac refl 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* Type 'a ->'b  is pointed                                                 *)
+(* ------------------------------------------------------------------------ *)
+
+val minimal_cfun = prove_goalw Cfun2.thy [UU_cfun_def] "UU_cfun << f"
+(fn prems =>
+	[
+	(rtac (less_cfun RS ssubst) 1),
+	(rtac (Abs_Cfun_inverse2 RS ssubst) 1),
+	(rtac contX_const 1),
+	(fold_goals_tac [UU_fun_def]),
+	(rtac minimal_fun 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* fapp yields continuous functions in 'a => 'b                             *)
+(* this is continuity of fapp in its 'second' argument                      *)
+(* contX_fapp2 ==> monofun_fapp2 & contlub_fapp2                            *)
+(* ------------------------------------------------------------------------ *)
+
+val contX_fapp2 = prove_goal Cfun2.thy "contX(fapp(fo))"
+(fn prems =>
+	[
+	(res_inst_tac [("P","contX")] CollectD 1),
+	(fold_goals_tac [Cfun_def]),
+	(rtac Rep_Cfun 1)
+	]);
+
+val monofun_fapp2 = contX_fapp2 RS contX2mono;
+(* monofun(fapp(?fo1)) *)
+
+
+val contlub_fapp2 = contX_fapp2 RS contX2contlub;
+(* contlub(fapp(?fo1)) *)
+
+(* ------------------------------------------------------------------------ *)
+(* expanded thms contX_fapp2, contlub_fapp2                                 *)
+(* looks nice with mixfix syntac _[_]                                       *)
+(* ------------------------------------------------------------------------ *)
+
+val contX_cfun_arg = (contX_fapp2 RS contXE RS spec RS mp);
+(* is_chain(?x1) ==> range(%i. ?fo3[?x1(i)]) <<| ?fo3[lub(range(?x1))]      *)
+ 
+val contlub_cfun_arg = (contlub_fapp2 RS contlubE RS spec RS mp);
+(* is_chain(?x1) ==> ?fo4[lub(range(?x1))] = lub(range(%i. ?fo4[?x1(i)]))   *)
+
+
+
+(* ------------------------------------------------------------------------ *)
+(* fapp is monotone in its 'first' argument                                 *)
+(* ------------------------------------------------------------------------ *)
+
+val monofun_fapp1 = prove_goalw Cfun2.thy [monofun] "monofun(fapp)"
+(fn prems =>
+	[
+	(strip_tac 1),
+	(etac (less_cfun RS subst) 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* monotonicity of application fapp in mixfix syntax [_]_                   *)
+(* ------------------------------------------------------------------------ *)
+
+val monofun_cfun_fun = prove_goal Cfun2.thy  "f1 << f2 ==> f1[x] << f2[x]"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("x","x")] spec 1),
+	(rtac (less_fun RS subst) 1),
+	(etac (monofun_fapp1 RS monofunE RS spec RS spec RS mp) 1)
+	]);
+
+
+val monofun_cfun_arg = (monofun_fapp2 RS monofunE RS spec RS spec RS mp);
+(* ?x2 << ?x1 ==> ?fo5[?x2] << ?fo5[?x1]                                    *)
+
+(* ------------------------------------------------------------------------ *)
+(* monotonicity of fapp in both arguments in mixfix syntax [_]_             *)
+(* ------------------------------------------------------------------------ *)
+
+val monofun_cfun = prove_goal Cfun2.thy
+	"[|f1<<f2;x1<<x2|] ==> f1[x1] << f2[x2]"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac trans_less 1),
+	(etac monofun_cfun_arg 1),
+	(etac monofun_cfun_fun 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* ch2ch - rules for the type 'a -> 'b                                      *)
+(* use MF2 lemmas from Cont.ML                                              *)
+(* ------------------------------------------------------------------------ *)
+
+val ch2ch_fappR = prove_goal Cfun2.thy 
+ "is_chain(Y) ==> is_chain(%i. f[Y(i)])"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac (monofun_fapp2 RS ch2ch_MF2R) 1)
+	]);
+
+
+val ch2ch_fappL = (monofun_fapp1 RS ch2ch_MF2L);
+(* is_chain(?F) ==> is_chain(%i. ?F(i)[?x])                                 *)
+
+
+(* ------------------------------------------------------------------------ *)
+(*  the lub of a chain of continous functions is monotone                   *)
+(* use MF2 lemmas from Cont.ML                                              *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_cfun_mono = prove_goal Cfun2.thy 
+	"is_chain(F) ==> monofun(% x.lub(range(% j.F(j)[x])))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac lub_MF2_mono 1),
+	(rtac monofun_fapp1 1),
+	(rtac (monofun_fapp2 RS allI) 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* a lemma about the exchange of lubs for type 'a -> 'b                     *)
+(* use MF2 lemmas from Cont.ML                                              *)
+(* ------------------------------------------------------------------------ *)
+
+val ex_lubcfun = prove_goal Cfun2.thy
+	"[| is_chain(F); is_chain(Y) |] ==>\
+\		lub(range(%j. lub(range(%i. F(j)[Y(i)])))) =\
+\		lub(range(%i. lub(range(%j. F(j)[Y(i)]))))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac ex_lubMF2 1),
+	(rtac monofun_fapp1 1),
+	(rtac (monofun_fapp2 RS allI) 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* the lub of a chain of cont. functions is continuous                      *)
+(* ------------------------------------------------------------------------ *)
+
+val contX_lubcfun = prove_goal Cfun2.thy 
+	"is_chain(F) ==> contX(% x.lub(range(% j.F(j)[x])))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac monocontlub2contX 1),
+	(etac lub_cfun_mono 1),
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac (contlub_cfun_arg RS ext RS ssubst) 1),
+	(atac 1),
+	(etac ex_lubcfun 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* type 'a -> 'b is chain complete                                          *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_cfun = prove_goal Cfun2.thy 
+  "is_chain(CCF) ==> range(CCF) <<| fabs(% x.lub(range(% i.CCF(i)[x])))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_lubI 1),
+	(rtac conjI 1),
+	(rtac ub_rangeI 1),  
+	(rtac allI 1),
+	(rtac (less_cfun RS ssubst) 1),
+	(rtac (Abs_Cfun_inverse2 RS ssubst) 1),
+	(etac contX_lubcfun 1),
+	(rtac (lub_fun RS is_lubE RS conjunct1 RS ub_rangeE RS spec) 1),
+	(etac (monofun_fapp1 RS ch2ch_monofun) 1),
+	(strip_tac 1),
+	(rtac (less_cfun RS ssubst) 1),
+	(rtac (Abs_Cfun_inverse2 RS ssubst) 1),
+	(etac contX_lubcfun 1),
+	(rtac (lub_fun RS is_lubE RS conjunct2 RS spec RS mp) 1),
+	(etac (monofun_fapp1 RS ch2ch_monofun) 1),
+	(etac (monofun_fapp1 RS ub2ub_monofun) 1)
+	]);
+
+val thelub_cfun = (lub_cfun RS thelubI);
+(* 
+is_chain(?CCF1) ==> lub(range(?CCF1)) = fabs(%x. lub(range(%i. ?CCF1(i)[x])))
+*)
+
+val cpo_fun = prove_goal Cfun2.thy 
+  "is_chain(CCF::nat=>('a::pcpo->'b::pcpo)) ==> ? x. range(CCF) <<| x"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac exI 1),
+	(etac lub_cfun 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* Extensionality in 'a -> 'b                                               *)
+(* ------------------------------------------------------------------------ *)
+
+val ext_cfun = prove_goal Cfun1.thy "(!!x. f[x] = g[x]) ==> f = g"
+ (fn prems =>
+	[
+	(res_inst_tac [("t","f")] (Rep_Cfun_inverse RS subst) 1),
+	(res_inst_tac [("t","g")] (Rep_Cfun_inverse RS subst) 1),
+	(res_inst_tac [("f","fabs")] arg_cong 1),
+	(rtac ext 1),
+	(resolve_tac prems 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* Monotonicity of fabs                                                     *)
+(* ------------------------------------------------------------------------ *)
+
+val semi_monofun_fabs = prove_goal Cfun2.thy 
+	"[|contX(f);contX(g);f<<g|]==>fabs(f)<<fabs(g)"
+ (fn prems =>
+	[
+	(rtac (less_cfun RS iffD2) 1),
+	(rtac (Abs_Cfun_inverse2 RS ssubst) 1),
+	(resolve_tac prems 1),
+	(rtac (Abs_Cfun_inverse2 RS ssubst) 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* Extenionality wrt. << in 'a -> 'b                                        *)
+(* ------------------------------------------------------------------------ *)
+
+val less_cfun2 = prove_goal Cfun2.thy "(!!x. f[x] << g[x]) ==> f << g"
+ (fn prems =>
+	[
+	(res_inst_tac [("t","f")] (Rep_Cfun_inverse RS subst) 1),
+	(res_inst_tac [("t","g")] (Rep_Cfun_inverse RS subst) 1),
+	(rtac semi_monofun_fabs 1),
+	(rtac contX_fapp2 1),
+	(rtac contX_fapp2 1),
+	(rtac (less_fun RS iffD2) 1),
+	(rtac allI 1),
+	(resolve_tac prems 1)
+	]);
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cfun2.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,39 @@
+(*  Title: 	HOLCF/cfun2.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Class Instance ->::(pcpo,pcpo)po
+
+*)
+
+Cfun2 = Cfun1 + 
+
+(* Witness for the above arity axiom is cfun1.ML *)
+arities "->" :: (pcpo,pcpo)po
+
+consts	
+	UU_cfun  :: "'a->'b"
+
+rules
+
+(* instance of << for type ['a -> 'b]  *)
+
+inst_cfun_po	"(op <<)::['a->'b,'a->'b]=>bool = less_cfun"
+
+(* definitions *)
+(* The least element in type 'a->'b *)
+
+UU_cfun_def	"UU_cfun == fabs(% x.UU)"
+
+end
+
+ML
+
+(* ----------------------------------------------------------------------*)
+(* unique setup of print translation for fapp                            *)
+(* ----------------------------------------------------------------------*)
+
+val print_translation = [("fapp",fapptr')];
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cfun3.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,403 @@
+(*  Title: 	HOLCF/cfun3.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+*)
+
+open Cfun3;
+
+(* ------------------------------------------------------------------------ *)
+(* the contlub property for fapp its 'first' argument                       *)
+(* ------------------------------------------------------------------------ *)
+
+val contlub_fapp1 = prove_goal Cfun3.thy "contlub(fapp)"
+(fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac (expand_fun_eq RS iffD2) 1),
+	(strip_tac 1),
+	(rtac (lub_cfun RS thelubI RS ssubst) 1),
+	(atac 1),
+	(rtac (Cfunapp2 RS ssubst) 1),
+	(etac contX_lubcfun 1),
+	(rtac (lub_fun RS thelubI RS ssubst) 1),
+	(etac (monofun_fapp1 RS ch2ch_monofun) 1),
+	(rtac refl 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* the contX property for fapp in its first argument                        *)
+(* ------------------------------------------------------------------------ *)
+
+val contX_fapp1 = prove_goal Cfun3.thy "contX(fapp)"
+(fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_fapp1 1),
+	(rtac contlub_fapp1 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* contlub, contX properties of fapp in its first argument in mixfix _[_]   *)
+(* ------------------------------------------------------------------------ *)
+
+val contlub_cfun_fun = prove_goal Cfun3.thy 
+"is_chain(FY) ==>\
+\ lub(range(FY))[x] = lub(range(%i.FY(i)[x]))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac trans 1),
+	(etac (contlub_fapp1 RS contlubE RS spec RS mp RS fun_cong) 1),
+	(rtac (thelub_fun RS ssubst) 1),
+	(etac (monofun_fapp1 RS ch2ch_monofun) 1),
+	(rtac refl 1)
+	]);
+
+
+val contX_cfun_fun = prove_goal Cfun3.thy 
+"is_chain(FY) ==>\
+\ range(%i.FY(i)[x]) <<| lub(range(FY))[x]"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac thelubE 1),
+	(etac ch2ch_fappL 1),
+	(etac (contlub_cfun_fun RS sym) 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* contlub, contX  properties of fapp in both argument in mixfix _[_]       *)
+(* ------------------------------------------------------------------------ *)
+
+val contlub_cfun = prove_goal Cfun3.thy 
+"[|is_chain(FY);is_chain(TY)|] ==>\
+\ lub(range(FY))[lub(range(TY))] = lub(range(%i.FY(i)[TY(i)]))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac contlub_CF2 1),
+	(rtac contX_fapp1 1),
+	(rtac allI 1),
+	(rtac contX_fapp2 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+val contX_cfun = prove_goal Cfun3.thy 
+"[|is_chain(FY);is_chain(TY)|] ==>\
+\ range(%i.FY(i)[TY(i)]) <<| lub(range(FY))[lub(range(TY))]"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac thelubE 1),
+	(rtac (monofun_fapp1 RS ch2ch_MF2LR) 1),
+	(rtac allI 1),
+	(rtac monofun_fapp2 1),
+	(atac 1),
+	(atac 1),
+	(etac (contlub_cfun RS sym) 1),
+	(atac 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* contX2contX lemma for fapp                                               *)
+(* ------------------------------------------------------------------------ *)
+
+val contX2contX_fapp = prove_goal Cfun3.thy 
+	"[|contX(%x.ft(x));contX(%x.tt(x))|] ==> contX(%x.(ft(x))[tt(x)])"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac contX2contX_app2 1),
+	(rtac contX2contX_app2 1),
+	(rtac contX_const 1),
+	(rtac contX_fapp1 1),
+	(atac 1),
+	(rtac contX_fapp2 1),
+	(atac 1)
+	]);
+
+
+
+(* ------------------------------------------------------------------------ *)
+(* contX2mono Lemma for %x. LAM y. c1(x,y)                                  *)
+(* ------------------------------------------------------------------------ *)
+
+val contX2mono_LAM = prove_goal Cfun3.thy 
+ "[|!x.contX(c1(x)); !y.monofun(%x.c1(x,y))|] ==>\
+\	 		monofun(%x. LAM y. c1(x,y))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac monofunI 1),
+	(strip_tac 1),
+	(rtac (less_cfun RS ssubst) 1),
+	(rtac (less_fun RS ssubst) 1),
+	(rtac allI 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(etac spec 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(etac spec 1),
+	(etac ((hd (tl prems)) RS spec RS monofunE RS spec RS spec RS mp) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* contX2contX Lemma for %x. LAM y. c1(x,y)                                 *)
+(* ------------------------------------------------------------------------ *)
+
+val contX2contX_LAM = prove_goal Cfun3.thy 
+ "[| !x.contX(c1(x)); !y.contX(%x.c1(x,y)) |] ==> contX(%x. LAM y. c1(x,y))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac monocontlub2contX 1),
+	(etac contX2mono_LAM 1),
+	(rtac (contX2mono RS allI) 1),
+	(etac spec 1),
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac (thelub_cfun RS ssubst) 1),
+	(rtac (contX2mono_LAM RS ch2ch_monofun) 1),
+	(atac 1),
+	(rtac (contX2mono RS allI) 1),
+	(etac spec 1),
+	(atac 1),
+	(res_inst_tac [("f","fabs")] arg_cong 1),
+	(rtac ext 1),
+	(rtac (beta_cfun RS ext RS ssubst) 1),
+	(etac spec 1),
+	(rtac (contX2contlub RS contlubE 
+		RS spec RS mp ) 1),
+	(etac spec 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* elimination of quantifier in premisses of contX2contX_LAM yields good    *)
+(* lemma for the contX tactic                                               *)
+(* ------------------------------------------------------------------------ *)
+
+val contX2contX_LAM2 = (allI RSN (2,(allI RS contX2contX_LAM)));
+(*
+	[| !!x. contX(?c1.0(x)); !!y. contX(%x. ?c1.0(x,y)) |] ==>
+					contX(%x. LAM y. ?c1.0(x,y))
+*)
+
+(* ------------------------------------------------------------------------ *)
+(* contX2contX tactic                                                       *)
+(* ------------------------------------------------------------------------ *)
+
+val contX_lemmas = [contX_const, contX_id, contX_fapp2,
+			contX2contX_fapp,contX2contX_LAM2];
+
+
+val contX_tac = (fn i => (resolve_tac contX_lemmas i));
+
+val contX_tacR = (fn i => (REPEAT (contX_tac i)));
+
+(* ------------------------------------------------------------------------ *)
+(* function application _[_]  is strict in its first arguments              *)
+(* ------------------------------------------------------------------------ *)
+
+val strict_fapp1 = prove_goal Cfun3.thy "UU[x] = UU"
+ (fn prems =>
+	[
+	(rtac (inst_cfun_pcpo RS ssubst) 1),
+	(rewrite_goals_tac [UU_cfun_def]),
+	(rtac (beta_cfun RS ssubst) 1),
+	(contX_tac 1),
+	(rtac refl 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* results about strictify                                                  *)
+(* ------------------------------------------------------------------------ *)
+
+val Istrictify1 = prove_goalw Cfun3.thy [Istrictify_def]
+	"Istrictify(f)(UU)=UU"
+ (fn prems =>
+	[
+	(rtac select_equality 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val Istrictify2 = prove_goalw Cfun3.thy [Istrictify_def]
+	"~x=UU ==> Istrictify(f)(x)=f[x]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac select_equality 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val monofun_Istrictify1 = prove_goal Cfun3.thy "monofun(Istrictify)"
+ (fn prems =>
+	[
+	(rtac monofunI 1),
+	(strip_tac 1),
+	(rtac (less_fun RS iffD2) 1),
+	(strip_tac 1),
+	(res_inst_tac [("Q","xa=UU")] (excluded_middle RS disjE) 1),
+	(rtac (Istrictify2 RS ssubst) 1),
+	(atac 1),
+	(rtac (Istrictify2 RS ssubst) 1),
+	(atac 1),
+	(rtac monofun_cfun_fun 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(rtac (Istrictify1 RS ssubst) 1),
+	(rtac (Istrictify1 RS ssubst) 1),
+	(rtac refl_less 1)
+	]);
+
+val monofun_Istrictify2 = prove_goal Cfun3.thy "monofun(Istrictify(f))"
+ (fn prems =>
+	[
+	(rtac monofunI 1),
+	(strip_tac 1),
+	(res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1),
+	(rtac (Istrictify2 RS ssubst) 1),
+	(etac notUU_I 1),
+	(atac 1),
+	(rtac (Istrictify2 RS ssubst) 1),
+	(atac 1),
+	(rtac monofun_cfun_arg 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(rtac (Istrictify1 RS ssubst) 1),
+	(rtac minimal 1)
+	]);
+
+
+val contlub_Istrictify1 = prove_goal Cfun3.thy "contlub(Istrictify)"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac (expand_fun_eq RS iffD2) 1),
+	(strip_tac 1),
+	(rtac (thelub_fun RS ssubst) 1),
+	(etac (monofun_Istrictify1 RS ch2ch_monofun) 1),
+	(res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1),
+	(rtac (Istrictify2 RS ssubst) 1),
+	(atac 1),
+	(rtac (Istrictify2 RS ext RS ssubst) 1),
+	(atac 1),
+	(rtac (thelub_cfun RS ssubst) 1),
+	(atac 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_lubcfun 1),
+	(atac 1),
+	(rtac refl 1),
+	(hyp_subst_tac 1),
+	(rtac (Istrictify1 RS ssubst) 1),
+	(rtac (Istrictify1 RS ext RS ssubst) 1),
+	(rtac (chain_UU_I_inverse RS sym) 1),
+	(rtac (refl RS allI) 1)
+	]);
+
+val contlub_Istrictify2 = prove_goal Cfun3.thy "contlub(Istrictify(f))"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(res_inst_tac [("Q","lub(range(Y))=UU")] classical2 1),
+	(res_inst_tac [("t","lub(range(Y))")] subst 1),
+	(rtac sym 1),
+	(atac 1),
+	(rtac (Istrictify1 RS ssubst) 1),
+	(rtac sym 1),
+	(rtac chain_UU_I_inverse 1),
+	(strip_tac 1),
+	(res_inst_tac [("t","Y(i)"),("s","UU")] subst 1),
+	(rtac sym 1),
+	(rtac (chain_UU_I RS spec) 1),
+	(atac 1),
+	(atac 1),
+	(rtac Istrictify1 1),
+	(rtac (Istrictify2 RS ssubst) 1),
+	(atac 1),
+	(res_inst_tac [("s","lub(range(%i. f[Y(i)]))")] trans 1),
+	(rtac contlub_cfun_arg 1),
+	(atac 1),
+	(rtac lub_equal2 1),
+	(rtac (chain_mono2 RS exE) 1),
+	(atac 2),
+	(rtac chain_UU_I_inverse2 1),
+	(atac 1),
+	(rtac exI 1),
+	(strip_tac 1),
+	(rtac (Istrictify2 RS sym) 1),
+	(fast_tac HOL_cs 1),
+	(rtac ch2ch_monofun 1),
+	(rtac monofun_fapp2 1),
+	(atac 1),
+	(rtac ch2ch_monofun 1),
+	(rtac monofun_Istrictify2 1),
+	(atac 1)
+	]);
+
+
+val contX_Istrictify1 =	(contlub_Istrictify1 RS 
+	(monofun_Istrictify1 RS monocontlub2contX)); 
+
+val contX_Istrictify2 = (contlub_Istrictify2 RS 
+	(monofun_Istrictify2 RS monocontlub2contX)); 
+
+
+val strictify1 = prove_goalw Cfun3.thy [strictify_def]
+	"strictify[f][UU]=UU"
+ (fn prems =>
+	[
+	(rtac (beta_cfun RS ssubst) 1),
+	(contX_tac 1),
+	(rtac contX_Istrictify2 1),
+	(rtac contX2contX_CF1L 1),
+	(rtac contX_Istrictify1 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Istrictify2 1),
+	(rtac Istrictify1 1)
+	]);
+
+val strictify2 = prove_goalw Cfun3.thy [strictify_def]
+	"~x=UU ==> strictify[f][x]=f[x]"
+ (fn prems =>
+	[
+	(rtac (beta_cfun RS ssubst) 1),
+	(contX_tac 1),
+	(rtac contX_Istrictify2 1),
+	(rtac contX2contX_CF1L 1),
+	(rtac contX_Istrictify1 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Istrictify2 1),
+	(rtac Istrictify2 1),
+	(resolve_tac prems 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* Instantiate the simplifier                                               *)
+(* ------------------------------------------------------------------------ *)
+
+val Cfun_rews  = [minimal,refl_less,beta_cfun,strict_fapp1,strictify1,
+		strictify2];
+
+(* ------------------------------------------------------------------------ *)
+(* use contX_tac as autotac.                                                *)
+(* ------------------------------------------------------------------------ *)
+
+val Cfun_ss = HOL_ss 
+	addsimps  Cfun_rews 
+	setsolver 
+	(fn thms => (resolve_tac (TrueI::refl::thms)) ORELSE' atac ORELSE'
+		    (fn i => DEPTH_SOLVE_1 (contX_tac i))
+	);
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cfun3.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,31 @@
+(*  Title: 	HOLCF/cfun3.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Class instance of  -> for class pcpo
+
+*)
+
+Cfun3 = Cfun2 +
+
+arities "->"	:: (pcpo,pcpo)pcpo		(* Witness cfun2.ML *)
+
+consts  
+	Istrictify   :: "('a->'b)=>'a=>'b"
+	strictify    :: "('a->'b)->'a->'b"
+
+rules 
+
+inst_cfun_pcpo	"UU::'a->'b = UU_cfun"
+
+Istrictify_def	"Istrictify(f,x) == (@z.\
+\			  ( x=UU --> z = UU)\
+\			& (~x=UU --> z = f[x]))"	
+
+strictify_def	"strictify == (LAM f x.Istrictify(f,x))"
+
+end
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cont.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,670 @@
+(*  Title: 	HOLCF/cont.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for cont.thy 
+*)
+
+open Cont;
+
+(* ------------------------------------------------------------------------ *)
+(* access to definition                                                     *)
+(* ------------------------------------------------------------------------ *)
+
+val contlubI = prove_goalw Cont.thy [contlub]
+	"! Y. is_chain(Y) --> f(lub(range(Y))) = lub(range(%i. f(Y(i))))==>\
+\	 contlub(f)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(atac 1)
+	]);
+
+val contlubE = prove_goalw Cont.thy [contlub]
+	" contlub(f)==>\
+\         ! Y. is_chain(Y) --> f(lub(range(Y))) = lub(range(%i. f(Y(i))))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(atac 1)
+	]);
+
+
+val contXI = prove_goalw Cont.thy [contX]
+ "! Y. is_chain(Y) --> range(% i.f(Y(i))) <<| f(lub(range(Y))) ==> contX(f)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(atac 1)
+	]);
+
+val contXE = prove_goalw Cont.thy [contX]
+ "contX(f) ==> ! Y. is_chain(Y) --> range(% i.f(Y(i))) <<| f(lub(range(Y)))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(atac 1)
+	]);
+
+
+val monofunI = prove_goalw Cont.thy [monofun]
+	"! x y. x << y --> f(x) << f(y) ==> monofun(f)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(atac 1)
+	]);
+
+val monofunE = prove_goalw Cont.thy [monofun]
+	"monofun(f) ==> ! x y. x << y --> f(x) << f(y)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* the main purpose of cont.thy is to show:                                 *)
+(*              monofun(f) & contlub(f)  <==> contX(f)                      *)
+(* ------------------------------------------------------------------------ *)
+
+(* ------------------------------------------------------------------------ *)
+(* monotone functions map chains to chains                                  *)
+(* ------------------------------------------------------------------------ *)
+
+val ch2ch_monofun= prove_goal Cont.thy 
+	"[| monofun(f); is_chain(Y) |] ==> is_chain(%i. f(Y(i)))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_chainI 1),
+	(rtac allI 1),
+	(etac (monofunE RS spec RS spec RS mp) 1),
+	(etac (is_chainE RS spec) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* monotone functions map upper bound to upper bounds                       *)
+(* ------------------------------------------------------------------------ *)
+
+val ub2ub_monofun = prove_goal Cont.thy 
+ "[| monofun(f); range(Y) <| u|]  ==> range(%i.f(Y(i))) <| f(u)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac ub_rangeI 1),
+	(rtac allI 1),
+	(etac (monofunE RS spec RS spec RS mp) 1),
+	(etac (ub_rangeE RS spec) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* left to right: monofun(f) & contlub(f)  ==> contX(f)                     *)
+(* ------------------------------------------------------------------------ *)
+
+val monocontlub2contX = prove_goalw Cont.thy [contX]
+	"[|monofun(f);contlub(f)|] ==> contX(f)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(rtac thelubE 1),
+	(etac ch2ch_monofun 1),
+	(atac 1),
+	(etac (contlubE RS spec RS mp RS sym) 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* first a lemma about binary chains                                        *)
+(* ------------------------------------------------------------------------ *)
+
+val binchain_contX =  prove_goal Cont.thy
+"[| contX(f); x << y |]  ==> range(%i. f(if(i = 0,x,y))) <<| f(y)"
+(fn prems => 
+	[
+	(cut_facts_tac prems 1),
+	(rtac subst 1), 
+	(etac (contXE RS spec RS mp) 2),
+	(etac bin_chain 2),
+	(res_inst_tac [("y","y")] arg_cong 1),
+	(etac (lub_bin_chain RS thelubI) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* right to left: contX(f) ==> monofun(f) & contlub(f)                      *)
+(* part1:         contX(f) ==> monofun(f                                    *)
+(* ------------------------------------------------------------------------ *)
+
+val contX2mono =  prove_goalw Cont.thy [monofun]
+	"contX(f) ==> monofun(f)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(res_inst_tac [("s","if(0 = 0,x,y)")] subst 1),
+	(rtac (binchain_contX RS is_ub_lub) 2),
+	(atac 2),
+	(atac 2),
+	(simp_tac nat_ss 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* right to left: contX(f) ==> monofun(f) & contlub(f)                      *)
+(* part2:         contX(f) ==>              contlub(f)                      *)
+(* ------------------------------------------------------------------------ *)
+
+val contX2contlub = prove_goalw Cont.thy [contlub]
+	"contX(f) ==> contlub(f)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(rtac (thelubI RS sym) 1),
+	(etac (contXE RS spec RS mp) 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* The following results are about a curried function that is monotone      *)
+(* in both arguments                                                        *)
+(* ------------------------------------------------------------------------ *)
+
+val ch2ch_MF2L = prove_goal Cont.thy 
+"[|monofun(MF2::('a::po=>'b::po=>'c::po));\
+\	is_chain(F)|] ==> is_chain(%i. MF2(F(i),x))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac (ch2ch_monofun RS ch2ch_fun) 1),
+	(atac 1)
+	]);
+
+
+val ch2ch_MF2R = prove_goal Cont.thy "[|monofun(MF2(f)::('b::po=>'c::po));\
+\	is_chain(Y)|] ==> is_chain(%i. MF2(f,Y(i)))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac ch2ch_monofun 1),
+	(atac 1)
+	]);
+
+val ch2ch_MF2LR = prove_goal Cont.thy 
+"[|monofun(MF2::('a::po=>'b::po=>'c::pcpo));\
+\  !f.monofun(MF2(f)::('b::po=>'c::pcpo));\
+\	is_chain(F); is_chain(Y)|] ==> \
+\  is_chain(%i. MF2(F(i))(Y(i)))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_chainI 1),
+	(strip_tac 1 ),
+	(rtac trans_less 1),
+	(etac (ch2ch_MF2L RS is_chainE RS spec) 1),
+	(atac 1),
+	((rtac (monofunE RS spec RS spec RS mp) 1) THEN (etac spec 1)),
+	(etac (is_chainE RS spec) 1)
+	]);
+
+val ch2ch_lubMF2R = prove_goal Cont.thy 
+"[|monofun(MF2::('a::po=>'b::po=>'c::pcpo));\
+\  !f.monofun(MF2(f)::('b::po=>'c::pcpo));\
+\	is_chain(F);is_chain(Y)|] ==> \
+\	is_chain(%j. lub(range(%i. MF2(F(j),Y(i)))))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (lub_mono RS allI RS is_chainI) 1),
+	((rtac ch2ch_MF2R 1) THEN (etac spec 1)),
+	(atac 1),
+	((rtac ch2ch_MF2R 1) THEN (etac spec 1)),
+	(atac 1),
+	(strip_tac 1),
+	(rtac (is_chainE RS spec) 1),
+	(etac ch2ch_MF2L 1),
+	(atac 1)
+	]);
+
+
+val ch2ch_lubMF2L = prove_goal Cont.thy 
+"[|monofun(MF2::('a::po=>'b::po=>'c::pcpo));\
+\  !f.monofun(MF2(f)::('b::po=>'c::pcpo));\
+\	is_chain(F);is_chain(Y)|] ==> \
+\	is_chain(%i. lub(range(%j. MF2(F(j),Y(i)))))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (lub_mono RS allI RS is_chainI) 1),
+	(etac ch2ch_MF2L 1),
+	(atac 1),
+	(etac ch2ch_MF2L 1),
+	(atac 1),
+	(strip_tac 1),
+	(rtac (is_chainE RS spec) 1),
+	((rtac ch2ch_MF2R 1) THEN (etac spec 1)),
+	(atac 1)
+	]);
+
+
+val lub_MF2_mono = prove_goal Cont.thy 
+"[|monofun(MF2::('a::po=>'b::po=>'c::pcpo));\
+\  !f.monofun(MF2(f)::('b::po=>'c::pcpo));\
+\	is_chain(F)|] ==> \
+\	monofun(% x.lub(range(% j.MF2(F(j),x))))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac monofunI 1),
+	(strip_tac 1),
+	(rtac lub_mono 1),
+	(etac ch2ch_MF2L 1),
+	(atac 1),
+	(etac ch2ch_MF2L 1),
+	(atac 1),
+	(strip_tac 1),
+	((rtac (monofunE RS spec RS spec RS mp) 1) THEN (etac spec 1)),
+	(atac 1)
+	]);
+
+
+val ex_lubMF2 = prove_goal Cont.thy 
+"[|monofun(MF2::('a::po=>'b::po=>'c::pcpo));\
+\  !f.monofun(MF2(f)::('b::po=>'c::pcpo));\
+\	is_chain(F); is_chain(Y)|] ==> \
+\		lub(range(%j. lub(range(%i. MF2(F(j),Y(i)))))) =\
+\		lub(range(%i. lub(range(%j. MF2(F(j),Y(i))))))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac antisym_less 1),
+	(rtac is_lub_thelub 1),
+	(etac ch2ch_lubMF2R 1),
+	(atac 1),(atac 1),(atac 1),
+	(rtac ub_rangeI 1),
+	(strip_tac 1),
+	(rtac lub_mono 1),
+	((rtac ch2ch_MF2R 1) THEN (etac spec 1)),
+	(atac 1),
+	(etac ch2ch_lubMF2L 1),
+	(atac 1),(atac 1),(atac 1),
+	(strip_tac 1),
+	(rtac is_ub_thelub 1),
+	(etac ch2ch_MF2L 1),(atac 1),
+	(rtac is_lub_thelub 1),
+	(etac ch2ch_lubMF2L 1),
+	(atac 1),(atac 1),(atac 1),
+	(rtac ub_rangeI 1),
+	(strip_tac 1),
+	(rtac lub_mono 1),
+	(etac ch2ch_MF2L 1),(atac 1),
+	(etac ch2ch_lubMF2R 1),
+	(atac 1),(atac 1),(atac 1),
+	(strip_tac 1),
+	(rtac is_ub_thelub 1),
+	((rtac ch2ch_MF2R 1) THEN (etac spec 1)),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* The following results are about a curried function that is continuous    *)
+(* in both arguments                                                        *)
+(* ------------------------------------------------------------------------ *)
+
+val diag_lubCF2_1 = prove_goal Cont.thy 
+"[|contX(CF2);!f.contX(CF2(f));is_chain(FY);is_chain(TY)|] ==>\
+\ lub(range(%i. lub(range(%j. CF2(FY(j))(TY(i)))))) =\
+\ lub(range(%i. CF2(FY(i))(TY(i))))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac antisym_less 1),
+	(rtac is_lub_thelub 1),
+	(rtac ch2ch_lubMF2L 1),
+	(rtac contX2mono 1),
+	(atac 1),
+	(rtac allI 1),
+	(rtac contX2mono 1),
+	(etac spec 1),
+	(atac 1),
+	(atac 1),
+	(rtac ub_rangeI 1),
+	(strip_tac 1 ),
+	(rtac is_lub_thelub 1),
+	((rtac ch2ch_MF2L 1) THEN (rtac contX2mono 1) THEN (atac 1)),
+	(atac 1),
+	(rtac ub_rangeI 1),
+	(strip_tac 1 ),
+	(res_inst_tac [("m","i"),("n","ia")] nat_less_cases 1),
+	(rtac trans_less 1),
+	(rtac is_ub_thelub 2),
+	(rtac (chain_mono RS mp) 1),
+	((rtac ch2ch_MF2R 1) THEN (rtac contX2mono 1) THEN (etac spec 1)),
+	(atac 1),
+	(atac 1),
+	((rtac ch2ch_MF2LR 1) THEN (etac contX2mono 1)),
+	(rtac allI 1),
+	((rtac contX2mono 1) THEN (etac spec 1)),
+	(atac 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(rtac is_ub_thelub 1),
+	((rtac ch2ch_MF2LR 1) THEN (etac contX2mono 1)),
+	(rtac allI 1),
+	((rtac contX2mono 1) THEN (etac spec 1)),
+	(atac 1),
+	(atac 1),
+	(rtac trans_less 1),
+	(rtac is_ub_thelub 2),
+	(res_inst_tac [("x1","ia")] (chain_mono RS mp) 1),
+	((rtac ch2ch_MF2L 1) THEN (etac contX2mono 1)),
+	(atac 1),
+	(atac 1),
+	((rtac ch2ch_MF2LR 1) THEN (etac contX2mono 1)),
+	(rtac allI 1),
+	((rtac contX2mono 1) THEN (etac spec 1)),
+	(atac 1),
+	(atac 1),
+	(rtac lub_mono 1),
+	((rtac ch2ch_MF2LR 1) THEN (etac contX2mono 1)),
+	(rtac allI 1),
+	((rtac contX2mono 1) THEN (etac spec 1)),
+	(atac 1),
+	(atac 1),
+	(rtac ch2ch_lubMF2L 1),
+	(rtac contX2mono 1),
+	(atac 1),
+	(rtac allI 1),
+	((rtac contX2mono 1) THEN (etac spec 1)),
+	(atac 1),
+	(atac 1),
+	(strip_tac 1 ),
+	(rtac is_ub_thelub 1),
+	((rtac ch2ch_MF2L 1) THEN (etac contX2mono 1)),
+	(atac 1)
+	]);
+
+
+val diag_lubCF2_2 = prove_goal Cont.thy 
+"[|contX(CF2);!f.contX(CF2(f));is_chain(FY);is_chain(TY)|] ==>\
+\ lub(range(%j. lub(range(%i. CF2(FY(j))(TY(i)))))) =\
+\ lub(range(%i. CF2(FY(i))(TY(i))))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac trans 1),
+	(rtac ex_lubMF2 1),
+	(rtac ((hd prems) RS contX2mono) 1), 
+	(rtac allI 1),
+	(rtac (((hd (tl prems)) RS spec RS contX2mono)) 1),
+	(atac 1),
+	(atac 1),
+	(rtac diag_lubCF2_1 1),
+	(atac 1),
+	(atac 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+
+val contlub_CF2 = prove_goal Cont.thy 
+"[|contX(CF2);!f.contX(CF2(f));is_chain(FY);is_chain(TY)|] ==>\
+\ CF2(lub(range(FY)))(lub(range(TY))) = lub(range(%i.CF2(FY(i))(TY(i))))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac ((hd prems) RS contX2contlub RS contlubE RS 
+		spec RS mp RS ssubst) 1),
+	(atac 1),
+	(rtac (thelub_fun RS ssubst) 1),
+	(rtac ((hd prems) RS contX2mono RS ch2ch_monofun) 1), 
+	(atac 1),
+	(rtac trans 1),
+	(rtac (((hd (tl prems)) RS spec RS contX2contlub) RS 
+	contlubE RS spec RS mp RS ext RS arg_cong RS arg_cong) 1),
+	(atac 1),
+	(rtac diag_lubCF2_2 1),
+	(atac 1),
+	(atac 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* The following results are about application for functions in 'a=>'b      *)
+(* ------------------------------------------------------------------------ *)
+
+val monofun_fun_fun = prove_goal Cont.thy 
+	"f1 << f2 ==> f1(x) << f2(x)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac (less_fun RS iffD1 RS spec) 1)
+	]);
+
+val monofun_fun_arg = prove_goal Cont.thy 
+	"[|monofun(f); x1 << x2|] ==> f(x1) << f(x2)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac (monofunE RS spec RS spec RS mp) 1),
+	(atac 1)
+	]);
+
+val monofun_fun = prove_goal Cont.thy 
+"[|monofun(f1); monofun(f2); f1 << f2; x1 << x2|] ==> f1(x1) << f2(x2)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac trans_less 1),
+	(etac monofun_fun_arg 1),
+	(atac 1),
+	(etac monofun_fun_fun 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* The following results are about the propagation of monotonicity and      *)
+(* continuity                                                               *)
+(* ------------------------------------------------------------------------ *)
+
+val mono2mono_MF1L = prove_goal Cont.thy 
+	"[|monofun(c1)|] ==> monofun(%x. c1(x,y))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac monofunI 1),
+	(strip_tac 1),
+	(etac (monofun_fun_arg RS monofun_fun_fun) 1),
+	(atac 1)
+	]);
+
+val contX2contX_CF1L = prove_goal Cont.thy 
+	"[|contX(c1)|] ==> contX(%x. c1(x,y))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac monocontlub2contX 1),
+	(etac (contX2mono RS mono2mono_MF1L) 1),
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac ((hd prems) RS contX2contlub RS 
+		contlubE RS spec RS mp RS ssubst) 1),
+	(atac 1),
+	(rtac (thelub_fun RS ssubst) 1),
+	(rtac ch2ch_monofun 1),
+	(etac contX2mono 1),
+	(atac 1),
+	(rtac refl 1)
+	]);
+
+(*********  Note "(%x.%y.c1(x,y)) = c1" ***********)
+
+val mono2mono_MF1L_rev = prove_goal Cont.thy
+	"!y.monofun(%x.c1(x,y)) ==> monofun(c1)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac monofunI 1),
+	(strip_tac 1),
+	(rtac (less_fun RS iffD2) 1),
+	(strip_tac 1),
+	(rtac ((hd prems) RS spec RS monofunE RS spec RS spec RS mp) 1),
+	(atac 1)
+	]);
+
+val contX2contX_CF1L_rev = prove_goal Cont.thy
+	"!y.contX(%x.c1(x,y)) ==> contX(c1)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac monocontlub2contX 1),
+	(rtac (contX2mono RS allI RS mono2mono_MF1L_rev ) 1),
+	(etac spec 1),
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac ext 1),
+	(rtac (thelub_fun RS ssubst) 1),
+	(rtac (contX2mono RS allI RS mono2mono_MF1L_rev RS ch2ch_monofun) 1),
+	(etac spec 1),
+	(atac 1),
+	(rtac 
+	((hd prems) RS spec RS contX2contlub RS contlubE RS spec RS mp) 1),
+	(atac 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* What D.A.Schmidt calls continuity of abstraction                         *)
+(* never used here                                                          *)
+(* ------------------------------------------------------------------------ *)
+
+val contlub_abstraction = prove_goal Cont.thy
+"[|is_chain(Y::nat=>'a);!y.contX(%x.(c::'a=>'b=>'c)(x,y))|] ==>\
+\ (%y.lub(range(%i.c(Y(i),y)))) = (lub(range(%i.%y.c(Y(i),y))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac trans 1),
+	(rtac (contX2contlub RS contlubE RS spec RS mp) 2),
+	(atac 3),
+	(etac contX2contX_CF1L_rev 2),
+	(rtac ext 1), 
+	(rtac (contX2contlub RS contlubE RS spec RS mp RS sym) 1),
+	(etac spec 1),
+	(atac 1)
+	]);
+
+
+val mono2mono_app = prove_goal Cont.thy 
+"[|monofun(ft);!x.monofun(ft(x));monofun(tt)|] ==>\
+\	 monofun(%x.(ft(x))(tt(x)))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac monofunI 1),
+	(strip_tac 1),
+	(res_inst_tac [("f1.0","ft(x)"),("f2.0","ft(y)")] monofun_fun 1),
+	(etac spec 1),
+	(etac spec 1),
+	(etac (monofunE RS spec RS spec RS mp) 1),
+	(atac 1),
+	(etac (monofunE RS spec RS spec RS mp) 1),
+	(atac 1)
+	]);
+
+val contX2contlub_app = prove_goal Cont.thy 
+"[|contX(ft);!x.contX(ft(x));contX(tt)|] ==>\
+\	 contlub(%x.(ft(x))(tt(x)))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(res_inst_tac [("f3","tt")] (contlubE RS spec RS mp RS ssubst) 1),
+	(rtac contX2contlub 1),
+	(resolve_tac prems 1),
+	(atac 1),
+	(rtac contlub_CF2 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1),
+	(atac 1),
+	(rtac (contX2mono RS ch2ch_monofun) 1),
+	(resolve_tac prems 1),
+	(atac 1)
+	]);
+
+
+val contX2contX_app = prove_goal Cont.thy 
+"[|contX(ft);!x.contX(ft(x));contX(tt)|] ==>\
+\	 contX(%x.(ft(x))(tt(x)))"
+ (fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac mono2mono_app 1),
+	(rtac contX2mono 1),
+	(resolve_tac prems 1),
+	(strip_tac 1),
+	(rtac contX2mono 1),
+	(cut_facts_tac prems 1),
+	(etac spec 1),
+	(rtac contX2mono 1),
+	(resolve_tac prems 1),
+	(rtac contX2contlub_app 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1)
+	]);
+
+
+val contX2contX_app2 = (allI RSN (2,contX2contX_app));
+(*  [| contX(?ft); !!x. contX(?ft(x)); contX(?tt) |] ==>                 *)
+(*                                      contX(%x. ?ft(x,?tt(x)))         *)
+
+
+(* ------------------------------------------------------------------------ *)
+(* The identity function is continuous                                      *)
+(* ------------------------------------------------------------------------ *)
+
+val contX_id = prove_goal Cont.thy "contX(% x.x)"
+ (fn prems =>
+	[
+	(rtac contXI 1),
+	(strip_tac 1),
+	(etac thelubE 1),
+	(rtac refl 1)
+	]);
+
+
+
+(* ------------------------------------------------------------------------ *)
+(* constant functions are continuous                                        *)
+(* ------------------------------------------------------------------------ *)
+
+val contX_const = prove_goalw Cont.thy [contX] "contX(%x.c)"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(rtac is_lubI 1),
+	(rtac conjI 1),
+	(rtac ub_rangeI 1),
+	(strip_tac 1),
+	(rtac refl_less 1),
+	(strip_tac 1),
+	(dtac ub_rangeE 1),
+	(etac spec 1)
+	]);
+
+
+val contX2contX_app3 = prove_goal Cont.thy 
+ "[|contX(f);contX(t) |] ==> contX(%x. f(t(x)))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac contX2contX_app2 1),
+	(rtac contX_const 1),
+	(atac 1),
+	(atac 1)
+	]);
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cont.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,41 @@
+(*  Title: 	HOLCF/cont.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+    Results about continuity and monotonicity
+*)
+
+Cont = Fun3 +
+
+(* 
+
+   Now we change the default class! Form now on all untyped typevariables are
+   of default class pcpo
+
+*)
+
+
+default pcpo
+
+consts  
+	monofun :: "('a::po => 'b::po) => bool"	(* monotonicity    *)
+	contlub	:: "('a => 'b) => bool"		(* first cont. def *)
+	contX	:: "('a => 'b) => bool"		(* secnd cont. def *)
+
+rules 
+
+monofun		"monofun(f) == ! x y. x << y --> f(x) << f(y)"
+
+contlub		"contlub(f) == ! Y. is_chain(Y) --> \
+\				f(lub(range(Y))) = lub(range(% i.f(Y(i))))"
+
+contX		"contX(f)   == ! Y. is_chain(Y) --> \
+\				range(% i.f(Y(i))) <<| f(lub(range(Y)))"
+
+(* ------------------------------------------------------------------------ *)
+(* the main purpose of cont.thy is to show:                                 *)
+(*              monofun(f) & contlub(f)  <==> contX(f)                      *)
+(* ------------------------------------------------------------------------ *)
+
+end
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cprod1.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,117 @@
+(*  Title: 	HOLCF/cprod1.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+Lemmas for theory cprod1.thy 
+*)
+
+open Cprod1;
+
+val less_cprod1b = prove_goalw Cprod1.thy [less_cprod_def]
+ "less_cprod(p1,p2) = ( fst(p1) << fst(p2) & snd(p1) << snd(p2))"
+ (fn prems =>
+	[
+	(rtac refl 1)
+	]);
+
+val less_cprod2a = prove_goalw Cprod1.thy [less_cprod_def]
+ "less_cprod(<x,y>,<UU,UU>) ==> x = UU & y = UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac conjE 1),
+	(dtac (fst_conv RS subst) 1),
+	(dtac (fst_conv RS subst) 1),
+	(dtac (fst_conv RS subst) 1),
+	(dtac (snd_conv RS subst) 1),
+	(dtac (snd_conv RS subst) 1),
+	(dtac (snd_conv RS subst) 1),
+	(rtac conjI 1),
+	(etac UU_I 1),
+	(etac UU_I 1)
+	]);
+
+val less_cprod2b = prove_goal Cprod1.thy 
+ "less_cprod(p,<UU,UU>) ==> p=<UU,UU>"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("p","p")] PairE 1),
+	(hyp_subst_tac 1),
+	(dtac less_cprod2a 1),
+	(asm_simp_tac HOL_ss 1)
+	]);
+
+val less_cprod2c = prove_goalw Cprod1.thy [less_cprod_def]
+ "less_cprod(<x1,y1>,<x2,y2>) ==> x1 << x2 & y1 << y2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac conjE 1),
+	(dtac (fst_conv RS subst) 1),
+	(dtac (fst_conv RS subst) 1),
+	(dtac (fst_conv RS subst) 1),
+	(dtac (snd_conv RS subst) 1),
+	(dtac (snd_conv RS subst) 1),
+	(dtac (snd_conv RS subst) 1),
+	(rtac conjI 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* less_cprod is a partial order on 'a * 'b                                 *)
+(* ------------------------------------------------------------------------ *)
+
+val refl_less_cprod = prove_goalw Cprod1.thy [less_cprod_def] "less_cprod(p,p)"
+ (fn prems =>
+	[
+	(res_inst_tac [("p","p")] PairE 1),
+	(hyp_subst_tac 1),
+	(simp_tac pair_ss 1),
+	(simp_tac Cfun_ss 1)
+	]);
+
+val antisym_less_cprod = prove_goal Cprod1.thy 
+ "[|less_cprod(p1,p2);less_cprod(p2,p1)|] ==> p1=p2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("p","p1")] PairE 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p2")] PairE 1),
+	(hyp_subst_tac 1),
+	(dtac less_cprod2c 1),
+	(dtac less_cprod2c 1),
+	(etac conjE 1),
+	(etac conjE 1),
+	(rtac (Pair_eq RS ssubst) 1),
+	(fast_tac (HOL_cs addSIs [antisym_less]) 1)
+	]);
+
+
+val trans_less_cprod = prove_goal Cprod1.thy 
+ "[|less_cprod(p1,p2);less_cprod(p2,p3)|] ==> less_cprod(p1,p3)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("p","p1")] PairE 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p3")] PairE 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p2")] PairE 1),
+	(hyp_subst_tac 1),
+	(dtac less_cprod2c 1),
+	(dtac less_cprod2c 1),
+	(rtac (less_cprod1b RS ssubst) 1),
+	(simp_tac pair_ss 1),
+	(etac conjE 1),
+	(etac conjE 1),
+	(rtac conjI 1),
+	(etac trans_less 1),
+	(atac 1),
+	(etac trans_less 1),
+	(atac 1)
+	]);
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cprod1.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,23 @@
+(*  Title: 	HOLCF/cprod1.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+
+Partial ordering for cartesian product of HOL theory prod.thy
+
+*)
+
+Cprod1 = Cfun3 +
+
+
+consts
+  less_cprod	:: "[('a::pcpo * 'b::pcpo),('a * 'b)] => bool"	
+
+rules
+
+  less_cprod_def "less_cprod(p1,p2) == ( fst(p1) << fst(p2) &\
+\					snd(p1) << snd(p2))"
+
+end
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cprod2.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,181 @@
+(*  Title: 	HOLCF/cprod2.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for cprod2.thy 
+*)
+
+open Cprod2;
+
+val less_cprod3a = prove_goal Cprod2.thy 
+	"p1=<UU,UU> ==> p1 << p2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (inst_cprod_po RS ssubst) 1),
+	(rtac (less_cprod1b RS ssubst) 1),
+	(hyp_subst_tac 1),
+	(asm_simp_tac pair_ss  1),
+	(rtac conjI 1),
+	(rtac minimal 1),
+	(rtac minimal 1)
+	]);
+
+val less_cprod3b = prove_goal Cprod2.thy
+ "(p1 << p2) = (fst(p1)<<fst(p2) & snd(p1)<<snd(p2))"
+ (fn prems =>
+	[
+	(rtac (inst_cprod_po RS ssubst) 1),
+	(rtac less_cprod1b 1)
+	]);
+
+val less_cprod4a = prove_goal Cprod2.thy 
+	"<x1,x2> << <UU,UU> ==> x1=UU & x2=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac less_cprod2a 1),
+	(etac (inst_cprod_po RS subst) 1)
+	]);
+
+val less_cprod4b = prove_goal Cprod2.thy 
+	"p << <UU,UU> ==> p = <UU,UU>"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac less_cprod2b 1),
+	(etac (inst_cprod_po RS subst) 1)
+	]);
+
+val less_cprod4c = prove_goal Cprod2.thy
+ " <xa,ya> << <x,y> ==> xa<<x & ya << y"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac less_cprod2c 1),
+	(etac (inst_cprod_po RS subst) 1),
+	(REPEAT (atac 1))
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* type cprod is pointed                                                    *)
+(* ------------------------------------------------------------------------ *)
+
+val minimal_cprod = prove_goal Cprod2.thy  "<UU,UU><<p"
+(fn prems =>
+	[
+	(rtac less_cprod3a 1),
+	(rtac refl 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* Pair <_,_>  is monotone in both arguments                                *)
+(* ------------------------------------------------------------------------ *)
+
+val monofun_pair1 = prove_goalw Cprod2.thy [monofun] "monofun(Pair)"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(rtac (less_fun RS iffD2) 1),
+	(strip_tac 1),
+	(rtac (less_cprod3b RS iffD2) 1),
+	(simp_tac pair_ss 1),
+	(asm_simp_tac Cfun_ss 1)
+	]);
+
+val monofun_pair2 = prove_goalw Cprod2.thy [monofun] "monofun(Pair(x))"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(rtac (less_cprod3b RS iffD2) 1),
+	(simp_tac pair_ss 1),
+	(asm_simp_tac Cfun_ss 1)
+	]);
+
+val monofun_pair = prove_goal Cprod2.thy 
+ "[|x1<<x2; y1<<y2|] ==> <x1,y1> << <x2,y2>"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac trans_less 1),
+	(rtac (monofun_pair1 RS monofunE RS spec RS spec RS mp RS 
+	(less_fun RS iffD1 RS spec)) 1),
+	(rtac (monofun_pair2 RS monofunE RS spec RS spec RS mp) 2),
+	(atac 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* fst and snd are monotone                                                 *)
+(* ------------------------------------------------------------------------ *)
+
+val monofun_fst = prove_goalw Cprod2.thy [monofun] "monofun(fst)"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(res_inst_tac [("p","x")] PairE 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","y")] PairE 1),
+	(hyp_subst_tac 1),
+	(asm_simp_tac pair_ss  1),
+	(etac (less_cprod4c RS conjunct1) 1)
+	]);
+
+val monofun_snd = prove_goalw Cprod2.thy [monofun] "monofun(snd)"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(res_inst_tac [("p","x")] PairE 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","y")] PairE 1),
+	(hyp_subst_tac 1),
+	(asm_simp_tac pair_ss  1),
+	(etac (less_cprod4c RS conjunct2) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* the type 'a * 'b is a cpo                                                *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_cprod = prove_goal Cprod2.thy 
+" is_chain(S) ==> range(S) <<| \
+\   < lub(range(%i.fst(S(i)))),lub(range(%i.snd(S(i))))> "
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_lubI 1),
+	(rtac conjI 1),
+	(rtac ub_rangeI 1),
+	(rtac allI 1),
+	(res_inst_tac [("t","S(i)")] (surjective_pairing RS ssubst) 1),
+	(rtac monofun_pair 1),
+	(rtac is_ub_thelub 1),
+	(etac (monofun_fst RS ch2ch_monofun) 1),
+	(rtac is_ub_thelub 1),
+	(etac (monofun_snd RS ch2ch_monofun) 1),
+	(strip_tac 1),
+	(res_inst_tac [("t","u")] (surjective_pairing RS ssubst) 1),
+	(rtac monofun_pair 1),
+	(rtac is_lub_thelub 1),
+	(etac (monofun_fst RS ch2ch_monofun) 1),
+	(etac (monofun_fst RS ub2ub_monofun) 1),
+	(rtac is_lub_thelub 1),
+	(etac (monofun_snd RS ch2ch_monofun) 1),
+	(etac (monofun_snd RS ub2ub_monofun) 1)
+	]);
+
+val thelub_cprod = (lub_cprod RS thelubI);
+(* "is_chain(?S1) ==> lub(range(?S1)) =                                *)
+(*  <lub(range(%i. fst(?S1(i)))), lub(range(%i. snd(?S1(i))))>"        *)
+
+
+val cpo_cprod = prove_goal Cprod2.thy 
+	"is_chain(S::nat=>'a*'b)==>? x.range(S)<<| x"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac exI 1),
+	(etac lub_cprod 1)
+	]);
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cprod2.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,25 @@
+(*  Title: 	HOLCF/cprod2.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Class Instance *::(pcpo,pcpo)po
+
+*)
+
+Cprod2 = Cprod1 + 
+
+(* Witness for the above arity axiom is cprod1.ML *)
+
+arities "*" :: (pcpo,pcpo)po
+
+rules
+
+(* instance of << for type ['a * 'b]  *)
+
+inst_cprod_po	"(op <<)::['a * 'b,'a * 'b]=>bool = less_cprod"
+
+end
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cprod3.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,315 @@
+(*  Title: 	HOLCF/cprod3.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for Cprod3.thy 
+*)
+
+open Cprod3;
+
+(* ------------------------------------------------------------------------ *)
+(* continuity of <_,_> , fst, snd                                           *)
+(* ------------------------------------------------------------------------ *)
+
+val Cprod3_lemma1 = prove_goal Cprod3.thy 
+"is_chain(Y::(nat=>'a)) ==>\
+\ <lub(range(Y)),(x::'b)> =\
+\ <lub(range(%i. fst(<Y(i),x>))),lub(range(%i. snd(<Y(i),x>)))>"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("f1","Pair")] (arg_cong RS cong) 1),
+	(rtac lub_equal 1),
+	(atac 1),
+	(rtac (monofun_fst RS ch2ch_monofun) 1),
+	(rtac ch2ch_fun 1),
+	(rtac (monofun_pair1 RS ch2ch_monofun) 1),
+	(atac 1),
+	(rtac allI 1),
+	(simp_tac pair_ss 1),
+	(rtac sym 1),
+	(simp_tac pair_ss 1),
+	(rtac (lub_const RS thelubI) 1)
+	]);
+
+val contlub_pair1 = prove_goal Cprod3.thy "contlub(Pair)"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac (expand_fun_eq RS iffD2) 1),
+	(strip_tac 1),
+	(rtac (lub_fun RS thelubI RS ssubst) 1),
+	(etac (monofun_pair1 RS ch2ch_monofun) 1),
+	(rtac trans 1),
+	(rtac (thelub_cprod RS sym) 2),
+	(rtac ch2ch_fun 2),
+	(etac (monofun_pair1 RS ch2ch_monofun) 2),
+	(etac Cprod3_lemma1 1)
+	]);
+
+val Cprod3_lemma2 = prove_goal Cprod3.thy 
+"is_chain(Y::(nat=>'a)) ==>\
+\ <(x::'b),lub(range(Y))> =\
+\ <lub(range(%i. fst(<x,Y(i)>))),lub(range(%i. snd(<x,Y(i)>)))>"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("f1","Pair")] (arg_cong RS cong) 1),
+	(rtac sym 1),
+	(simp_tac pair_ss 1),
+	(rtac (lub_const RS thelubI) 1),
+	(rtac lub_equal 1),
+	(atac 1),
+	(rtac (monofun_snd RS ch2ch_monofun) 1),
+	(rtac (monofun_pair2 RS ch2ch_monofun) 1),
+	(atac 1),
+	(rtac allI 1),
+	(simp_tac pair_ss 1)
+	]);
+
+val contlub_pair2 = prove_goal Cprod3.thy "contlub(Pair(x))"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac trans 1),
+	(rtac (thelub_cprod RS sym) 2),
+	(etac (monofun_pair2 RS ch2ch_monofun) 2),
+	(etac Cprod3_lemma2 1)
+	]);
+
+val contX_pair1 = prove_goal Cprod3.thy "contX(Pair)"
+(fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_pair1 1),
+	(rtac contlub_pair1 1)
+	]);
+
+val contX_pair2 = prove_goal Cprod3.thy "contX(Pair(x))"
+(fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_pair2 1),
+	(rtac contlub_pair2 1)
+	]);
+
+val contlub_fst = prove_goal Cprod3.thy "contlub(fst)"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac (lub_cprod RS thelubI RS ssubst) 1),
+	(atac 1),
+	(simp_tac pair_ss 1)
+	]);
+
+val contlub_snd = prove_goal Cprod3.thy "contlub(snd)"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac (lub_cprod RS thelubI RS ssubst) 1),
+	(atac 1),
+	(simp_tac pair_ss 1)
+	]);
+
+val contX_fst = prove_goal Cprod3.thy "contX(fst)"
+(fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_fst 1),
+	(rtac contlub_fst 1)
+	]);
+
+val contX_snd = prove_goal Cprod3.thy "contX(snd)"
+(fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_snd 1),
+	(rtac contlub_snd 1)
+	]);
+
+(* 
+ -------------------------------------------------------------------------- 
+ more lemmas for Cprod3.thy 
+ 
+ -------------------------------------------------------------------------- 
+*)
+
+(* ------------------------------------------------------------------------ *)
+(* convert all lemmas to the continuous versions                            *)
+(* ------------------------------------------------------------------------ *)
+
+val beta_cfun_cprod = prove_goalw Cprod3.thy [cpair_def]
+	"(LAM x y.<x,y>)[a][b] = <a,b>"
+ (fn prems =>
+	[
+	(rtac (beta_cfun RS ssubst) 1),
+	(contX_tac 1),
+	(rtac contX_pair2 1),
+	(rtac contX2contX_CF1L 1),
+	(rtac contX_pair1 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_pair2 1),
+	(rtac refl 1)
+	]);
+
+val inject_cpair = prove_goalw Cprod3.thy [cpair_def]
+	" (a#b)=(aa#ba)  ==> a=aa & b=ba"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(dtac (beta_cfun_cprod RS subst) 1),
+	(dtac (beta_cfun_cprod RS subst) 1),
+	(etac Pair_inject 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val inst_cprod_pcpo2 = prove_goalw Cprod3.thy [cpair_def] "UU = (UU#UU)"
+ (fn prems =>
+	[
+	(rtac sym 1),
+	(rtac trans 1),
+	(rtac beta_cfun_cprod 1),
+	(rtac sym 1),
+	(rtac inst_cprod_pcpo 1)
+	]);
+
+val defined_cpair_rev = prove_goal Cprod3.thy
+ "(a#b) = UU ==> a = UU & b = UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(dtac (inst_cprod_pcpo2 RS subst) 1),
+	(etac inject_cpair 1)
+	]);
+
+val Exh_Cprod2 = prove_goalw Cprod3.thy [cpair_def]
+	"? a b. z=(a#b) "
+ (fn prems =>
+	[
+	(rtac PairE 1),
+	(rtac exI 1),
+	(rtac exI 1),
+	(etac (beta_cfun_cprod RS ssubst) 1)
+	]);
+
+val cprodE = prove_goalw Cprod3.thy [cpair_def]
+"[|!!x y. [|p=(x#y) |] ==> Q|] ==> Q"
+ (fn prems =>
+	[
+	(rtac PairE 1),
+	(resolve_tac prems 1),
+	(etac (beta_cfun_cprod RS ssubst) 1)
+	]);
+
+val cfst2 = prove_goalw Cprod3.thy [cfst_def,cpair_def] 
+	"cfst[x#y]=x"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (beta_cfun_cprod RS ssubst) 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_fst 1),
+	(simp_tac pair_ss  1)
+	]);
+
+val csnd2 = prove_goalw Cprod3.thy [csnd_def,cpair_def] 
+	"csnd[x#y]=y"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (beta_cfun_cprod RS ssubst) 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_snd 1),
+	(simp_tac pair_ss  1)
+	]);
+
+val surjective_pairing_Cprod2 = prove_goalw Cprod3.thy 
+	[cfst_def,csnd_def,cpair_def] "(cfst[p] # csnd[p]) = p"
+ (fn prems =>
+	[
+	(rtac (beta_cfun_cprod RS ssubst) 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_snd 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_fst 1),
+	(rtac (surjective_pairing RS sym) 1)
+	]);
+
+
+val less_cprod5b = prove_goalw Cprod3.thy [cfst_def,csnd_def,cpair_def]
+ " (p1 << p2) = (cfst[p1]<<cfst[p2] & csnd[p1]<<csnd[p2])"
+ (fn prems =>
+	[
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_snd 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_snd 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_fst 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_fst 1),
+	(rtac less_cprod3b 1)
+	]);
+
+val less_cprod5c = prove_goalw Cprod3.thy [cfst_def,csnd_def,cpair_def]
+ "xa#ya << x#y ==>xa<<x & ya << y"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac less_cprod4c 1),
+	(dtac (beta_cfun_cprod RS subst) 1),
+	(dtac (beta_cfun_cprod RS subst) 1),
+	(atac 1)
+	]);
+
+
+val lub_cprod2 = prove_goalw Cprod3.thy [cfst_def,csnd_def,cpair_def]
+"[|is_chain(S)|] ==> range(S) <<| \
+\ (lub(range(%i.cfst[S(i)])) # lub(range(%i.csnd[S(i)])))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (beta_cfun_cprod RS ssubst) 1),
+	(rtac (beta_cfun RS ext RS ssubst) 1),
+	(rtac contX_snd 1),
+	(rtac (beta_cfun RS ext RS ssubst) 1),
+	(rtac contX_fst 1),
+	(rtac lub_cprod 1),
+	(atac 1)
+	]);
+
+val thelub_cprod2 = (lub_cprod2 RS thelubI);
+(*  "is_chain(?S1) ==> lub(range(?S1)) =                         *)
+(*    lub(range(%i. cfst[?S1(i)]))#lub(range(%i. csnd[?S1(i)]))" *)
+
+val csplit2 = prove_goalw Cprod3.thy [csplit_def]
+	"csplit[f][x#y]=f[x][y]"
+ (fn prems =>
+	[
+	(rtac (beta_cfun RS ssubst) 1),
+	(contX_tacR 1),
+	(simp_tac Cfun_ss 1),
+	(simp_tac (Cfun_ss addsimps [cfst2,csnd2]) 1)
+	]);
+
+val csplit3 = prove_goalw Cprod3.thy [csplit_def]
+  "csplit[cpair][z]=z"
+ (fn prems =>
+	[
+	(rtac (beta_cfun RS ssubst) 1),
+	(contX_tacR 1),
+	(simp_tac (Cfun_ss addsimps [surjective_pairing_Cprod2]) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* install simplifier for Cprod                                             *)
+(* ------------------------------------------------------------------------ *)
+
+val Cprod_rews = [cfst2,csnd2,csplit2];
+
+val Cprod_ss = Cfun_ss addsimps Cprod_rews;
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Cprod3.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,43 @@
+(*  Title: 	HOLCF/cprod3.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+
+Class instance of  * for class pcpo
+
+*)
+
+Cprod3 = Cprod2 +
+
+arities "*" :: (pcpo,pcpo)pcpo			(* Witness cprod2.ML *)
+
+consts  
+	"@cpair"     :: "'a => 'b => ('a*'b)" ("_#_" [101,100] 100)
+	"cop @cpair" :: "'a -> 'b -> ('a*'b)" ("cpair")
+					(* continuous  pairing *)
+	cfst         :: "('a*'b)->'a"
+	csnd         :: "('a*'b)->'b"
+	csplit       :: "('a->'b->'c)->('a*'b)->'c"
+
+rules 
+
+inst_cprod_pcpo	"UU::'a*'b = <UU,UU>"
+
+cpair_def	"cpair  == (LAM x y.<x,y>)"
+cfst_def	"cfst   == (LAM p.fst(p))"
+csnd_def	"csnd   == (LAM p.snd(p))"	
+csplit_def	"csplit == (LAM f p.f[cfst[p]][csnd[p]])"
+
+end
+
+ML
+
+(* ----------------------------------------------------------------------*)
+(* parse translations for the above mixfix                               *)
+(* ----------------------------------------------------------------------*)
+
+val parse_translation = [("@cpair",mk_cinfixtr "@cpair")];
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Dnat.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,471 @@
+(*  Title: 	HOLCF/dnat.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for dnat.thy 
+*)
+
+open Dnat;
+
+(* ------------------------------------------------------------------------*)
+(* The isomorphisms dnat_rep_iso and dnat_abs_iso are strict               *)
+(* ------------------------------------------------------------------------*)
+
+val dnat_iso_strict= dnat_rep_iso RS (dnat_abs_iso RS 
+	(allI  RSN (2,allI RS iso_strict)));
+
+val dnat_rews = [dnat_iso_strict RS conjunct1,
+		dnat_iso_strict RS conjunct2];
+
+(* ------------------------------------------------------------------------*)
+(* Properties of dnat_copy                                                 *)
+(* ------------------------------------------------------------------------*)
+
+fun prover defs thm =  prove_goalw Dnat.thy defs thm
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps 
+		(dnat_rews @ [dnat_abs_iso,dnat_rep_iso])) 1)
+	]);
+
+val dnat_copy = 
+	[
+	prover [dnat_copy_def] "dnat_copy[f][UU]=UU",
+	prover [dnat_copy_def,dzero_def] "dnat_copy[f][dzero]= dzero",
+	prover [dnat_copy_def,dsucc_def] 
+		"n~=UU ==> dnat_copy[f][dsucc[n]] = dsucc[f[n]]"
+	];
+
+val dnat_rews =  dnat_copy @ dnat_rews; 
+
+(* ------------------------------------------------------------------------*)
+(* Exhaustion and elimination for dnat                                     *)
+(* ------------------------------------------------------------------------*)
+
+val Exh_dnat = prove_goalw Dnat.thy [dsucc_def,dzero_def]
+	"n = UU | n = dzero | (? x . x~=UU & n = dsucc[x])"
+ (fn prems =>
+	[
+	(simp_tac HOLCF_ss  1),
+	(rtac (dnat_rep_iso RS subst) 1),
+	(res_inst_tac [("p","dnat_rep[n]")] ssumE 1),
+	(rtac disjI1 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1),
+	(rtac (disjI1 RS disjI2) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1),
+	(res_inst_tac [("p","x")] oneE 1),
+	(contr_tac 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1),
+	(rtac (disjI2 RS disjI2) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val dnatE = prove_goal Dnat.thy 
+ "[| n=UU ==> Q; n=dzero ==> Q; !!x.[|n=dsucc[x];x~=UU|]==>Q|]==>Q"
+ (fn prems =>
+	[
+	(rtac (Exh_dnat RS disjE) 1),
+	(eresolve_tac prems 1),
+	(etac disjE 1),
+	(eresolve_tac prems 1),
+	(REPEAT (etac exE 1)),
+	(resolve_tac prems 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+(* ------------------------------------------------------------------------*)
+(* Properties of dnat_when                                                 *)
+(* ------------------------------------------------------------------------*)
+
+fun prover defs thm =  prove_goalw Dnat.thy defs thm
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps 
+		(dnat_rews @ [dnat_abs_iso,dnat_rep_iso])) 1)
+	]);
+
+
+val dnat_when = [
+	prover [dnat_when_def] "dnat_when[c][f][UU]=UU",
+	prover [dnat_when_def,dzero_def] "dnat_when[c][f][dzero]=c",
+	prover [dnat_when_def,dsucc_def] 
+		"n~=UU ==> dnat_when[c][f][dsucc[n]]=f[n]"
+	];
+
+val dnat_rews = dnat_when @ dnat_rews;
+
+(* ------------------------------------------------------------------------*)
+(* Rewrites for  discriminators and  selectors                             *)
+(* ------------------------------------------------------------------------*)
+
+fun prover defs thm = prove_goalw Dnat.thy defs thm
+ (fn prems =>
+	[
+	(simp_tac (HOLCF_ss addsimps dnat_rews) 1)
+	]);
+
+val dnat_discsel = [
+	prover [is_dzero_def] "is_dzero[UU]=UU",
+	prover [is_dsucc_def] "is_dsucc[UU]=UU",
+	prover [dpred_def] "dpred[UU]=UU"
+	];
+
+
+fun prover defs thm = prove_goalw Dnat.thy defs thm
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1)
+	]);
+
+val dnat_discsel = [
+	prover [is_dzero_def] "is_dzero[dzero]=TT",
+	prover [is_dzero_def] "n~=UU ==>is_dzero[dsucc[n]]=FF",
+	prover [is_dsucc_def] "is_dsucc[dzero]=FF",
+	prover [is_dsucc_def] "n~=UU ==> is_dsucc[dsucc[n]]=TT",
+	prover [dpred_def] "dpred[dzero]=UU",
+	prover [dpred_def] "n~=UU ==> dpred[dsucc[n]]=n"
+	] @ dnat_discsel;
+
+val dnat_rews = dnat_discsel @ dnat_rews;
+
+(* ------------------------------------------------------------------------*)
+(* Definedness and strictness                                              *)
+(* ------------------------------------------------------------------------*)
+
+fun prover contr thm = prove_goal Dnat.thy thm
+ (fn prems =>
+	[
+	(res_inst_tac [("P1",contr)] classical3 1),
+	(simp_tac (HOLCF_ss addsimps dnat_rews) 1),
+	(dtac sym 1),
+	(asm_simp_tac HOLCF_ss  1),
+	(simp_tac (HOLCF_ss addsimps (prems @ dnat_rews)) 1)
+	]);
+
+val dnat_constrdef = [
+	prover "is_dzero[UU] ~= UU" "dzero~=UU",
+	prover "is_dsucc[UU] ~= UU" "n~=UU ==> dsucc[n]~=UU"
+	]; 
+
+
+fun prover defs thm = prove_goalw Dnat.thy defs thm
+ (fn prems =>
+	[
+	(simp_tac (HOLCF_ss addsimps dnat_rews) 1)
+	]);
+
+val dnat_constrdef = [
+	prover [dsucc_def] "dsucc[UU]=UU"
+	] @ dnat_constrdef;
+
+val dnat_rews = dnat_constrdef @ dnat_rews;
+
+
+(* ------------------------------------------------------------------------*)
+(* Distinctness wrt. << and =                                              *)
+(* ------------------------------------------------------------------------*)
+
+fun prover contrfun thm = prove_goal Dnat.thy thm
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("P1","TT << FF")] classical3 1),
+	(resolve_tac dist_less_tr 1),
+	(dres_inst_tac [("fo5",contrfun)] monofun_cfun_arg 1),
+	(etac box_less 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1)
+	]);
+
+val dnat_dist_less = 
+	[
+prover "is_dzero" "n~=UU ==> ~dzero << dsucc[n]",
+prover "is_dsucc" "n~=UU ==> ~dsucc[n] << dzero"
+	];
+
+fun prover contrfun thm = prove_goal Dnat.thy thm
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("P1","TT = FF")] classical3 1),
+	(resolve_tac dist_eq_tr 1),
+	(dres_inst_tac [("f",contrfun)] cfun_arg_cong 1),
+	(etac box_equals 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1)
+	]);
+
+val dnat_dist_eq = 
+	[
+prover "is_dzero" "n~=UU ==> dzero ~= dsucc[n]",
+prover "is_dsucc" "n~=UU ==> dsucc[n] ~= dzero"
+	];
+
+val dnat_rews = dnat_dist_less @ dnat_dist_eq @ dnat_rews;
+
+(* ------------------------------------------------------------------------*)
+(* Invertibility                                                           *)
+(* ------------------------------------------------------------------------*)
+
+val dnat_invert = 
+	[
+prove_goal Dnat.thy 
+"[|x1~=UU; y1~=UU; dsucc[x1] << dsucc[y1] |] ==> x1<< y1"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(dres_inst_tac [("fo5","dnat_when[c][LAM x.x]")] monofun_cfun_arg 1),
+	(etac box_less 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1)
+	])
+	];
+
+(* ------------------------------------------------------------------------*)
+(* Injectivity                                                             *)
+(* ------------------------------------------------------------------------*)
+
+val dnat_inject = 
+	[
+prove_goal Dnat.thy 
+"[|x1~=UU; y1~=UU; dsucc[x1] = dsucc[y1] |] ==> x1= y1"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(dres_inst_tac [("f","dnat_when[c][LAM x.x]")] cfun_arg_cong 1),
+	(etac box_equals 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1)
+	])
+	];
+
+(* ------------------------------------------------------------------------*)
+(* definedness for  discriminators and  selectors                          *)
+(* ------------------------------------------------------------------------*)
+
+
+fun prover thm = prove_goal Dnat.thy thm
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac dnatE 1),
+	(contr_tac 1),
+	(REPEAT (asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1))
+	]);
+
+val dnat_discsel_def = 
+	[
+	prover  "n~=UU ==> is_dzero[n]~=UU",
+	prover  "n~=UU ==> is_dsucc[n]~=UU"
+	];
+
+val dnat_rews = dnat_discsel_def @ dnat_rews;
+
+ 
+(* ------------------------------------------------------------------------*)
+(* Properties dnat_take                                                    *)
+(* ------------------------------------------------------------------------*)
+
+val dnat_take =
+	[
+prove_goalw Dnat.thy [dnat_take_def] "dnat_take(n)[UU]=UU"
+ (fn prems =>
+	[
+	(res_inst_tac [("n","n")] natE 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac iterate_ss 1),
+	(simp_tac (HOLCF_ss addsimps dnat_rews) 1)
+	]),
+prove_goalw Dnat.thy [dnat_take_def] "dnat_take(0)[xs]=UU"
+ (fn prems =>
+	[
+	(asm_simp_tac iterate_ss 1)
+	])];
+
+fun prover thm = prove_goalw Dnat.thy [dnat_take_def] thm
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(simp_tac iterate_ss 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1)
+	]);
+
+val dnat_take = [
+prover "dnat_take(Suc(n))[dzero]=dzero",
+prover "xs~=UU ==> dnat_take(Suc(n))[dsucc[xs]]=dsucc[dnat_take(n)[xs]]"
+	] @ dnat_take;
+
+
+val dnat_rews = dnat_take @ dnat_rews;
+
+(* ------------------------------------------------------------------------*)
+(* take lemma for dnats                                                  *)
+(* ------------------------------------------------------------------------*)
+
+fun prover reach defs thm  = prove_goalw Dnat.thy defs thm
+ (fn prems =>
+	[
+	(res_inst_tac [("t","s1")] (reach RS subst) 1),
+	(res_inst_tac [("t","s2")] (reach RS subst) 1),
+	(rtac (fix_def2 RS ssubst) 1),
+	(rtac (contlub_cfun_fun RS ssubst) 1),
+	(rtac is_chain_iterate 1),
+	(rtac (contlub_cfun_fun RS ssubst) 1),
+	(rtac is_chain_iterate 1),
+	(rtac lub_equal 1),
+	(rtac (is_chain_iterate RS ch2ch_fappL) 1),
+	(rtac (is_chain_iterate RS ch2ch_fappL) 1),
+	(rtac allI 1),
+	(resolve_tac prems 1)
+	]);
+
+val dnat_take_lemma = prover dnat_reach  [dnat_take_def]
+	"(!!n.dnat_take(n)[s1]=dnat_take(n)[s2]) ==> s1=s2";
+
+
+(* ------------------------------------------------------------------------*)
+(* Co -induction for dnats                                                 *)
+(* ------------------------------------------------------------------------*)
+
+val dnat_coind_lemma = prove_goalw Dnat.thy [dnat_bisim_def] 
+"dnat_bisim(R) ==> ! p q.R(p,q) --> dnat_take(n)[p]=dnat_take(n)[q]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(nat_ind_tac "n" 1),
+	(simp_tac (HOLCF_ss addsimps dnat_take) 1),
+	(strip_tac 1),
+	((etac allE 1) THEN (etac allE 1) THEN (etac (mp RS disjE) 1)),
+	(atac 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_take) 1),
+	(etac disjE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_take) 1),
+	(etac exE 1),
+	(etac exE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_take) 1),
+	(REPEAT (etac conjE 1)),
+	(rtac cfun_arg_cong 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val dnat_coind = prove_goal Dnat.thy "[|dnat_bisim(R);R(p,q)|] ==> p = q"
+ (fn prems =>
+	[
+	(rtac dnat_take_lemma 1),
+	(rtac (dnat_coind_lemma RS spec RS spec RS mp) 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1)
+	]);
+
+
+(* ------------------------------------------------------------------------*)
+(* structural induction for admissible predicates                          *)
+(* ------------------------------------------------------------------------*)
+
+val dnat_ind = prove_goal Dnat.thy
+"[| adm(P);\
+\   P(UU);\
+\   P(dzero);\
+\   !! s1.[|s1~=UU ; P(s1)|] ==> P(dsucc[s1])|] ==> P(s)"
+ (fn prems =>
+	[
+	(rtac (dnat_reach RS subst) 1),
+	(res_inst_tac [("x","s")] spec 1),
+	(rtac fix_ind 1),
+	(rtac adm_all2 1),
+	(rtac adm_subst 1),
+	(contX_tacR 1),
+	(resolve_tac prems 1),
+	(simp_tac HOLCF_ss 1),
+	(resolve_tac prems 1),
+	(strip_tac 1),
+	(res_inst_tac [("n","xa")] dnatE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_copy) 1),
+	(resolve_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_copy) 1),
+	(resolve_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_copy) 1),
+	(res_inst_tac [("Q","x[xb]=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1),
+	(resolve_tac prems 1),
+	(eresolve_tac prems 1),
+	(etac spec 1)
+	]);
+
+
+val dnat_flat = prove_goalw Dnat.thy [flat_def] "flat(dzero)"
+ (fn prems =>
+	[
+	(rtac allI 1),
+	(res_inst_tac [("s","x")] dnat_ind 1),
+	(REPEAT (resolve_tac adm_thms 1)),
+	(contX_tacR 1),
+	(REPEAT (resolve_tac adm_thms 1)),
+	(contX_tacR 1),
+	(REPEAT (resolve_tac adm_thms 1)),
+	(contX_tacR 1),
+	(fast_tac HOL_cs 1),
+	(rtac allI 1),
+	(res_inst_tac [("n","y")] dnatE 1),
+	(fast_tac (HOL_cs addSIs [UU_I]) 1),
+	(asm_simp_tac HOLCF_ss 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_dist_less) 1),
+	(rtac allI 1),
+	(res_inst_tac [("n","y")] dnatE 1),
+	(fast_tac (HOL_cs addSIs [UU_I]) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1),
+	(hyp_subst_tac 1),
+	(strip_tac 1),
+	(rtac disjI2 1),
+	(forward_tac dnat_invert 1),
+	(atac 2),
+	(atac 1),
+	(etac allE 1),
+	(dtac mp 1),
+	(atac 1),
+	(etac disjE 1),
+	(contr_tac 1),
+	(asm_simp_tac HOLCF_ss 1)
+	]);
+
+val dnat_ind = prove_goal Dnat.thy
+"[| adm(P);\
+\   P(UU);\
+\   P(dzero);\
+\   !! s1.[|s1~=UU ; P(s1)|] ==> P(dsucc[s1])|] ==> P(s)"
+ (fn prems =>
+	[
+	(rtac (dnat_reach RS subst) 1),
+	(res_inst_tac [("x","s")] spec 1),
+	(rtac fix_ind 1),
+	(rtac adm_all2 1),
+	(rtac adm_subst 1),
+	(contX_tacR 1),
+	(resolve_tac prems 1),
+	(simp_tac HOLCF_ss 1),
+	(resolve_tac prems 1),
+	(strip_tac 1),
+	(res_inst_tac [("n","xa")] dnatE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_copy) 1),
+	(resolve_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_copy) 1),
+	(resolve_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_copy) 1),
+	(res_inst_tac [("Q","x[xb]=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1),
+	(resolve_tac prems 1),
+	(eresolve_tac prems 1),
+	(etac spec 1)
+	]);
+
+val dnat_ind2 = dnat_flat RS adm_flat RS dnat_ind;
+(*  "[| ?P(UU); ?P(dzero);
+    !!s1. [| s1 ~= UU; ?P(s1) |] ==> ?P(dsucc[s1]) |] ==> ?P(?s)" : thm
+*)
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Dnat.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,101 @@
+(*  Title: 	HOLCF/dnat.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Theory for the domain of natural numbers
+
+*)
+
+Dnat = HOLCF +
+
+types dnat 0
+
+(* ----------------------------------------------------------------------- *)
+(* arrity axiom is valuated by semantical reasoning                        *)
+
+arities dnat::pcpo
+
+consts
+
+(* ----------------------------------------------------------------------- *)
+(* essential constants                                                     *)
+
+dnat_rep	:: " dnat -> (one ++ dnat)"
+dnat_abs	:: "(one ++ dnat) -> dnat"
+
+(* ----------------------------------------------------------------------- *)
+(* abstract constants and auxiliary constants                              *)
+
+dnat_copy	:: "(dnat -> dnat) -> dnat -> dnat"
+
+dzero		:: "dnat"
+dsucc		:: "dnat -> dnat"
+dnat_when	:: "'b -> (dnat -> 'b) -> dnat -> 'b"
+is_dzero	:: "dnat -> tr"
+is_dsucc	:: "dnat -> tr"
+dpred		:: "dnat -> dnat"
+dnat_take	:: "nat => dnat -> dnat"
+dnat_bisim	:: "(dnat => dnat => bool) => bool"
+
+rules
+
+(* ----------------------------------------------------------------------- *)
+(* axiomatization of recursive type dnat                                   *)
+(* ----------------------------------------------------------------------- *)
+(* (dnat,dnat_abs) is the initial F-algebra where                          *)
+(* F is the locally continuous functor determined by domain equation       *)
+(* X = one ++ X                                                            *)
+(* ----------------------------------------------------------------------- *)
+(* dnat_abs is an isomorphism with inverse dnat_rep                        *)
+(* identity is the least endomorphism on dnat                              *)
+
+dnat_abs_iso	"dnat_rep[dnat_abs[x]] = x"
+dnat_rep_iso	"dnat_abs[dnat_rep[x]] = x"
+dnat_copy_def	"dnat_copy == (LAM f. dnat_abs oo \
+\		 (when[sinl][sinr oo f]) oo dnat_rep )"
+dnat_reach	"(fix[dnat_copy])[x]=x"
+
+(* ----------------------------------------------------------------------- *)
+(* properties of additional constants                                      *)
+(* ----------------------------------------------------------------------- *)
+(* constructors                                                            *)
+
+dzero_def	"dzero == dnat_abs[sinl[one]]"
+dsucc_def	"dsucc == (LAM n. dnat_abs[sinr[n]])"
+
+(* ----------------------------------------------------------------------- *)
+(* discriminator functional                                                *)
+
+dnat_when_def	"dnat_when == (LAM f1 f2 n.when[LAM x.f1][f2][dnat_rep[n]])"
+
+
+(* ----------------------------------------------------------------------- *)
+(* discriminators and selectors                                            *)
+
+is_dzero_def	"is_dzero == dnat_when[TT][LAM x.FF]"
+is_dsucc_def	"is_dsucc == dnat_when[FF][LAM x.TT]"
+dpred_def	"dpred == dnat_when[UU][LAM x.x]"
+
+
+(* ----------------------------------------------------------------------- *)
+(* the taker for dnats                                                   *)
+
+dnat_take_def "dnat_take == (%n.iterate(n,dnat_copy,UU))"
+
+(* ----------------------------------------------------------------------- *)
+(* definition of bisimulation is determined by domain equation             *)
+(* simplification and rewriting for abstract constants yields def below    *)
+
+dnat_bisim_def "dnat_bisim ==\
+\(%R.!s1 s2.\
+\ 	R(s1,s2) -->\
+\  ((s1=UU & s2=UU) |(s1=dzero & s2=dzero) |\
+\  (? s11 s21. s11~=UU & s21~=UU & s1=dsucc[s11] &\
+\		 s2 = dsucc[s21] & R(s11,s21))))"
+
+end
+
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Dnat2.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,52 @@
+(*  Title: 	HOLCF/dnat2.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for theory Dnat2.thy
+*)
+
+open Dnat2;
+
+
+(* ------------------------------------------------------------------------- *)
+(* expand fixed point properties                                             *)
+(* ------------------------------------------------------------------------- *)
+
+val iterator_def2 = fix_prover Dnat2.thy iterator_def 
+	"iterator = (LAM n f x. dnat_when[x][LAM m.f[iterator[m][f][x]]][n])";
+
+(* ------------------------------------------------------------------------- *)
+(* recursive  properties                                                     *)
+(* ------------------------------------------------------------------------- *)
+
+val iterator1 = prove_goal Dnat2.thy "iterator[UU][f][x] = UU"
+ (fn prems =>
+	[
+	(rtac (iterator_def2 RS ssubst) 1),
+	(simp_tac (HOLCF_ss addsimps dnat_when) 1)
+	]);
+
+val iterator2 = prove_goal Dnat2.thy "iterator[dzero][f][x] = x"
+ (fn prems =>
+	[
+	(rtac (iterator_def2 RS ssubst) 1),
+	(simp_tac (HOLCF_ss addsimps dnat_when) 1)
+	]);
+
+val iterator3 = prove_goal Dnat2.thy 
+"n~=UU ==> iterator[dsucc[n]][f][x] = f[iterator[n][f][x]]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac trans 1),
+	(rtac (iterator_def2 RS ssubst) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dnat_rews) 1),
+	(rtac refl 1)
+	]);
+
+val dnat2_rews = 
+	[iterator1, iterator2, iterator3];
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Dnat2.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,32 @@
+(*  Title: 	HOLCF/dnat2.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Additional constants for dnat
+
+*)
+
+Dnat2 = Dnat +
+
+consts
+
+iterator	:: "dnat -> ('a -> 'a) -> 'a -> 'a"
+
+
+rules
+
+iterator_def	"iterator = fix[LAM h n f x.\
+\	dnat_when[x][LAM m.f[h[m][f][x]]][n]]"
+
+
+end
+
+
+(*
+
+		iterator[UU][f][x] = UU
+		iterator[dzero][f][x] = x
+      n~=UU --> iterator[dsucc[n]][f][x] = f[iterator[n][f][x]]
+*)
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Fix.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,1140 @@
+(*  Title: 	HOLCF/fix.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+Lemmas for fix.thy 
+*)
+
+open Fix;
+
+(* ------------------------------------------------------------------------ *)
+(* derive inductive properties of iterate from primitive recursion          *)
+(* ------------------------------------------------------------------------ *)
+
+val iterate_0 = prove_goal Fix.thy "iterate(0,F,x) = x"
+ (fn prems =>
+	[
+	(resolve_tac (nat_recs iterate_def) 1)
+	]);
+
+val iterate_Suc = prove_goal Fix.thy "iterate(Suc(n),F,x) = F[iterate(n,F,x)]"
+ (fn prems =>
+	[
+	(resolve_tac (nat_recs iterate_def) 1)
+	]);
+
+val iterate_ss = Cfun_ss addsimps [iterate_0,iterate_Suc];
+
+val iterate_Suc2 = prove_goal Fix.thy "iterate(Suc(n),F,x) = iterate(n,F,F[x])"
+ (fn prems =>
+	[
+	(nat_ind_tac "n" 1),
+	(simp_tac iterate_ss 1),
+	(asm_simp_tac iterate_ss 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* the sequence of function itertaions is a chain                           *)
+(* This property is essential since monotonicity of iterate makes no sense  *)
+(* ------------------------------------------------------------------------ *)
+
+val is_chain_iterate2 = prove_goalw Fix.thy [is_chain] 
+	" x << F[x] ==> is_chain(%i.iterate(i,F,x))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(simp_tac iterate_ss 1),
+	(nat_ind_tac "i" 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac iterate_ss 1),
+	(etac monofun_cfun_arg 1)
+	]);
+
+
+val is_chain_iterate = prove_goal Fix.thy  
+	"is_chain(%i.iterate(i,F,UU))"
+ (fn prems =>
+	[
+	(rtac is_chain_iterate2 1),
+	(rtac minimal 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* Kleene's fixed point theorems for continuous functions in pointed        *)
+(* omega cpo's                                                              *)
+(* ------------------------------------------------------------------------ *)
+
+
+val Ifix_eq = prove_goalw Fix.thy  [Ifix_def] "Ifix(F)=F[Ifix(F)]"
+ (fn prems =>
+	[
+	(rtac (contlub_cfun_arg RS ssubst) 1),
+	(rtac is_chain_iterate 1),
+	(rtac antisym_less 1),
+	(rtac lub_mono 1),
+	(rtac is_chain_iterate 1),
+	(rtac ch2ch_fappR 1),
+	(rtac is_chain_iterate 1),
+	(rtac allI 1),
+	(rtac (iterate_Suc RS subst) 1),
+	(rtac (is_chain_iterate RS is_chainE RS spec) 1),
+	(rtac is_lub_thelub 1),
+	(rtac ch2ch_fappR 1),
+	(rtac is_chain_iterate 1),
+	(rtac ub_rangeI 1),
+	(rtac allI 1),
+	(rtac (iterate_Suc RS subst) 1),
+	(rtac is_ub_thelub 1),
+	(rtac is_chain_iterate 1)
+	]);
+
+
+val Ifix_least = prove_goalw Fix.thy [Ifix_def] "F[x]=x ==> Ifix(F) << x"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_lub_thelub 1),
+	(rtac is_chain_iterate 1),
+	(rtac ub_rangeI 1),
+	(strip_tac 1),
+	(nat_ind_tac "i" 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac iterate_ss 1),
+	(res_inst_tac [("t","x")] subst 1),
+	(atac 1),
+	(etac monofun_cfun_arg 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* monotonicity and continuity of iterate                                   *)
+(* ------------------------------------------------------------------------ *)
+
+val monofun_iterate = prove_goalw Fix.thy  [monofun] "monofun(iterate(i))"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(nat_ind_tac "i" 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac iterate_ss 1),
+	(rtac (less_fun RS iffD2) 1),
+	(rtac allI 1),
+	(rtac monofun_cfun 1),
+	(atac 1),
+	(rtac (less_fun RS iffD1 RS spec) 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* the following lemma uses contlub_cfun which itself is based on a         *)
+(* diagonalisation lemma for continuous functions with two arguments.       *)
+(* In this special case it is the application function fapp                 *)
+(* ------------------------------------------------------------------------ *)
+
+val contlub_iterate = prove_goalw Fix.thy  [contlub] "contlub(iterate(i))"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(nat_ind_tac "i" 1),
+	(asm_simp_tac iterate_ss 1),
+	(rtac (lub_const RS thelubI RS sym) 1),
+	(asm_simp_tac iterate_ss 1),
+	(rtac ext 1),
+	(rtac (thelub_fun RS ssubst) 1),
+	(rtac is_chainI 1),
+	(rtac allI 1),
+	(rtac (less_fun RS iffD2) 1),
+	(rtac allI 1),
+	(rtac (is_chainE RS spec) 1),
+	(rtac (monofun_fapp1 RS ch2ch_MF2LR) 1),
+	(rtac allI 1),
+	(rtac monofun_fapp2 1),
+	(atac 1),
+	(rtac ch2ch_fun 1),
+	(rtac (monofun_iterate RS ch2ch_monofun) 1),
+	(atac 1),
+	(rtac (thelub_fun RS ssubst) 1),
+	(rtac (monofun_iterate RS ch2ch_monofun) 1),
+	(atac 1),
+	(rtac contlub_cfun  1),
+	(atac 1),
+	(etac (monofun_iterate RS ch2ch_monofun RS ch2ch_fun) 1)
+	]);
+
+
+val contX_iterate = prove_goal Fix.thy "contX(iterate(i))"
+ (fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_iterate 1),
+	(rtac contlub_iterate 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* a lemma about continuity of iterate in its third argument                *)
+(* ------------------------------------------------------------------------ *)
+
+val monofun_iterate2 = prove_goal Fix.thy "monofun(iterate(n,F))"
+ (fn prems =>
+	[
+	(rtac monofunI 1),
+	(strip_tac 1),
+	(nat_ind_tac "n" 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac iterate_ss 1),
+	(etac monofun_cfun_arg 1)
+	]);
+
+val contlub_iterate2 = prove_goal Fix.thy "contlub(iterate(n,F))"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(nat_ind_tac "n" 1),
+	(simp_tac iterate_ss 1),
+	(simp_tac iterate_ss 1),
+	(res_inst_tac [("t","iterate(n1, F, lub(range(%u. Y(u))))"),
+	("s","lub(range(%i. iterate(n1, F, Y(i))))")] ssubst 1),
+	(atac 1),
+	(rtac contlub_cfun_arg 1),
+	(etac (monofun_iterate2 RS ch2ch_monofun) 1)
+	]);
+
+val contX_iterate2 = prove_goal Fix.thy "contX(iterate(n,F))"
+ (fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_iterate2 1),
+	(rtac contlub_iterate2 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* monotonicity and continuity of Ifix                                      *)
+(* ------------------------------------------------------------------------ *)
+
+val monofun_Ifix = prove_goalw Fix.thy  [monofun,Ifix_def] "monofun(Ifix)"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(rtac lub_mono 1),
+	(rtac is_chain_iterate 1),
+	(rtac is_chain_iterate 1),
+	(rtac allI 1),
+	(rtac (less_fun RS iffD1 RS spec) 1),
+	(etac (monofun_iterate RS monofunE RS spec RS spec RS mp) 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* since iterate is not monotone in its first argument, special lemmas must *)
+(* be derived for lubs in this argument                                     *)
+(* ------------------------------------------------------------------------ *)
+
+val is_chain_iterate_lub = prove_goal Fix.thy   
+"is_chain(Y) ==> is_chain(%i. lub(range(%ia. iterate(ia,Y(i),UU))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_chainI 1),
+	(strip_tac 1),
+	(rtac lub_mono 1),
+	(rtac is_chain_iterate 1),
+	(rtac is_chain_iterate 1),
+	(strip_tac 1),
+	(etac (monofun_iterate RS ch2ch_monofun RS ch2ch_fun RS is_chainE 
+         RS spec) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* this exchange lemma is analog to the one for monotone functions          *)
+(* observe that monotonicity is not really needed. The propagation of       *)
+(* chains is the essential argument which is usually derived from monot.    *)
+(* ------------------------------------------------------------------------ *)
+
+val contlub_Ifix_lemma1 = prove_goal Fix.thy 
+"is_chain(Y) ==> iterate(n,lub(range(Y)),y) = lub(range(%i. iterate(n,Y(i),y)))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (thelub_fun RS subst) 1),
+	(rtac (monofun_iterate RS ch2ch_monofun) 1),
+	(atac 1),
+	(rtac fun_cong 1),
+	(rtac (contlub_iterate RS contlubE RS spec RS mp RS ssubst) 1),
+	(atac 1),
+	(rtac refl 1)
+	]);
+
+
+val ex_lub_iterate = prove_goal Fix.thy  "is_chain(Y) ==>\
+\         lub(range(%i. lub(range(%ia. iterate(i,Y(ia),UU))))) =\
+\         lub(range(%i. lub(range(%ia. iterate(ia,Y(i),UU)))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac antisym_less 1),
+	(rtac is_lub_thelub 1),
+	(rtac (contlub_Ifix_lemma1 RS ext RS subst) 1),
+	(atac 1),
+	(rtac is_chain_iterate 1),
+	(rtac ub_rangeI 1),
+	(strip_tac 1),
+	(rtac lub_mono 1),
+	(etac (monofun_iterate RS ch2ch_monofun RS ch2ch_fun) 1),
+	(etac is_chain_iterate_lub 1),
+	(strip_tac 1),
+	(rtac is_ub_thelub 1),
+	(rtac is_chain_iterate 1),
+	(rtac is_lub_thelub 1),
+	(etac is_chain_iterate_lub 1),
+	(rtac ub_rangeI 1),
+	(strip_tac 1),
+	(rtac lub_mono 1),
+	(rtac is_chain_iterate 1),
+	(rtac (contlub_Ifix_lemma1 RS ext RS subst) 1),
+	(atac 1),
+	(rtac is_chain_iterate 1),
+	(strip_tac 1),
+	(rtac is_ub_thelub 1),
+	(etac (monofun_iterate RS ch2ch_monofun RS ch2ch_fun) 1)
+	]);
+
+
+val contlub_Ifix = prove_goalw Fix.thy  [contlub,Ifix_def] "contlub(Ifix)"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(rtac (contlub_Ifix_lemma1 RS ext RS ssubst) 1),
+	(atac 1),
+	(etac ex_lub_iterate 1)
+	]);
+
+
+val contX_Ifix = prove_goal Fix.thy "contX(Ifix)"
+ (fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_Ifix 1),
+	(rtac contlub_Ifix 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* propagate properties of Ifix to its continuous counterpart               *)
+(* ------------------------------------------------------------------------ *)
+
+val fix_eq = prove_goalw Fix.thy  [fix_def] "fix[F]=F[fix[F]]"
+ (fn prems =>
+	[
+	(asm_simp_tac (Cfun_ss addsimps [contX_Ifix]) 1),
+	(rtac Ifix_eq 1)
+	]);
+
+val fix_least = prove_goalw Fix.thy [fix_def] "F[x]=x ==> fix[F] << x"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(asm_simp_tac (Cfun_ss addsimps [contX_Ifix]) 1),
+	(etac Ifix_least 1)
+	]);
+
+
+val fix_eq2 = prove_goal Fix.thy "f == fix[F] ==> f = F[f]"
+ (fn prems =>
+	[
+	(rewrite_goals_tac prems),
+	(rtac fix_eq 1)
+	]);
+
+val fix_eq3 = prove_goal Fix.thy "f == fix[F] ==> f[x] = F[f][x]"
+ (fn prems =>
+	[
+	(rtac trans 1),
+	(rtac ((hd prems) RS fix_eq2 RS cfun_fun_cong) 1),
+	(rtac refl 1)
+	]);
+
+fun fix_tac3 thm i  = ((rtac trans i) THEN (rtac (thm RS fix_eq3) i)); 
+
+val fix_eq4 = prove_goal Fix.thy "f = fix[F] ==> f = F[f]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(hyp_subst_tac 1),
+	(rtac fix_eq 1)
+	]);
+
+val fix_eq5 = prove_goal Fix.thy "f = fix[F] ==> f[x] = F[f][x]"
+ (fn prems =>
+	[
+	(rtac trans 1),
+	(rtac ((hd prems) RS fix_eq4 RS cfun_fun_cong) 1),
+	(rtac refl 1)
+	]);
+
+fun fix_tac5 thm i  = ((rtac trans i) THEN (rtac (thm RS fix_eq5) i)); 
+
+fun fix_prover thy fixdef thm = prove_goal thy thm
+ (fn prems =>
+        [
+        (rtac trans 1),
+        (rtac (fixdef RS fix_eq4) 1),
+        (rtac trans 1),
+        (rtac beta_cfun 1),
+        (contX_tacR 1),
+        (rtac refl 1)
+        ]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* better access to definitions                                             *)
+(* ------------------------------------------------------------------------ *)
+
+
+val Ifix_def2 = prove_goal Fix.thy "Ifix=(%x. lub(range(%i. iterate(i,x,UU))))"
+ (fn prems =>
+	[
+	(rtac ext 1),
+	(rewrite_goals_tac [Ifix_def]),
+	(rtac refl 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* direct connection between fix and iteration without Ifix                 *)
+(* ------------------------------------------------------------------------ *)
+
+val fix_def2 = prove_goalw Fix.thy [fix_def]
+ "fix[F] = lub(range(%i. iterate(i,F,UU)))"
+ (fn prems =>
+	[
+	(fold_goals_tac [Ifix_def]),
+	(asm_simp_tac (Cfun_ss addsimps [contX_Ifix]) 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* Lemmas about admissibility and fixed point induction                     *)
+(* ------------------------------------------------------------------------ *)
+
+(* ------------------------------------------------------------------------ *)
+(* access to definitions                                                    *)
+(* ------------------------------------------------------------------------ *)
+
+val adm_def2 = prove_goalw Fix.thy [adm_def]
+	"adm(P) = (!Y. is_chain(Y) --> (!i.P(Y(i))) --> P(lub(range(Y))))"
+ (fn prems =>
+	[
+	(rtac refl 1)
+	]);
+
+val admw_def2 = prove_goalw Fix.thy [admw_def]
+	"admw(P) = (!F.((!n.P(iterate(n,F,UU)))-->\
+\			 P(lub(range(%i.iterate(i,F,UU))))))"
+ (fn prems =>
+	[
+	(rtac refl 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* an admissible formula is also weak admissible                            *)
+(* ------------------------------------------------------------------------ *)
+
+val adm_impl_admw = prove_goalw  Fix.thy [admw_def] "adm(P)==>admw(P)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(rtac (adm_def2 RS iffD1 RS spec RS mp RS mp) 1),
+	(atac 1),
+	(rtac is_chain_iterate 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* fixed point induction                                                    *)
+(* ------------------------------------------------------------------------ *)
+
+val fix_ind = prove_goal  Fix.thy  
+"[| adm(P);P(UU);!!x. P(x) ==> P(F[x])|] ==> P(fix[F])"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (fix_def2 RS ssubst) 1),
+	(rtac (adm_def2 RS iffD1 RS spec RS mp RS mp) 1),
+	(atac 1),
+	(rtac is_chain_iterate 1),
+	(rtac allI 1),
+	(nat_ind_tac "i" 1),
+	(rtac (iterate_0 RS ssubst) 1),
+	(atac 1),
+	(rtac (iterate_Suc RS ssubst) 1),
+	(resolve_tac prems 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* computational induction for weak admissible formulae                     *)
+(* ------------------------------------------------------------------------ *)
+
+val wfix_ind = prove_goal  Fix.thy  
+"[| admw(P); !n. P(iterate(n,F,UU))|] ==> P(fix[F])"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (fix_def2 RS ssubst) 1),
+	(rtac (admw_def2 RS iffD1 RS spec RS mp) 1),
+	(atac 1),
+	(rtac allI 1),
+	(etac spec 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* for chain-finite (easy) types every formula is admissible                *)
+(* ------------------------------------------------------------------------ *)
+
+val adm_max_in_chain = prove_goalw  Fix.thy  [adm_def]
+"!Y. is_chain(Y::nat=>'a) --> (? n.max_in_chain(n,Y)) ==> adm(P::'a=>bool)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(rtac exE 1),
+	(rtac mp 1),
+	(etac spec 1),
+	(atac 1),
+	(rtac (lub_finch1 RS thelubI RS ssubst) 1),
+	(atac 1),
+	(atac 1),
+	(etac spec 1)
+	]);
+
+
+val adm_chain_finite = prove_goalw  Fix.thy  [chain_finite_def]
+	"chain_finite(x::'a) ==> adm(P::'a=>bool)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac adm_max_in_chain 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* flat types are chain_finite                                              *)
+(* ------------------------------------------------------------------------ *)
+
+val flat_imp_chain_finite = prove_goalw  Fix.thy  [flat_def,chain_finite_def]
+	"flat(x::'a)==>chain_finite(x::'a)"
+ (fn prems =>
+	[
+	(rewrite_goals_tac [max_in_chain_def]),
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(res_inst_tac [("Q","!i.Y(i)=UU")] classical2 1),
+	(res_inst_tac [("x","0")] exI 1),
+	(strip_tac 1),
+	(rtac trans 1),
+	(etac spec 1),
+	(rtac sym 1),
+	(etac spec 1),
+	(rtac (chain_mono2 RS exE) 1),
+	(fast_tac HOL_cs 1),
+	(atac 1),
+	(res_inst_tac [("x","Suc(x)")] exI 1),
+	(strip_tac 1),
+	(rtac disjE 1),
+	(atac 3),
+	(rtac mp 1),
+	(dtac spec 1),
+	(etac spec 1),
+	(etac (le_imp_less_or_eq RS disjE) 1),
+	(etac (chain_mono RS mp) 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(rtac refl_less 1),
+	(res_inst_tac [("P","Y(Suc(x)) = UU")] notE 1),
+	(atac 2),
+	(rtac mp 1),
+	(etac spec 1),
+	(asm_simp_tac nat_ss 1)
+	]);
+
+
+val adm_flat = flat_imp_chain_finite RS adm_chain_finite;
+(* flat(?x::?'a) ==> adm(?P::?'a => bool) *)
+
+val flat_void = prove_goalw Fix.thy [flat_def] "flat(UU::void)"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(rtac disjI1 1),
+	(rtac unique_void2 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* continuous isomorphisms are strict                                       *)
+(* a prove for embedding projection pairs is similar                        *)
+(* ------------------------------------------------------------------------ *)
+
+val iso_strict = prove_goal  Fix.thy  
+"!!f g.[|!y.f[g[y]]=(y::'b) ; !x.g[f[x]]=(x::'a) |] \
+\ ==> f[UU]=UU & g[UU]=UU"
+ (fn prems =>
+	[
+	(rtac conjI 1),
+	(rtac UU_I 1),
+	(res_inst_tac [("s","f[g[UU::'b]]"),("t","UU::'b")] subst 1),
+	(etac spec 1),
+	(rtac (minimal RS monofun_cfun_arg) 1),
+	(rtac UU_I 1),
+	(res_inst_tac [("s","g[f[UU::'a]]"),("t","UU::'a")] subst 1),
+	(etac spec 1),
+	(rtac (minimal RS monofun_cfun_arg) 1)
+	]);
+
+
+val isorep_defined = prove_goal Fix.thy 
+	"[|!x.rep[abs[x]]=x;!y.abs[rep[y]]=y;z~=UU|] ==> rep[z]~=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac swap 1),
+	(dtac notnotD 1),
+	(dres_inst_tac [("f","abs")] cfun_arg_cong 1),
+	(etac box_equals 1),
+	(fast_tac HOL_cs 1),
+	(etac (iso_strict RS conjunct1) 1),
+	(atac 1)
+	]);
+
+val isoabs_defined = prove_goal Fix.thy 
+	"[|!x.rep[abs[x]]=x;!y.abs[rep[y]]=y;z~=UU|] ==> abs[z]~=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac swap 1),
+	(dtac notnotD 1),
+	(dres_inst_tac [("f","rep")] cfun_arg_cong 1),
+	(etac box_equals 1),
+	(fast_tac HOL_cs 1),
+	(etac (iso_strict RS conjunct2) 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* propagation of flatness and chainfiniteness by continuous isomorphisms   *)
+(* ------------------------------------------------------------------------ *)
+
+val chfin2chfin = prove_goalw  Fix.thy  [chain_finite_def]
+"!!f g.[|chain_finite(x::'a); !y.f[g[y]]=(y::'b) ; !x.g[f[x]]=(x::'a) |] \
+\ ==> chain_finite(y::'b)"
+ (fn prems =>
+	[
+	(rewrite_goals_tac [max_in_chain_def]),
+	(strip_tac 1),
+	(rtac exE 1),
+	(res_inst_tac [("P","is_chain(%i.g[Y(i)])")] mp 1),
+	(etac spec 1),
+	(etac ch2ch_fappR 1),
+	(rtac exI 1),
+	(strip_tac 1),
+	(res_inst_tac [("s","f[g[Y(x)]]"),("t","Y(x)")] subst 1),
+	(etac spec 1),
+	(res_inst_tac [("s","f[g[Y(j)]]"),("t","Y(j)")] subst 1),
+	(etac spec 1),
+	(rtac cfun_arg_cong 1),
+	(rtac mp 1),
+	(etac spec 1),
+	(atac 1)
+	]);
+
+val flat2flat = prove_goalw  Fix.thy  [flat_def]
+"!!f g.[|flat(x::'a); !y.f[g[y]]=(y::'b) ; !x.g[f[x]]=(x::'a) |] \
+\ ==> flat(y::'b)"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(rtac disjE 1),
+	(res_inst_tac [("P","g[x]<<g[y]")] mp 1),
+	(etac monofun_cfun_arg 2),
+	(dtac spec 1),
+	(etac spec 1),
+	(rtac disjI1 1),
+	(rtac trans 1),
+	(res_inst_tac [("s","f[g[x]]"),("t","x")] subst 1),
+	(etac spec 1),
+	(etac cfun_arg_cong 1),
+	(rtac (iso_strict RS conjunct1) 1),
+	(atac 1),
+	(atac 1),
+	(rtac disjI2 1),
+	(res_inst_tac [("s","f[g[x]]"),("t","x")] subst 1),
+	(etac spec 1),
+	(res_inst_tac [("s","f[g[y]]"),("t","y")] subst 1),
+	(etac spec 1),
+	(etac cfun_arg_cong 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* admissibility of special formulae and propagation                        *)
+(* ------------------------------------------------------------------------ *)
+
+val adm_less = prove_goalw  Fix.thy [adm_def]
+	"[|contX(u);contX(v)|]==> adm(%x.u(x)<<v(x))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(etac (contX2contlub RS contlubE RS spec RS mp RS ssubst) 1),
+	(atac 1),
+	(etac (contX2contlub RS contlubE RS spec RS mp RS ssubst) 1),
+	(atac 1),
+	(rtac lub_mono 1),
+	(cut_facts_tac prems 1),
+	(etac (contX2mono RS ch2ch_monofun) 1),
+	(atac 1),
+	(cut_facts_tac prems 1),
+	(etac (contX2mono RS ch2ch_monofun) 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+val adm_conj = prove_goal  Fix.thy  
+	"[| adm(P); adm(Q) |] ==> adm(%x.P(x)&Q(x))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (adm_def2 RS iffD2) 1),
+	(strip_tac 1),
+	(rtac conjI 1),
+	(rtac (adm_def2 RS iffD1 RS spec RS mp RS mp) 1),
+	(atac 1),
+	(atac 1),
+	(fast_tac HOL_cs 1),
+	(rtac (adm_def2 RS iffD1 RS spec RS mp RS mp) 1),
+	(atac 1),
+	(atac 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val adm_cong = prove_goal  Fix.thy  
+	"(!x. P(x) = Q(x)) ==> adm(P)=adm(Q)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("s","P"),("t","Q")] subst 1),
+	(rtac refl 2),
+	(rtac ext 1),
+	(etac spec 1)
+	]);
+
+val adm_not_free = prove_goalw  Fix.thy [adm_def] "adm(%x.t)"
+ (fn prems =>
+	[
+	(fast_tac HOL_cs 1)
+	]);
+
+val adm_not_less = prove_goalw  Fix.thy [adm_def]
+	"contX(t) ==> adm(%x.~ t(x) << u)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(rtac contrapos 1),
+	(etac spec 1),
+	(rtac trans_less 1),
+	(atac 2),
+	(etac (contX2mono RS monofun_fun_arg) 1),
+	(rtac is_ub_thelub 1),
+	(atac 1)
+	]);
+
+val adm_all = prove_goal  Fix.thy  
+	" !y.adm(P(y)) ==> adm(%x.!y.P(y,x))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (adm_def2 RS iffD2) 1),
+	(strip_tac 1),
+	(rtac (adm_def2 RS iffD1 RS spec RS mp RS mp) 1),
+	(etac spec 1),
+	(atac 1),
+	(rtac allI 1),
+	(dtac spec 1),
+	(etac spec 1)
+	]);
+
+val adm_subst = prove_goal  Fix.thy  
+	"[|contX(t); adm(P)|] ==> adm(%x.P(t(x)))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (adm_def2 RS iffD2) 1),
+	(strip_tac 1),
+	(rtac (contX2contlub RS contlubE RS spec RS mp RS ssubst) 1),
+	(atac 1),
+	(atac 1),
+	(rtac (adm_def2 RS iffD1 RS spec RS mp RS mp) 1),
+	(atac 1),
+	(rtac (contX2mono RS ch2ch_monofun) 1),
+	(atac 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+val adm_UU_not_less = prove_goal  Fix.thy "adm(%x.~ UU << t(x))"
+ (fn prems =>
+	[
+	(res_inst_tac [("P2","%x.False")] (adm_cong RS iffD1) 1),
+	(asm_simp_tac Cfun_ss 1),
+	(rtac adm_not_free 1)
+	]);
+
+val adm_not_UU = prove_goalw  Fix.thy [adm_def] 
+	"contX(t)==> adm(%x.~ t(x) = UU)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(rtac contrapos 1),
+	(etac spec 1),
+	(rtac (chain_UU_I RS spec) 1),
+	(rtac (contX2mono RS ch2ch_monofun) 1),
+	(atac 1),
+	(atac 1),
+	(rtac (contX2contlub RS contlubE RS spec RS mp RS subst) 1),
+	(atac 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+val adm_eq = prove_goal  Fix.thy 
+	"[|contX(u);contX(v)|]==> adm(%x.u(x)= v(x))"
+ (fn prems =>
+	[
+	(rtac (adm_cong RS iffD1) 1),
+	(rtac allI 1),
+	(rtac iffI 1),
+	(rtac antisym_less 1),
+	(rtac antisym_less_inverse 3),
+	(atac 3),
+	(etac conjunct1 1),
+	(etac conjunct2 1),
+	(rtac adm_conj 1),
+	(rtac adm_less 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1),
+	(rtac adm_less 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* admissibility for disjunction is hard to prove. It takes 10 Lemmas       *)
+(* ------------------------------------------------------------------------ *)
+
+val adm_disj_lemma1 = prove_goal  Pcpo.thy 
+"[| is_chain(Y); !n.P(Y(n))|Q(Y(n))|]\
+\ ==> (? i.!j. i<j --> Q(Y(j))) | (!i.? j.i<j & P(Y(j)))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val adm_disj_lemma2 = prove_goal  Fix.thy  
+"[| adm(Q); ? X.is_chain(X) & (!n.Q(X(n))) &\
+\   lub(range(Y))=lub(range(X))|] ==> Q(lub(range(Y)))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac exE 1),
+	(etac conjE 1),
+	(etac conjE 1),
+	(res_inst_tac [("s","lub(range(X))"),("t","lub(range(Y))")] ssubst 1),
+	(atac 1),
+	(rtac (adm_def2 RS iffD1 RS spec RS mp RS mp) 1),
+	(atac 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+val adm_disj_lemma3 = prove_goal  Fix.thy
+"[| is_chain(Y); ! j. i < j --> Q(Y(j)) |] ==>\
+\         is_chain(%m. if(m < Suc(i),Y(Suc(i)),Y(m)))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_chainI 1),
+	(rtac allI 1),
+	(res_inst_tac [("m","i"),("n","ia")] nat_less_cases 1),
+	(res_inst_tac [("s","False"),("t","ia < Suc(i)")] ssubst 1),
+	(rtac iffI 1),
+	(etac FalseE 2),
+	(rtac notE 1),
+	(rtac (not_less_eq RS iffD2) 1),
+	(atac 1),
+	(atac 1),
+	(res_inst_tac [("s","False"),("t","Suc(ia) < Suc(i)")] ssubst 1),
+	(asm_simp_tac nat_ss  1),
+	(rtac iffI 1),
+	(etac FalseE 2),
+	(rtac notE 1),
+	(etac (less_not_sym RS mp) 1),	
+	(atac 1),
+	(asm_simp_tac Cfun_ss  1),
+	(etac (is_chainE RS spec) 1),
+	(hyp_subst_tac 1),
+	(asm_simp_tac nat_ss 1),
+	(rtac refl_less 1),
+	(asm_simp_tac nat_ss 1),
+	(rtac refl_less 1)
+	]);
+
+val adm_disj_lemma4 = prove_goal  Fix.thy
+"[| ! j. i < j --> Q(Y(j)) |] ==>\
+\	 ! n. Q(if(n < Suc(i),Y(Suc(i)),Y(n)))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac allI 1),
+	(res_inst_tac [("m","n"),("n","Suc(i)")] nat_less_cases 1),
+	(res_inst_tac[("s","Y(Suc(i))"),("t","if(n<Suc(i),Y(Suc(i)),Y(n))")]
+		ssubst 1),
+	(asm_simp_tac nat_ss 1),
+	(etac allE 1),
+	(rtac mp 1),
+	(atac 1),
+	(asm_simp_tac nat_ss 1),
+	(res_inst_tac[("s","Y(n)"),("t","if(n<Suc(i),Y(Suc(i)),Y(n))")] 
+		ssubst 1),
+	(asm_simp_tac nat_ss 1),
+	(hyp_subst_tac 1),
+	(dtac spec 1),
+	(rtac mp 1),
+	(atac 1),
+	(asm_simp_tac nat_ss 1),
+	(res_inst_tac [("s","Y(n)"),("t","if(n < Suc(i),Y(Suc(i)),Y(n))")] 
+		ssubst 1),
+	(res_inst_tac [("s","False"),("t","n < Suc(i)")] ssubst 1),
+	(rtac iffI 1),
+	(etac FalseE 2),
+	(rtac notE 1),
+	(etac (less_not_sym RS mp) 1),	
+	(atac 1),
+	(asm_simp_tac nat_ss 1),
+	(dtac spec 1),
+	(rtac mp 1),
+	(atac 1),
+	(etac Suc_lessD 1)
+	]);
+
+val adm_disj_lemma5 = prove_goal  Fix.thy
+"[| is_chain(Y::nat=>'a); ! j. i < j --> Q(Y(j)) |] ==>\
+\         lub(range(Y)) = lub(range(%m. if(m < Suc(i),Y(Suc(i)),Y(m))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac lub_equal2 1),
+	(atac 2),
+	(rtac adm_disj_lemma3 2),
+	(atac 2),
+	(atac 2),
+	(res_inst_tac [("x","i")] exI 1),
+	(strip_tac 1),
+	(res_inst_tac [("s","False"),("t","ia < Suc(i)")] ssubst 1),
+	(rtac iffI 1),
+	(etac FalseE 2),
+	(rtac notE 1),
+	(rtac (not_less_eq RS iffD2) 1),
+	(atac 1),
+	(atac 1),
+	(rtac (if_False RS ssubst) 1),
+	(rtac refl 1)
+	]);
+
+val adm_disj_lemma6 = prove_goal  Fix.thy
+"[| is_chain(Y::nat=>'a); ? i. ! j. i < j --> Q(Y(j)) |] ==>\
+\         ? X. is_chain(X) & (! n. Q(X(n))) & lub(range(Y)) = lub(range(X))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac exE 1),
+	(res_inst_tac [("x","%m.if(m< Suc(i),Y(Suc(i)),Y(m))")] exI 1),
+	(rtac conjI 1),
+	(rtac adm_disj_lemma3 1),
+	(atac 1),
+	(atac 1),
+	(rtac conjI 1),
+	(rtac adm_disj_lemma4 1),
+	(atac 1),
+	(rtac adm_disj_lemma5 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+
+val adm_disj_lemma7 = prove_goal  Fix.thy 
+"[| is_chain(Y::nat=>'a); ! i. ? j. i < j & P(Y(j))  |] ==>\
+\         is_chain(%m. Y(theleast(%j. m<j & P(Y(j)))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_chainI 1),
+	(rtac allI 1),
+	(rtac chain_mono3 1),
+	(atac 1),
+	(rtac theleast2 1),
+	(rtac conjI 1),
+	(rtac Suc_lessD 1),
+	(etac allE 1),
+	(etac exE 1),
+	(rtac (theleast1 RS conjunct1) 1),
+	(atac 1),
+	(etac allE 1),
+	(etac exE 1),
+	(rtac (theleast1 RS conjunct2) 1),
+	(atac 1)
+	]);
+
+val adm_disj_lemma8 = prove_goal  Fix.thy 
+"[| ! i. ? j. i < j & P(Y(j)) |] ==> ! m. P(Y(theleast(%j. m<j & P(Y(j)))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(etac allE 1),
+	(etac exE 1),
+	(etac (theleast1 RS conjunct2) 1)
+	]);
+
+val adm_disj_lemma9 = prove_goal  Fix.thy
+"[| is_chain(Y::nat=>'a); ! i. ? j. i < j & P(Y(j)) |] ==>\
+\         lub(range(Y)) = lub(range(%m. Y(theleast(%j. m<j & P(Y(j))))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac antisym_less 1),
+	(rtac lub_mono 1),
+	(atac 1),
+	(rtac adm_disj_lemma7 1),
+	(atac 1),
+	(atac 1),
+	(strip_tac 1),
+	(rtac (chain_mono RS mp) 1),
+	(atac 1),
+	(etac allE 1),
+	(etac exE 1),
+	(rtac (theleast1 RS conjunct1) 1),
+	(atac 1),
+	(rtac lub_mono3 1),
+	(rtac adm_disj_lemma7 1),
+	(atac 1),
+	(atac 1),
+	(atac 1),
+	(strip_tac 1),
+	(rtac exI 1),
+	(rtac (chain_mono RS mp) 1),
+	(atac 1),
+	(rtac lessI 1)
+	]);
+
+val adm_disj_lemma10 = prove_goal  Fix.thy
+"[| is_chain(Y::nat=>'a); ! i. ? j. i < j & P(Y(j)) |] ==>\
+\         ? X. is_chain(X) & (! n. P(X(n))) & lub(range(Y)) = lub(range(X))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("x","%m. Y(theleast(%j. m<j & P(Y(j))))")] exI 1),
+	(rtac conjI 1),
+	(rtac adm_disj_lemma7 1),
+	(atac 1),
+	(atac 1),
+	(rtac conjI 1),
+	(rtac adm_disj_lemma8 1),
+	(atac 1),
+	(rtac adm_disj_lemma9 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+val adm_disj = prove_goal  Fix.thy  
+	"[| adm(P); adm(Q) |] ==> adm(%x.P(x)|Q(x))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (adm_def2 RS iffD2) 1),
+	(strip_tac 1),
+	(rtac (adm_disj_lemma1 RS disjE) 1),
+	(atac 1),
+	(atac 1),
+	(rtac disjI2 1),
+	(rtac adm_disj_lemma2 1),
+	(atac 1),
+	(rtac adm_disj_lemma6 1),
+	(atac 1),
+	(atac 1),
+	(rtac disjI1 1),
+	(rtac adm_disj_lemma2 1),
+	(atac 1),
+	(rtac adm_disj_lemma10 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+val adm_impl = prove_goal  Fix.thy  
+	"[| adm(%x.~P(x)); adm(Q) |] ==> adm(%x.P(x)-->Q(x))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("P2","%x.~P(x)|Q(x)")] (adm_cong RS iffD1) 1),
+	(fast_tac HOL_cs 1),
+	(rtac adm_disj 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+
+val adm_all2 = (allI RS adm_all);
+
+val adm_thms = [adm_impl,adm_disj,adm_eq,adm_not_UU,adm_UU_not_less,
+	adm_all2,adm_not_less,adm_not_free,adm_conj,adm_less
+	];
+
+(* ------------------------------------------------------------------------- *)
+(* a result about functions with flat codomain                               *)
+(* ------------------------------------------------------------------------- *)
+
+val flat_codom = prove_goalw Fix.thy [flat_def]
+"[|flat(y::'b);f[x::'a]=(c::'b)|] ==> f[UU::'a]=UU::'b | (!z.f[z::'a]=c)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("Q","f[x::'a]=UU::'b")] classical2 1),
+	(rtac disjI1 1),
+	(rtac UU_I 1),
+	(res_inst_tac [("s","f[x]"),("t","UU::'b")] subst 1),
+	(atac 1),
+	(rtac (minimal RS monofun_cfun_arg) 1),
+	(res_inst_tac [("Q","f[UU::'a]=UU::'b")] classical2 1),
+	(etac disjI1 1),
+	(rtac disjI2 1),
+	(rtac allI 1),
+	(res_inst_tac [("s","f[x]"),("t","c")] subst 1),
+	(atac 1),
+	(res_inst_tac [("a","f[UU::'a]")] (refl RS box_equals) 1),
+	(etac allE 1),(etac allE 1),
+	(dtac mp 1),
+	(res_inst_tac [("fo5","f")] (minimal RS monofun_cfun_arg) 1),
+	(etac disjE 1),
+	(contr_tac 1),
+	(atac 1),
+	(etac allE 1),
+	(etac allE 1),
+	(dtac mp 1),
+	(res_inst_tac [("fo5","f")] (minimal RS monofun_cfun_arg) 1),
+	(etac disjE 1),
+	(contr_tac 1),
+	(atac 1)
+	]);
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Fix.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,42 @@
+(*  Title: 	HOLCF/fix.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+
+definitions for fixed point operator and admissibility
+
+*)
+
+Fix = Cfun3 +
+
+consts
+
+iterate :: "nat=>('a->'a)=>'a=>'a"
+Ifix    :: "('a->'a)=>'a"
+fix     :: "('a->'a)->'a"
+adm          :: "('a=>bool)=>bool"
+admw         :: "('a=>bool)=>bool"
+chain_finite :: "'a=>bool"
+flat         :: "'a=>bool"
+
+rules
+
+iterate_def   "iterate(n,F,c) == nat_rec(n,c,%n x.F[x])"
+Ifix_def      "Ifix(F) == lub(range(%i.iterate(i,F,UU)))"
+fix_def       "fix == (LAM f. Ifix(f))"
+
+adm_def       "adm(P) == !Y. is_chain(Y) --> \
+\                        (!i.P(Y(i))) --> P(lub(range(Y)))"
+
+admw_def      "admw(P)== (!F.((!n.P(iterate(n,F,UU)))-->\
+\			 P(lub(range(%i.iterate(i,F,UU))))))" 
+
+chain_finite_def  "chain_finite(x::'a)==\
+\                        !Y. is_chain(Y::nat=>'a) --> (? n.max_in_chain(n,Y))"
+
+flat_def          "flat(x::'a) ==\
+\                        ! x y. x::'a << y --> (x = UU) | (x=y)"
+
+end
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Fun1.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,49 @@
+(*  Title: 	HOLCF/fun1.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+Lemmas for fun1.thy 
+*)
+
+open Fun1;
+
+(* ------------------------------------------------------------------------ *)
+(* less_fun is a partial order on 'a => 'b                                  *)
+(* ------------------------------------------------------------------------ *)
+
+val refl_less_fun = prove_goalw Fun1.thy [less_fun_def] "less_fun(f,f)"
+(fn prems =>
+	[
+	(fast_tac (HOL_cs addSIs [refl_less]) 1)
+	]);
+
+val antisym_less_fun = prove_goalw Fun1.thy [less_fun_def] 
+	"[|less_fun(f1,f2); less_fun(f2,f1)|] ==> f1 = f2"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (expand_fun_eq RS ssubst) 1),
+	(fast_tac (HOL_cs addSIs [antisym_less]) 1)
+	]);
+
+val trans_less_fun = prove_goalw Fun1.thy [less_fun_def] 
+	"[|less_fun(f1,f2); less_fun(f2,f3)|] ==> less_fun(f1,f3)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(rtac trans_less 1),
+	(etac allE 1),
+	(atac 1),
+	((etac allE 1) THEN (atac 1))
+	]);
+
+(* 
+ -------------------------------------------------------------------------- 
+   Since less_fun :: "['a::term=>'b::po,'a::term=>'b::po] => bool" the
+   lemmas refl_less_fun, antisym_less_fun, trans_less_fun justify
+   the class arity fun::(term,po)po !!
+ -------------------------------------------------------------------------- 
+*)
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Fun1.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,30 @@
+(*  Title: 	HOLCF/fun1.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+
+Definition of the partial ordering for the type of all functions => (fun)
+
+REMARK: The ordering on 'a => 'b is only defined if 'b is in class po !!
+
+*)
+
+Fun1 = Pcpo +
+
+(* default class is still term *)
+
+consts
+  less_fun	:: "['a=>'b::po,'a=>'b] => bool"	
+
+rules
+   (* definition of the ordering less_fun            *)
+   (* in fun1.ML it is proved that less_fun is a po *)
+   
+  less_fun_def "less_fun(f1,f2) == ! x. f1(x) << f2(x)"  
+
+end
+
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Fun2.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,106 @@
+(*  Title: 	HOLCF/fun2.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for fun2.thy 
+*)
+
+open Fun2;
+
+(* ------------------------------------------------------------------------ *)
+(* Type 'a::term => 'b::pcpo is pointed                                     *)
+(* ------------------------------------------------------------------------ *)
+
+val minimal_fun = prove_goalw  Fun2.thy [UU_fun_def] "UU_fun << f"
+(fn prems =>
+	[
+	(rtac (inst_fun_po RS ssubst) 1),
+	(rewrite_goals_tac [less_fun_def]),
+	(fast_tac (HOL_cs addSIs [minimal]) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* make the symbol << accessible for type fun                               *)
+(* ------------------------------------------------------------------------ *)
+
+val less_fun = prove_goal  Fun2.thy  "(f1 << f2) = (! x. f1(x) << f2(x))"
+(fn prems =>
+	[
+	(rtac (inst_fun_po RS ssubst) 1),
+	(fold_goals_tac [less_fun_def]),
+	(rtac refl 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* chains of functions yield chains in the po range                         *)
+(* ------------------------------------------------------------------------ *)
+
+val ch2ch_fun = prove_goal  Fun2.thy 
+	"is_chain(S::nat=>('a::term => 'b::po)) ==> is_chain(% i.S(i)(x))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rewrite_goals_tac [is_chain]),
+	(rtac allI 1),
+	(rtac spec 1),
+	(rtac (less_fun RS subst) 1),
+	(etac allE 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* upper bounds of function chains yield upper bound in the po range        *)
+(* ------------------------------------------------------------------------ *)
+
+val ub2ub_fun = prove_goal Fun2.thy 
+   " range(S::nat=>('a::term => 'b::po)) <| u ==> range(%i. S(i,x)) <| u(x)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac ub_rangeI 1),
+	(rtac allI 1),
+	(rtac allE 1),
+	(rtac (less_fun RS subst) 1),
+	(etac (ub_rangeE RS spec) 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* Type 'a::term => 'b::pcpo is chain complete                              *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_fun = prove_goal  Fun2.thy
+	"is_chain(S::nat=>('a::term => 'b::pcpo)) ==> \
+\        range(S) <<| (% x.lub(range(% i.S(i)(x))))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_lubI 1),
+	(rtac conjI 1),
+	(rtac ub_rangeI 1),
+	(rtac allI 1),
+	(rtac (less_fun RS ssubst) 1),
+	(rtac allI 1),
+	(rtac is_ub_thelub 1),
+	(etac ch2ch_fun 1),
+	(strip_tac 1),
+	(rtac (less_fun RS ssubst) 1),
+	(rtac allI 1),
+	(rtac is_lub_thelub 1),
+	(etac ch2ch_fun 1),
+	(etac ub2ub_fun 1)
+	]);
+
+val thelub_fun = (lub_fun RS thelubI);
+(* is_chain(?S1) ==> lub(range(?S1)) = (%x. lub(range(%i. ?S1(i,x)))) *)
+
+val cpo_fun = prove_goal  Fun2.thy
+	"is_chain(S::nat=>('a::term => 'b::pcpo)) ==> ? x. range(S) <<| x"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac exI 1),
+	(etac lub_fun 1)
+	]);
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Fun2.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,40 @@
+(*  Title: 	HOLCF/fun2.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Class Instance =>::(term,po)po
+Definiton of least element
+*)
+
+Fun2 = Fun1 + 
+
+(* default class is still term !*)
+
+(* Witness for the above arity axiom is fun1.ML *)
+
+arities fun :: (term,po)po
+
+consts	
+	UU_fun  :: "'a::term => 'b::pcpo"
+
+rules
+
+(* instance of << for type ['a::term => 'b::po]  *)
+
+inst_fun_po	"(op <<)::['a=>'b::po,'a=>'b::po ]=>bool = less_fun"
+
+(* definitions *)
+(* The least element in type 'a::term => 'b::pcpo *)
+
+UU_fun_def	"UU_fun == (% x.UU)"
+
+end
+
+
+
+
+
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Fun3.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,7 @@
+(*  Title: 	HOLCF/fun3.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+*)
+
+open Fun3;
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Fun3.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,23 @@
+(*  Title: 	HOLCF/fun3.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Class instance of  => (fun) for class pcpo
+
+*)
+
+Fun3 = Fun2 +
+
+(* default class is still term *)
+
+arities fun  :: (term,pcpo)pcpo		(* Witness fun2.ML *)
+
+rules 
+
+inst_fun_pcpo	"UU::'a=>'b::pcpo = UU_fun"
+
+end
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/HOLCF.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,20 @@
+(*  Title: 	HOLCF/HOLCF.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+*)
+
+open HOLCF;
+
+val HOLCF_ss = ccc1_ss 
+		addsimps one_when 
+		addsimps dist_less_one
+		addsimps dist_eq_one 
+		addsimps dist_less_tr
+		addsimps dist_eq_tr
+		addsimps tr_when
+		addsimps andalso_thms
+		addsimps orelse_thms
+		addsimps ifte_thms;
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/HOLCF.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,13 @@
+(*  Title: 	HOLCF/HOLCF.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+
+Top theory for HOLCF system
+
+*)
+
+HOLCF = Tr2 
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Holcfb.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,152 @@
+(*  Title: 	HOLCF/holcfb.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+Lemmas for Holcfb.thy 
+*)
+
+open Holcfb;
+
+(* ------------------------------------------------------------------------ *)
+(* <::nat=>nat=>bool is well-founded                                        *)
+(* ------------------------------------------------------------------------ *)
+
+val well_founded_nat = prove_goal  Nat.thy 
+	"!P. P(x::nat) --> (? y. P(y) & (! x. P(x) --> y <= x))"
+ (fn prems =>
+	[
+	(res_inst_tac [("n","x")] less_induct 1),
+	(strip_tac 1),
+	(res_inst_tac [("Q","? k.k<n & P(k)")] (excluded_middle RS disjE) 1),
+	(etac exE 2),
+	(etac conjE 2),
+	(rtac mp 2),
+	(etac allE 2),
+	(etac impE 2),
+	(atac 2),
+	(etac spec 2),
+	(atac 2),
+	(res_inst_tac [("x","n")] exI 1),
+	(rtac conjI 1),
+	(atac 1),
+	(strip_tac 1),
+	(rtac leI  1),
+	(fast_tac HOL_cs 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* Lemmas for selecting the least element in a nonempty set                 *)
+(* ------------------------------------------------------------------------ *)
+
+val theleast = prove_goalw  Holcfb.thy [theleast_def] 
+"P(x) ==> P(theleast(P)) & (!x.P(x)--> theleast(P) <= x)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (well_founded_nat RS spec RS mp RS exE) 1),
+	(atac 1),
+	(rtac selectI 1),
+	(atac 1)
+	]);
+
+val theleast1= theleast RS conjunct1;
+(* ?P1(?x1) ==> ?P1(theleast(?P1)) *)
+
+val theleast2 = prove_goal  Holcfb.thy  "P(x) ==> theleast(P) <= x"
+ (fn prems =>
+	[
+	(rtac (theleast RS conjunct2 RS spec RS mp) 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* Some lemmas in HOL.thy                                                   *)
+(* ------------------------------------------------------------------------ *)
+
+
+val de_morgan1 = prove_goal HOL.thy "(~a & ~b)=(~(a | b))"
+(fn prems =>
+	[
+	(rtac iffI 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val de_morgan2 = prove_goal HOL.thy "(~a | ~b)=(~(a & b))"
+(fn prems =>
+	[
+	(rtac iffI 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+
+val notall2ex = prove_goal HOL.thy "(~ (!x.P(x))) = (? x.~P(x))"
+(fn prems =>
+	[
+	(rtac iffI 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val notex2all = prove_goal HOL.thy "(~ (? x.P(x))) = (!x.~P(x))"
+(fn prems =>
+	[
+	(rtac iffI 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+
+val selectI2 = prove_goal HOL.thy "(? x. P(x)) ==> P(@ x.P(x))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac exE 1),
+	(etac selectI 1)
+	]);
+
+val selectE = prove_goal HOL.thy "P(@ x.P(x)) ==> (? x. P(x))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac exI 1)
+	]);
+
+val select_eq_Ex = prove_goal HOL.thy "(P(@ x.P(x))) =  (? x. P(x))"
+(fn prems =>
+	[
+	(rtac (iff RS mp  RS mp) 1),
+	(strip_tac 1),
+	(etac selectE 1),
+	(strip_tac 1),
+	(etac selectI2 1)
+	]);
+
+
+val notnotI = prove_goal HOL.thy "P ==> ~~P"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+
+val classical2 = prove_goal HOL.thy "[|Q ==> R; ~Q ==> R|]==>R"
+ (fn prems =>
+	[
+	(rtac disjE 1),
+	(rtac excluded_middle 1),
+	(eresolve_tac prems 1),
+	(eresolve_tac prems 1)
+	]);
+
+
+
+val classical3 = (notE RS notI);
+(* [| ?P ==> ~ ?P1; ?P ==> ?P1 |] ==> ~ ?P *)
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Holcfb.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,25 @@
+(*  Title: 	HOLCF/holcfb.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+Basic definitions for the embedding of LCF into HOL.
+
+*)
+
+Holcfb = Nat + 
+
+consts
+
+theleast     :: "(nat=>bool)=>nat"
+
+rules
+
+theleast_def    "theleast(P) == (@z.(P(z) & (!n.P(n)-->z<=n)))"
+
+end
+
+
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Lift1.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,188 @@
+(*  Title: 	HOLCF/lift1.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+*)
+
+open Lift1;
+
+val Exh_Lift = prove_goalw Lift1.thy [UU_lift_def,Iup_def ]
+	"z = UU_lift | (? x. z = Iup(x))"
+ (fn prems =>
+	[
+	(rtac (Rep_Lift_inverse RS subst) 1),
+	(res_inst_tac [("s","Rep_Lift(z)")] sumE 1),
+	(rtac disjI1 1),
+	(res_inst_tac [("f","Abs_Lift")] arg_cong 1),
+	(rtac (unique_void2 RS subst) 1),
+	(atac 1),
+	(rtac disjI2 1),
+	(rtac exI 1),
+	(res_inst_tac [("f","Abs_Lift")] arg_cong 1),
+	(atac 1)
+	]);
+
+val inj_Abs_Lift = prove_goal Lift1.thy "inj(Abs_Lift)"
+ (fn prems =>
+	[
+	(rtac inj_inverseI 1),
+	(rtac Abs_Lift_inverse 1)
+	]);
+
+val inj_Rep_Lift = prove_goal Lift1.thy "inj(Rep_Lift)"
+ (fn prems =>
+	[
+	(rtac inj_inverseI 1),
+	(rtac Rep_Lift_inverse 1)
+	]);
+
+val inject_Iup = prove_goalw Lift1.thy [Iup_def] "Iup(x)=Iup(y) ==> x=y"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (inj_Inr RS injD) 1),
+	(rtac (inj_Abs_Lift RS injD) 1),
+	(atac 1)
+	]);
+
+val defined_Iup=prove_goalw Lift1.thy [Iup_def,UU_lift_def] "~ Iup(x)=UU_lift"
+ (fn prems =>
+	[
+	(rtac notI 1),
+	(rtac notE 1),
+	(rtac Inl_not_Inr 1),
+	(rtac sym 1),
+	(etac (inj_Abs_Lift RS  injD) 1)
+	]);
+
+
+val liftE = prove_goal  Lift1.thy
+	"[| p=UU_lift ==> Q; !!x. p=Iup(x)==>Q|] ==>Q"
+ (fn prems =>
+	[
+	(rtac (Exh_Lift RS disjE) 1),
+	(eresolve_tac prems 1),
+	(etac exE 1),
+	(eresolve_tac prems 1)
+	]);
+
+val Ilift1 = prove_goalw  Lift1.thy [Ilift_def,UU_lift_def]
+	"Ilift(f)(UU_lift)=UU"
+ (fn prems =>
+	[
+	(rtac (Abs_Lift_inverse RS ssubst) 1),
+	(rtac (case_Inl RS ssubst) 1),
+	(rtac refl 1)
+	]);
+
+val Ilift2 = prove_goalw  Lift1.thy [Ilift_def,Iup_def]
+	"Ilift(f)(Iup(x))=f[x]"
+ (fn prems =>
+	[
+	(rtac (Abs_Lift_inverse RS ssubst) 1),
+	(rtac (case_Inr RS ssubst) 1),
+	(rtac refl 1)
+	]);
+
+val Lift_ss = Cfun_ss addsimps [Ilift1,Ilift2];
+
+val less_lift1a = prove_goalw  Lift1.thy [less_lift_def,UU_lift_def]
+	"less_lift(UU_lift)(z)"
+ (fn prems =>
+	[
+	(rtac (Abs_Lift_inverse RS ssubst) 1),
+	(rtac (case_Inl RS ssubst) 1),
+	(rtac TrueI 1)
+	]);
+
+val less_lift1b = prove_goalw  Lift1.thy [Iup_def,less_lift_def,UU_lift_def]
+	"~less_lift(Iup(x),UU_lift)"
+ (fn prems =>
+	[
+	(rtac notI 1),
+	(rtac iffD1 1),
+	(atac 2),
+	(rtac (Abs_Lift_inverse RS ssubst) 1),
+	(rtac (Abs_Lift_inverse RS ssubst) 1),
+	(rtac (case_Inr RS ssubst) 1),
+	(rtac (case_Inl RS ssubst) 1),
+	(rtac refl 1)
+	]);
+
+val less_lift1c = prove_goalw  Lift1.thy [Iup_def,less_lift_def,UU_lift_def]
+	"less_lift(Iup(x),Iup(y))=(x<<y)"
+ (fn prems =>
+	[
+	(rtac (Abs_Lift_inverse RS ssubst) 1),
+	(rtac (Abs_Lift_inverse RS ssubst) 1),
+	(rtac (case_Inr RS ssubst) 1),
+	(rtac (case_Inr RS ssubst) 1),
+	(rtac refl 1)
+	]);
+
+
+val refl_less_lift = prove_goal  Lift1.thy "less_lift(p,p)"
+ (fn prems =>
+	[
+	(res_inst_tac [("p","p")] liftE 1),
+	(hyp_subst_tac 1),
+	(rtac less_lift1a 1),
+	(hyp_subst_tac 1),
+	(rtac (less_lift1c RS iffD2) 1),
+	(rtac refl_less 1)
+	]);
+
+val antisym_less_lift = prove_goal  Lift1.thy 
+	"[|less_lift(p1,p2);less_lift(p2,p1)|] ==> p1=p2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("p","p1")] liftE 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p2")] liftE 1),
+	(hyp_subst_tac 1),
+	(rtac refl 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("P","less_lift(Iup(x),UU_lift)")] notE 1),
+	(rtac less_lift1b 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p2")] liftE 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("P","less_lift(Iup(x),UU_lift)")] notE 1),
+	(rtac less_lift1b 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(rtac arg_cong 1),
+	(rtac antisym_less 1),
+	(etac (less_lift1c RS iffD1) 1),
+	(etac (less_lift1c RS iffD1) 1)
+	]);
+
+val trans_less_lift = prove_goal  Lift1.thy 
+	"[|less_lift(p1,p2);less_lift(p2,p3)|] ==> less_lift(p1,p3)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("p","p1")] liftE 1),
+	(hyp_subst_tac 1),
+	(rtac less_lift1a 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p2")] liftE 1),
+	(hyp_subst_tac 1),
+	(rtac notE 1),
+	(rtac less_lift1b 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p3")] liftE 1),
+	(hyp_subst_tac 1),
+	(rtac notE 1),
+	(rtac less_lift1b 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(rtac (less_lift1c RS iffD2) 1),
+	(rtac trans_less 1),
+	(etac (less_lift1c RS iffD1) 1),
+	(etac (less_lift1c RS iffD1) 1)
+	]);
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Lift1.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,55 @@
+(*  Title: 	HOLCF/lift1.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+
+Lifting
+
+*)
+
+Lift1 = Cfun3 +
+
+(* new type for lifting *)
+
+types "u" 1
+
+arities "u" :: (pcpo)term	
+
+consts
+
+  Rep_Lift	:: "('a)u => (void + 'a)"
+  Abs_Lift	:: "(void + 'a) => ('a)u"
+
+  Iup           :: "'a => ('a)u"
+  UU_lift       :: "('a)u"
+  Ilift         :: "('a->'b)=>('a)u => 'b"
+  less_lift     :: "('a)u => ('a)u => bool"
+
+rules
+
+  (*faking a type definition... *)
+  (* ('a)u is isomorphic to void + 'a  *)
+
+  Rep_Lift_inverse	"Abs_Lift(Rep_Lift(p)) = p"	
+  Abs_Lift_inverse	"Rep_Lift(Abs_Lift(p)) = p"
+
+   (*defining the abstract constants*)
+
+  UU_lift_def   "UU_lift == Abs_Lift(Inl(UU))"
+  Iup_def       "Iup(x)  == Abs_Lift(Inr(x))"
+
+  Ilift_def     "Ilift(f)(x)==\
+\                case  (Rep_Lift(x)) (%y.UU) (%z.f[z])"
+ 
+  less_lift_def "less_lift(x1)(x2) == \
+\          (case (Rep_Lift(x1))\
+\                (% y1.True)\
+\                (% y2.case (Rep_Lift(x2))\
+\                           (% z1.False)\
+\                           (% z2.y2<<z2)))"
+
+end
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Lift2.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,182 @@
+(*  Title: 	HOLCF/lift2.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for lift2.thy 
+*)
+
+open Lift2;
+
+(* -------------------------------------------------------------------------*)
+(* type ('a)u is pointed                                                    *)
+(* ------------------------------------------------------------------------ *)
+
+val minimal_lift = prove_goal Lift2.thy "UU_lift << z"
+ (fn prems =>
+	[
+	(rtac (inst_lift_po RS ssubst) 1),
+	(rtac less_lift1a 1)
+	]);
+
+(* -------------------------------------------------------------------------*)
+(* access to less_lift in class po                                          *)
+(* ------------------------------------------------------------------------ *)
+
+val less_lift2b = prove_goal Lift2.thy "~ Iup(x) << UU_lift"
+ (fn prems =>
+	[
+	(rtac (inst_lift_po RS ssubst) 1),
+	(rtac less_lift1b 1)
+	]);
+
+val less_lift2c = prove_goal Lift2.thy "(Iup(x)<<Iup(y)) = (x<<y)"
+ (fn prems =>
+	[
+	(rtac (inst_lift_po RS ssubst) 1),
+	(rtac less_lift1c 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* Iup and Ilift are monotone                                               *)
+(* ------------------------------------------------------------------------ *)
+
+val monofun_Iup = prove_goalw Lift2.thy [monofun] "monofun(Iup)"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(etac (less_lift2c RS iffD2) 1)
+	]);
+
+val monofun_Ilift1 = prove_goalw Lift2.thy [monofun] "monofun(Ilift)"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(rtac (less_fun RS iffD2) 1),
+	(strip_tac 1),
+	(res_inst_tac [("p","xa")] liftE 1),
+	(asm_simp_tac Lift_ss 1),
+	(asm_simp_tac Lift_ss 1),
+	(etac monofun_cfun_fun 1)
+	]);
+
+val monofun_Ilift2 = prove_goalw Lift2.thy [monofun] "monofun(Ilift(f))"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(res_inst_tac [("p","x")] liftE 1),
+	(asm_simp_tac Lift_ss 1),
+	(asm_simp_tac Lift_ss 1),
+	(res_inst_tac [("p","y")] liftE 1),
+	(hyp_subst_tac 1),
+	(hyp_subst_tac 1),
+	(rtac notE 1),
+	(rtac less_lift2b 1),
+	(atac 1),
+	(asm_simp_tac Lift_ss 1),
+	(rtac monofun_cfun_arg 1),
+	(hyp_subst_tac 1),
+	(hyp_subst_tac 1),
+	(etac (less_lift2c  RS iffD1) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* Some kind of surjectivity lemma                                          *)
+(* ------------------------------------------------------------------------ *)
+
+
+val lift_lemma1 = prove_goal Lift2.thy  "z=Iup(x) ==> Iup(Ilift(LAM x.x)(z)) = z"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(asm_simp_tac Lift_ss 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* ('a)u is a cpo                                                           *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_lift1a = prove_goal Lift2.thy 
+"[|is_chain(Y);? i x.Y(i)=Iup(x)|] ==>\
+\ range(Y) <<| Iup(lub(range(%i.(Ilift (LAM x.x) (Y(i))))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_lubI 1),
+	(rtac conjI 1),
+	(rtac ub_rangeI 1),
+	(rtac allI 1),
+	(res_inst_tac [("p","Y(i)")] liftE 1),
+	(res_inst_tac [("s","UU_lift"),("t","Y(i)")] subst 1),
+	(etac sym 1),
+	(rtac minimal_lift 1),
+	(res_inst_tac [("t","Y(i)")] (lift_lemma1 RS subst) 1),
+	(atac 1),
+	(rtac (less_lift2c RS iffD2) 1),
+	(rtac is_ub_thelub 1),
+	(etac (monofun_Ilift2 RS ch2ch_monofun) 1),
+	(strip_tac 1),
+	(res_inst_tac [("p","u")] liftE 1),
+	(etac exE 1),
+	(etac exE 1),
+	(res_inst_tac [("P","Y(i)<<UU_lift")] notE 1),
+	(res_inst_tac [("s","Iup(x)"),("t","Y(i)")] ssubst 1),
+	(atac 1),
+	(rtac less_lift2b 1),
+	(hyp_subst_tac 1),
+	(etac (ub_rangeE RS spec) 1),
+	(res_inst_tac [("t","u")] (lift_lemma1 RS subst) 1),
+	(atac 1),
+	(rtac (less_lift2c RS iffD2) 1),
+	(rtac is_lub_thelub 1),
+	(etac (monofun_Ilift2 RS ch2ch_monofun) 1),
+	(etac (monofun_Ilift2 RS ub2ub_monofun) 1)
+	]);
+
+val lub_lift1b = prove_goal Lift2.thy 
+"[|is_chain(Y);!i x.~Y(i)=Iup(x)|] ==>\
+\ range(Y) <<| UU_lift"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_lubI 1),
+	(rtac conjI 1),
+	(rtac ub_rangeI 1),
+	(rtac allI 1),
+	(res_inst_tac [("p","Y(i)")] liftE 1),
+	(res_inst_tac [("s","UU_lift"),("t","Y(i)")] ssubst 1),
+	(atac 1),
+	(rtac refl_less 1),
+	(rtac notE 1),
+	(dtac spec 1),
+	(dtac spec 1),
+	(atac 1),
+	(atac 1),
+	(strip_tac 1),
+	(rtac minimal_lift 1)
+	]);
+
+val thelub_lift1a = lub_lift1a RS thelubI;
+(* [| is_chain(?Y1); ? i x. ?Y1(i) = Iup(x) |] ==>                *)
+(* lub(range(?Y1)) = Iup(lub(range(%i. Ilift(LAM x. x,?Y1(i)))))  *)
+
+val thelub_lift1b = lub_lift1b RS thelubI;
+(* [| is_chain(?Y1); ! i x. ~ ?Y1(i) = Iup(x) |] ==>              *)
+(*                                     lub(range(?Y1)) = UU_lift  *)
+
+
+val cpo_lift = prove_goal Lift2.thy 
+	"is_chain(Y::nat=>('a)u) ==> ? x.range(Y) <<|x"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac disjE 1),
+	(rtac exI 2),
+	(etac lub_lift1a 2),
+	(atac 2),
+	(rtac exI 2),
+	(etac lub_lift1b 2),
+	(atac 2),
+	(fast_tac HOL_cs 1)
+	]);
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Lift2.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,25 @@
+(*  Title: 	HOLCF/lift2.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Class Instance u::(pcpo)po
+
+*)
+
+Lift2 = Lift1 + 
+
+(* Witness for the above arity axiom is lift1.ML *)
+
+arities "u" :: (pcpo)po
+
+rules
+
+(* instance of << for type ('a)u  *)
+
+inst_lift_po	"(op <<)::[('a)u,('a)u]=>bool = less_lift"
+
+end
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Lift3.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,349 @@
+(*  Title: 	HOLCF/lift3.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for lift3.thy
+*)
+
+open Lift3;
+
+(* -------------------------------------------------------------------------*)
+(* some lemmas restated for class pcpo                                      *)
+(* ------------------------------------------------------------------------ *)
+
+val less_lift3b = prove_goal Lift3.thy "~ Iup(x) << UU"
+ (fn prems =>
+	[
+	(rtac (inst_lift_pcpo RS ssubst) 1),
+	(rtac less_lift2b 1)
+	]);
+
+val defined_Iup2 = prove_goal Lift3.thy "~ Iup(x) = UU"
+ (fn prems =>
+	[
+	(rtac (inst_lift_pcpo RS ssubst) 1),
+	(rtac defined_Iup 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* continuity for Iup                                                       *)
+(* ------------------------------------------------------------------------ *)
+
+val contlub_Iup = prove_goal Lift3.thy "contlub(Iup)"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac trans 1),
+	(rtac (thelub_lift1a RS sym) 2),
+	(fast_tac HOL_cs 3),
+	(etac (monofun_Iup RS ch2ch_monofun) 2),
+	(res_inst_tac [("f","Iup")] arg_cong  1),
+	(rtac lub_equal 1),
+	(atac 1),
+	(rtac (monofun_Ilift2 RS ch2ch_monofun) 1),
+	(etac (monofun_Iup RS ch2ch_monofun) 1),
+	(asm_simp_tac Lift_ss 1)
+	]);
+
+val contX_Iup = prove_goal Lift3.thy "contX(Iup)"
+ (fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_Iup 1),
+	(rtac contlub_Iup 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* continuity for Ilift                                                     *)
+(* ------------------------------------------------------------------------ *)
+
+val contlub_Ilift1 = prove_goal Lift3.thy "contlub(Ilift)"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac trans 1),
+	(rtac (thelub_fun RS sym) 2),
+	(etac (monofun_Ilift1 RS ch2ch_monofun) 2),
+	(rtac ext 1),
+	(res_inst_tac [("p","x")] liftE 1),
+	(asm_simp_tac Lift_ss 1),
+	(rtac (lub_const RS thelubI RS sym) 1),
+	(asm_simp_tac Lift_ss 1),
+	(etac contlub_cfun_fun 1)
+	]);
+
+
+val contlub_Ilift2 = prove_goal Lift3.thy "contlub(Ilift(f))"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac disjE 1),
+	(rtac (thelub_lift1a RS ssubst) 2),
+	(atac 2),
+	(atac 2),
+	(asm_simp_tac Lift_ss 2),
+	(rtac (thelub_lift1b RS ssubst) 3),
+	(atac 3),
+	(atac 3),
+	(fast_tac HOL_cs 1),
+	(asm_simp_tac Lift_ss 2),
+	(rtac (chain_UU_I_inverse RS sym) 2),
+	(rtac allI 2),
+	(res_inst_tac [("p","Y(i)")] liftE 2),
+	(asm_simp_tac Lift_ss 2),
+	(rtac notE 2),
+	(dtac spec 2),
+	(etac spec 2),
+	(atac 2),
+	(rtac (contlub_cfun_arg RS ssubst) 1),
+	(etac (monofun_Ilift2 RS ch2ch_monofun) 1),
+	(rtac lub_equal2 1),
+	(rtac (monofun_fapp2 RS ch2ch_monofun) 2),
+	(etac (monofun_Ilift2 RS ch2ch_monofun) 2),
+	(etac (monofun_Ilift2 RS ch2ch_monofun) 2),
+	(rtac (chain_mono2 RS exE) 1),
+	(atac 2),
+	(etac exE 1),
+	(etac exE 1),
+	(rtac exI 1),
+	(res_inst_tac [("s","Iup(x)"),("t","Y(i)")] ssubst 1),
+	(atac 1),
+	(rtac defined_Iup2 1),
+	(rtac exI 1),
+	(strip_tac 1),
+	(res_inst_tac [("p","Y(i)")] liftE 1),
+	(asm_simp_tac Lift_ss 2),
+	(res_inst_tac [("P","Y(i) = UU")] notE 1),
+	(fast_tac HOL_cs 1),
+	(rtac (inst_lift_pcpo RS ssubst) 1),
+	(atac 1)
+	]);
+
+val contX_Ilift1 = prove_goal Lift3.thy "contX(Ilift)"
+ (fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_Ilift1 1),
+	(rtac contlub_Ilift1 1)
+	]);
+
+val contX_Ilift2 = prove_goal Lift3.thy "contX(Ilift(f))"
+ (fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_Ilift2 1),
+	(rtac contlub_Ilift2 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* continuous versions of lemmas for ('a)u                                  *)
+(* ------------------------------------------------------------------------ *)
+
+val Exh_Lift1 = prove_goalw Lift3.thy [up_def] "z = UU | (? x. z = up[x])"
+ (fn prems =>
+	[
+	(simp_tac (Lift_ss addsimps [contX_Iup]) 1),
+	(rtac (inst_lift_pcpo RS ssubst) 1),
+	(rtac Exh_Lift 1)
+	]);
+
+val inject_up = prove_goalw Lift3.thy [up_def] "up[x]=up[y] ==> x=y"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac inject_Iup 1),
+	(etac box_equals 1),
+	(simp_tac (Lift_ss addsimps [contX_Iup]) 1),
+	(simp_tac (Lift_ss addsimps [contX_Iup]) 1)
+	]);
+
+val defined_up = prove_goalw Lift3.thy [up_def] "~ up[x]=UU"
+ (fn prems =>
+	[
+	(simp_tac (Lift_ss addsimps [contX_Iup]) 1),
+	(rtac defined_Iup2 1)
+	]);
+
+val liftE1 = prove_goalw Lift3.thy [up_def] 
+	"[| p=UU ==> Q; !!x. p=up[x]==>Q|] ==>Q"
+ (fn prems =>
+	[
+	(rtac liftE 1),
+	(resolve_tac prems 1),
+	(etac (inst_lift_pcpo RS ssubst) 1),
+	(resolve_tac (tl prems) 1),
+	(asm_simp_tac (Lift_ss addsimps [contX_Iup]) 1)
+	]);
+
+
+val lift1 = prove_goalw Lift3.thy [up_def,lift_def] "lift[f][UU]=UU"
+ (fn prems =>
+	[
+	(rtac (inst_lift_pcpo RS ssubst) 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(REPEAT (resolve_tac (contX_lemmas @ [contX_Iup,contX_Ilift1,
+		contX_Ilift2,contX2contX_CF1L]) 1)),
+	(rtac (beta_cfun RS ssubst) 1),
+	(REPEAT (resolve_tac (contX_lemmas @ [contX_Iup,contX_Ilift1,
+		contX_Ilift2,contX2contX_CF1L]) 1)),
+	(simp_tac (Lift_ss addsimps [contX_Iup,contX_Ilift1,contX_Ilift2]) 1)
+	]);
+
+val lift2 = prove_goalw Lift3.thy [up_def,lift_def] "lift[f][up[x]]=f[x]"
+ (fn prems =>
+	[
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Iup 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(REPEAT (resolve_tac (contX_lemmas @ [contX_Iup,contX_Ilift1,
+		contX_Ilift2,contX2contX_CF1L]) 1)),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Ilift2 1),
+	(simp_tac (Lift_ss addsimps [contX_Iup,contX_Ilift1,contX_Ilift2]) 1)
+	]);
+
+val less_lift4b = prove_goalw Lift3.thy [up_def,lift_def] "~ up[x] << UU"
+ (fn prems =>
+	[
+	(simp_tac (Lift_ss addsimps [contX_Iup]) 1),
+	(rtac less_lift3b 1)
+	]);
+
+val less_lift4c = prove_goalw Lift3.thy [up_def,lift_def]
+	 "(up[x]<<up[y]) = (x<<y)"
+ (fn prems =>
+	[
+	(simp_tac (Lift_ss addsimps [contX_Iup]) 1),
+	(rtac less_lift2c 1)
+	]);
+
+val thelub_lift2a = prove_goalw Lift3.thy [up_def,lift_def] 
+"[| is_chain(Y); ? i x. Y(i) = up[x] |] ==>\
+\      lub(range(Y)) = up[lub(range(%i. lift[LAM x. x][Y(i)]))]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(REPEAT (resolve_tac (contX_lemmas @ [contX_Iup,contX_Ilift1,
+		contX_Ilift2,contX2contX_CF1L]) 1)),
+	(rtac (beta_cfun RS ssubst) 1),
+	(REPEAT (resolve_tac (contX_lemmas @ [contX_Iup,contX_Ilift1,
+		contX_Ilift2,contX2contX_CF1L]) 1)),
+
+	(rtac (beta_cfun RS ext RS ssubst) 1),
+	(REPEAT (resolve_tac (contX_lemmas @ [contX_Iup,contX_Ilift1,
+		contX_Ilift2,contX2contX_CF1L]) 1)),
+	(rtac thelub_lift1a 1),
+	(atac 1),
+	(etac exE 1),
+	(etac exE 1),
+	(rtac exI 1),
+	(rtac exI 1),
+	(etac box_equals 1),
+	(rtac refl 1),
+	(simp_tac (Lift_ss addsimps [contX_Iup]) 1)
+	]);
+
+
+
+val thelub_lift2b = prove_goalw Lift3.thy [up_def,lift_def] 
+"[| is_chain(Y); ! i x. ~ Y(i) = up[x] |] ==> lub(range(Y)) = UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (inst_lift_pcpo RS ssubst) 1),
+	(rtac thelub_lift1b 1),
+	(atac 1),
+	(strip_tac 1),
+	(dtac spec 1),
+	(dtac spec 1),
+	(rtac swap 1),
+	(atac 1),
+	(dtac notnotD 1),
+	(etac box_equals 1),
+	(rtac refl 1),
+	(simp_tac (Lift_ss addsimps [contX_Iup]) 1)
+	]);
+
+
+val lift_lemma2 = prove_goal Lift3.thy  " (? x.z = up[x]) = (~z=UU)"
+ (fn prems =>
+	[
+	(rtac iffI 1),
+	(etac exE 1),
+	(hyp_subst_tac 1),
+	(rtac defined_up 1),
+	(res_inst_tac [("p","z")] liftE1 1),
+	(etac notE 1),
+	(atac 1),
+	(etac exI 1)
+	]);
+
+
+val thelub_lift2a_rev = prove_goal Lift3.thy  
+"[| is_chain(Y); lub(range(Y)) = up[x] |] ==> ? i x. Y(i) = up[x]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac exE 1),
+	(rtac chain_UU_I_inverse2 1),
+	(rtac (lift_lemma2 RS iffD1) 1),
+	(etac exI 1),
+	(rtac exI 1),
+	(rtac (lift_lemma2 RS iffD2) 1),
+	(atac 1)
+	]);
+
+val thelub_lift2b_rev = prove_goal Lift3.thy  
+"[| is_chain(Y); lub(range(Y)) = UU |] ==> ! i x. ~ Y(i) = up[x]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac allI 1),
+	(rtac (notex2all RS iffD1) 1),
+	(rtac contrapos 1),
+	(etac (lift_lemma2 RS iffD1) 2),
+	(rtac notnotI 1),
+	(rtac (chain_UU_I RS spec) 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+
+val thelub_lift3 = prove_goal Lift3.thy  
+"is_chain(Y) ==> lub(range(Y)) = UU |\
+\                lub(range(Y)) = up[lub(range(%i. lift[LAM x. x][Y(i)]))]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac disjE 1),
+	(rtac disjI1 2),
+	(rtac thelub_lift2b 2),
+	(atac 2),
+	(atac 2),
+	(rtac disjI2 2),
+	(rtac thelub_lift2a 2),
+	(atac 2),
+	(atac 2),
+	(fast_tac HOL_cs 1)
+	]);
+
+val lift3 = prove_goal Lift3.thy "lift[up][x]=x"
+ (fn prems =>
+	[
+	(res_inst_tac [("p","x")] liftE1 1),
+	(asm_simp_tac (Cfun_ss addsimps [lift1,lift2]) 1),
+	(asm_simp_tac (Cfun_ss addsimps [lift1,lift2]) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* install simplifier for ('a)u                                             *)
+(* ------------------------------------------------------------------------ *)
+
+val lift_rews = [lift1,lift2,defined_up];
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Lift3.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,29 @@
+(*  Title: 	HOLCF/lift3.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+
+Class instance of  ('a)u for class pcpo
+
+*)
+
+Lift3 = Lift2 +
+
+arities "u" :: (pcpo)pcpo			(* Witness lift2.ML *)
+
+consts  
+	up	     :: "'a -> ('a)u" 
+	lift         :: "('a->'c)-> ('a)u -> 'c"
+
+rules 
+
+inst_lift_pcpo	"UU::('a)u = UU_lift"
+
+up_def		"up     == (LAM x.Iup(x))"
+lift_def	"lift   == (LAM f p.Ilift(f)(p))"
+
+end
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Makefile	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,49 @@
+############################################################################
+#                                                                          #
+#                   Makefile for Isabelle (HOLCF)                          #
+#                                                                          #
+############################################################################
+
+#To make the system, cd to this directory and type  
+#	make -f Makefile 
+
+#Environment variable ISABELLECOMP specifies the compiler.
+#Environment variable ISABELLEBIN specifies the destination directory.
+#For Poly/ML, ISABELLEBIN must begin with a /
+
+#Makes HOL Isabelle if this file is ABSENT -- but not 
+#if it is out of date, since this Makefile does not know its dependencies!
+
+BIN = $(ISABELLEBIN)
+COMP = $(ISABELLECOMP)
+FILES = ROOT.ML void.thy void.ML porder.thy porder.ML pcpo.thy \
+	pcpo.ML fun1.thy fun1.ML fun2.thy fun2.ML fun3.thy fun3.ML \
+	cfun1.thy cfun1.ML cfun2.thy cfun2.ML cfun3.thy cfun3.ML \
+	cinfix.ML\
+	sprod0.thy sprod0.ML sprod1.thy sprod1.ML sprod2.thy sprod2.ML\
+	sprod3.thy sprod3.ML
+
+EX_FILES = ex/coind.thy ex/coind.ML \
+           ex/hoare.thy ex/hoare.ML ex/loop.thy ex/loop.ML
+
+$(BIN)/HOLCF:   $(BIN)/HOL  $(FILES) 
+	case "$(COMP)" in \
+	poly*)  echo 'make_database"$(BIN)/HOLCF"; quit();'  \
+		     | $(COMP) $(BIN)/HOL ;\
+		echo 'use"ROOT";' | $(COMP) $(BIN)/HOLCF ;;\
+	sml*)	echo 'use"ROOT.ML"; xML"$(BIN)/HOLCF" banner;' | $(BIN)/HOL ;;\
+	*)	echo Bad value for ISABELLECOMP;;\
+	esac
+
+$(BIN)/HOL:
+	cd ../HOL;  $(MAKE)
+
+test:   ex/ROOT.ML  $(BIN)/HOLCF  $(EX_FILES) 
+	case "$(COMP)" in \
+	poly*)	echo 'use"ex/ROOT.ML"; quit();' | $(COMP) $(BIN)/HOLCF ;;\
+	sml*)	echo 'use"ex/ROOT.ML"' | $(BIN)/HOLCF;;\
+	*)	echo Bad value for ISABELLECOMP;;\
+	esac
+
+.PRECIOUS:  $(BIN)/HOL  $(BIN)/HOLCF 
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/One.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,96 @@
+(*  Title: 	HOLCF/one.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for one.thy 
+*)
+
+open One;
+
+(* ------------------------------------------------------------------------ *)
+(* Exhaustion and Elimination for type one                                  *)
+(* ------------------------------------------------------------------------ *)
+
+val Exh_one = prove_goalw One.thy [one_def] "z=UU | z = one"
+ (fn prems =>
+	[
+	(res_inst_tac [("p","rep_one[z]")] liftE1 1),
+	(rtac disjI1 1),
+	(rtac ((abs_one_iso RS allI) RS ((rep_one_iso RS allI) RS iso_strict )
+		RS conjunct2 RS subst) 1),
+	(rtac (abs_one_iso RS subst) 1),
+	(etac cfun_arg_cong 1),
+	(rtac disjI2 1),
+	(rtac (abs_one_iso RS subst) 1),
+	(rtac cfun_arg_cong 1),
+	(rtac (unique_void2 RS subst) 1),
+	(atac 1)
+	]);
+
+val oneE = prove_goal One.thy
+	"[| p=UU ==> Q; p = one ==>Q|] ==>Q"
+ (fn prems =>
+	[
+	(rtac (Exh_one RS disjE) 1),
+	(eresolve_tac prems 1),
+	(eresolve_tac prems 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* distinctness for type one : stored in a list                             *)
+(* ------------------------------------------------------------------------ *)
+
+val dist_less_one = [
+prove_goalw One.thy [one_def] "~one << UU"
+ (fn prems =>
+	[
+	(rtac classical3 1),
+	(rtac less_lift4b 1),
+	(rtac (rep_one_iso RS subst) 1),
+	(rtac (rep_one_iso RS subst) 1),
+	(rtac monofun_cfun_arg 1),
+	(etac ((abs_one_iso RS allI) RS ((rep_one_iso RS allI) RS iso_strict ) 
+		RS conjunct2 RS ssubst) 1)
+	])
+];
+
+val  dist_eq_one = [prove_goal One.thy "~one=UU"
+ (fn prems =>
+	[
+	(rtac not_less2not_eq 1),
+	(resolve_tac dist_less_one 1)
+	])];
+
+val dist_eq_one = dist_eq_one @ (map (fn thm => (thm RS not_sym)) dist_eq_one);
+
+(* ------------------------------------------------------------------------ *)
+(* one is flat                                                              *)
+(* ------------------------------------------------------------------------ *)
+
+val prems = goalw One.thy [flat_def] "flat(one)";
+by (rtac allI 1);
+by (rtac allI 1);
+by (res_inst_tac [("p","x")] oneE 1);
+by (asm_simp_tac ccc1_ss  1);
+by (res_inst_tac [("p","y")] oneE 1);
+by (asm_simp_tac (ccc1_ss addsimps dist_less_one) 1);
+by (asm_simp_tac ccc1_ss  1);
+val flat_one = result();
+
+
+(* ------------------------------------------------------------------------ *)
+(* properties of one_when                                                   *)
+(* here I tried a generic prove procedure                                   *)
+(* ------------------------------------------------------------------------ *)
+
+fun prover s =  prove_goalw One.thy [one_when_def,one_def] s
+ (fn prems =>
+	[
+	(simp_tac (ccc1_ss addsimps [(rep_one_iso ),
+	(abs_one_iso RS allI) RS ((rep_one_iso RS allI) 
+	RS iso_strict) RS conjunct1] )1)
+	]);
+
+val one_when = map prover ["one_when[x][UU] = UU","one_when[x][one] = x"];
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/One.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,53 @@
+(*  Title: 	HOLCF/one.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Introduve atomic type one = (void)u
+
+This is the first type that is introduced using a domain isomorphism.
+The type axiom 
+
+	arities one :: pcpo
+
+and the continuity of the Isomorphisms are taken for granted. Since the
+type is not recursive, it could be easily introduced in a purely conservative
+style as it was used for the types sprod, ssum, lift. The definition of the 
+ordering is canonical using abstraction and representation, but this would take
+again a lot of internal constants. It can easily be seen that the axioms below
+are consistent.
+
+The partial ordering on type one is implicitly defined via the
+isomorphism axioms and the continuity of abs_one and rep_one.
+
+We could also introduce the function less_one with definition
+
+less_one(x,y) = rep_one[x] << rep_one[y]
+
+
+*)
+
+One = ccc1+
+
+types one 0
+arities one :: pcpo
+
+consts
+	abs_one		:: "(void)u -> one"
+	rep_one		:: "one -> (void)u"
+	one 		:: "one"
+	one_when 	:: "'c -> one -> 'c"
+
+rules
+  abs_one_iso	"abs_one[rep_one[u]] = u"
+  rep_one_iso  "rep_one[abs_one[x]] = x"
+
+  one_def	"one == abs_one[up[UU]]"
+  one_when_def "one_when == (LAM c u.lift[LAM x.c][rep_one[u]])"
+
+end
+
+
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Pcpo.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,272 @@
+(*  Title: 	HOLCF/pcpo.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for pcpo.thy
+*)
+ 
+open Pcpo;
+
+(* ------------------------------------------------------------------------ *)
+(* in pcpo's everthing equal to THE lub has lub properties for every chain  *)
+(* ------------------------------------------------------------------------ *)
+
+val thelubE = prove_goal  Pcpo.thy 
+	"[| is_chain(S);lub(range(S)) = l::'a::pcpo|] ==> range(S) <<| l "
+(fn prems =>
+	[
+	(cut_facts_tac prems 1), 
+	(hyp_subst_tac 1),
+	(rtac lubI 1),
+	(etac cpo 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* Properties of the lub                                                    *)
+(* ------------------------------------------------------------------------ *)
+
+
+val is_ub_thelub = (cpo RS lubI RS is_ub_lub);
+(* is_chain(?S1) ==> ?S1(?x) << lub(range(?S1))                             *)
+
+val is_lub_thelub = (cpo RS lubI RS is_lub_lub);
+(* [| is_chain(?S5); range(?S5) <| ?x1 |] ==> lub(range(?S5)) << ?x1        *)
+
+
+(* ------------------------------------------------------------------------ *)
+(* the << relation between two chains is preserved by their lubs            *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_mono = prove_goal Pcpo.thy 
+	"[|is_chain(C1::(nat=>'a::pcpo));is_chain(C2); ! k. C1(k) << C2(k)|]\
+\           ==> lub(range(C1)) << lub(range(C2))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac is_lub_thelub 1),
+	(rtac ub_rangeI 1),
+	(rtac allI 1),
+	(rtac trans_less 1),
+	(etac spec 1),
+	(etac is_ub_thelub 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* the = relation between two chains is preserved by their lubs            *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_equal = prove_goal Pcpo.thy
+"[| is_chain(C1::(nat=>'a::pcpo));is_chain(C2);!k.C1(k)=C2(k)|]\
+\	==> lub(range(C1))=lub(range(C2))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac antisym_less 1),
+	(rtac lub_mono 1),
+	(atac 1),
+	(atac 1),
+	(strip_tac 1),
+	(rtac (antisym_less_inverse RS conjunct1) 1),
+	(etac spec 1),
+	(rtac lub_mono 1),
+	(atac 1),
+	(atac 1),
+	(strip_tac 1),
+	(rtac (antisym_less_inverse RS conjunct2) 1),
+	(etac spec 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* more results about mono and = of lubs of chains                          *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_mono2 = prove_goal Pcpo.thy 
+"[|? j.!i. j<i --> X(i::nat)=Y(i);is_chain(X::nat=>'a::pcpo);is_chain(Y)|]\
+\ ==> lub(range(X))<<lub(range(Y))"
+ (fn prems =>
+	[
+	(rtac  exE 1),
+	(resolve_tac prems 1),
+	(rtac is_lub_thelub 1),
+	(resolve_tac prems 1),
+	(rtac ub_rangeI 1),
+	(strip_tac 1),
+	(res_inst_tac [("Q","x<i")] classical2 1),
+	(res_inst_tac [("s","Y(i)"),("t","X(i)")] subst 1),
+	(rtac sym 1),
+	(fast_tac HOL_cs 1),
+	(rtac is_ub_thelub 1),
+	(resolve_tac prems 1),
+	(res_inst_tac [("y","X(Suc(x))")] trans_less 1),
+	(rtac (chain_mono RS mp) 1),
+	(resolve_tac prems 1),
+	(rtac (not_less_eq RS subst) 1),
+	(atac 1),
+	(res_inst_tac [("s","Y(Suc(x))"),("t","X(Suc(x))")] subst 1),
+	(rtac sym 1),
+	(asm_simp_tac nat_ss 1),
+	(rtac is_ub_thelub 1),
+	(resolve_tac prems 1)
+	]);
+
+val lub_equal2 = prove_goal Pcpo.thy 
+"[|? j.!i. j<i --> X(i)=Y(i);is_chain(X::nat=>'a::pcpo);is_chain(Y)|]\
+\ ==> lub(range(X))=lub(range(Y))"
+ (fn prems =>
+	[
+	(rtac antisym_less 1),
+	(rtac lub_mono2 1),
+	(REPEAT (resolve_tac prems 1)),
+	(cut_facts_tac prems 1),
+	(rtac lub_mono2 1),
+	(safe_tac HOL_cs),
+	(step_tac HOL_cs 1),
+	(safe_tac HOL_cs),
+	(rtac sym 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val lub_mono3 = prove_goal Pcpo.thy "[|is_chain(Y::nat=>'a::pcpo);is_chain(X);\
+\! i. ? j. Y(i)<< X(j)|]==> lub(range(Y))<<lub(range(X))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_lub_thelub 1),
+	(atac 1),
+	(rtac ub_rangeI 1),
+	(strip_tac 1),
+	(etac allE 1),
+	(etac exE 1),
+	(rtac trans_less 1),
+	(rtac is_ub_thelub 2),
+	(atac 2),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* usefull lemmas about UU                                                  *)
+(* ------------------------------------------------------------------------ *)
+
+val eq_UU_iff = prove_goal Pcpo.thy "(x=UU)=(x<<UU)"
+ (fn prems =>
+	[
+	(rtac iffI 1),
+	(hyp_subst_tac 1),
+	(rtac refl_less 1),
+	(rtac antisym_less 1),
+	(atac 1),
+	(rtac minimal 1)
+	]);
+
+val UU_I = prove_goal Pcpo.thy "x << UU ==> x = UU"
+ (fn prems =>
+	[
+	(rtac (eq_UU_iff RS ssubst) 1),
+	(resolve_tac prems 1)
+	]);
+
+val not_less2not_eq = prove_goal Pcpo.thy "~x<<y ==> ~x=y"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac classical3 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(rtac refl_less 1)
+	]);
+
+
+val chain_UU_I = prove_goal Pcpo.thy
+	"[|is_chain(Y);lub(range(Y))=UU|] ==> ! i.Y(i)=UU"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac allI 1),
+	(rtac antisym_less 1),
+	(rtac minimal 2),
+	(res_inst_tac [("t","UU")] subst 1),
+	(atac 1),
+	(etac is_ub_thelub 1)
+	]);
+
+
+val chain_UU_I_inverse = prove_goal Pcpo.thy 
+	"!i.Y(i::nat)=UU ==> lub(range(Y::(nat=>'a::pcpo)))=UU"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac lub_chain_maxelem 1),
+	(rtac is_chainI 1),
+	(rtac allI 1),
+	(res_inst_tac [("s","UU"),("t","Y(i)")] subst 1),
+	(rtac sym 1),
+	(etac spec 1),
+	(rtac minimal 1),
+	(rtac exI 1),
+	(etac spec 1),
+	(rtac allI 1),
+	(rtac (antisym_less_inverse RS conjunct1) 1),
+	(etac spec 1)
+	]);
+
+val chain_UU_I_inverse2 = prove_goal Pcpo.thy 
+	"~lub(range(Y::(nat=>'a::pcpo)))=UU ==> ? i.~ Y(i)=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (notall2ex RS iffD1) 1),
+	(rtac swap 1),
+	(rtac chain_UU_I_inverse 2),
+	(etac notnotD 2),
+	(atac 1)
+	]);
+
+
+val notUU_I = prove_goal Pcpo.thy "[| x<<y; ~x=UU |] ==> ~y=UU"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac contrapos 1),
+	(rtac UU_I 1),
+	(hyp_subst_tac 1),
+	(atac 1)
+	]);
+
+
+val chain_mono2 = prove_goal Pcpo.thy 
+"[|? j.~Y(j)=UU;is_chain(Y::nat=>'a::pcpo)|]\
+\ ==> ? j.!i.j<i-->~Y(i)=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(safe_tac HOL_cs),
+	(step_tac HOL_cs 1),
+	(strip_tac 1),
+	(rtac notUU_I 1),
+	(atac 2),
+	(etac (chain_mono RS mp) 1),
+	(atac 1)
+	]);
+
+
+
+
+(* ------------------------------------------------------------------------ *)
+(* uniqueness in void                                                       *)
+(* ------------------------------------------------------------------------ *)
+
+val unique_void2 = prove_goal Pcpo.thy "x::void=UU"
+ (fn prems =>
+	[
+	(rtac (inst_void_pcpo RS ssubst) 1),
+	(rtac (Rep_Void_inverse RS subst) 1),
+	(rtac (Rep_Void_inverse RS subst) 1),
+	(rtac arg_cong 1),
+	(rtac box_equals 1),
+	(rtac refl 1),
+	(rtac (unique_void RS sym) 1),
+	(rtac (unique_void RS sym) 1)
+	]);
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Pcpo.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,39 @@
+(*  Title: 	HOLCF/pcpo.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Definition of class pcpo (pointed complete partial order)
+
+The prototype theory for this class is porder.thy 
+
+*)
+
+Pcpo = Porder +
+
+(* Introduction of new class. The witness is type void. *)
+
+classes pcpo < po
+
+(* default class is still term *)
+(* void is the prototype in pcpo *)
+
+arities void :: pcpo
+
+consts	
+	UU	::	"'a::pcpo"		(* UU is the least element *)
+rules
+
+(* class axioms: justification is theory Porder *)
+
+minimal		"UU << x"			(* witness is minimal_void *)
+
+cpo		"is_chain(S) ==> ? x. range(S) <<| x::('a::pcpo)" 
+						(* witness is cpo_void     *)
+						(* needs explicit type     *)
+
+(* instance of UU for the prototype void *)
+
+inst_void_pcpo	"UU::void = UU_void"
+
+end 
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Porder.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,427 @@
+(*  Title: 	HOLCF/porder.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for theory porder.thy 
+*)
+
+open Porder;
+
+
+val box_less = prove_goal Porder.thy 
+"[| a << b; c << a; b << d|] ==> c << d"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac trans_less 1),
+	(etac trans_less 1),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* lubs are unique                                                          *)
+(* ------------------------------------------------------------------------ *)
+
+val unique_lub  = prove_goalw Porder.thy [is_lub, is_ub] 
+	"[| S <<| x ; S <<| y |] ==> x=y"
+( fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac conjE 1),
+	(etac conjE 1),
+	(rtac antisym_less 1),
+	(rtac mp 1),((etac allE 1) THEN (atac 1) THEN (atac 1)),
+	(rtac mp 1),((etac allE 1) THEN (atac 1) THEN (atac 1))
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* chains are monotone functions                                            *)
+(* ------------------------------------------------------------------------ *)
+
+val chain_mono = prove_goalw Porder.thy [is_chain]
+	" is_chain(F) ==> x<y --> F(x)<<F(y)"
+( fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(nat_ind_tac "y" 1),
+	(rtac impI 1),
+	(etac less_zeroE 1),
+	(rtac (less_Suc_eq RS ssubst) 1),
+	(strip_tac 1),
+	(etac disjE 1),
+	(rtac trans_less 1),
+	(etac allE 2),
+	(atac 2),
+	(fast_tac HOL_cs 1),
+	(hyp_subst_tac 1),
+	(etac allE 1),
+	(atac 1)
+	]);
+
+val chain_mono3 = prove_goal  Porder.thy 
+	"[| is_chain(F); x <= y |] ==> F(x) << F(y)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (le_imp_less_or_eq RS disjE) 1),
+	(atac 1),
+	(etac (chain_mono RS mp) 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(rtac refl_less 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* Lemma for reasoning by cases on the natural numbers                      *)
+(* ------------------------------------------------------------------------ *)
+
+val nat_less_cases = prove_goal Porder.thy 
+	"[| m::nat < n ==> P(n,m); m=n ==> P(n,m);n < m ==> P(n,m)|]==>P(n,m)"
+( fn prems =>
+	[
+	(res_inst_tac [("m1","n"),("n1","m")] (less_linear RS disjE) 1),
+	(etac disjE 2),
+	(etac (hd (tl (tl prems))) 1),
+	(etac (sym RS hd (tl prems)) 1),
+	(etac (hd prems) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* The range of a chain is a totaly ordered     <<                           *)
+(* ------------------------------------------------------------------------ *)
+
+val chain_is_tord = prove_goalw Porder.thy [is_tord]
+	"is_chain(F) ==> is_tord(range(F))"
+( fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rewrite_goals_tac [range_def]),
+	(rtac allI 1 ),
+	(rtac allI 1 ),
+	(rtac (mem_Collect_eq RS ssubst) 1),
+	(rtac (mem_Collect_eq RS ssubst) 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(etac exE 1),
+	(etac exE 1),
+	(hyp_subst_tac 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("m","xa"),("n","xb")] (nat_less_cases) 1),
+	(rtac disjI1 1),
+	(rtac (chain_mono RS mp) 1),
+	(atac 1),
+	(atac 1),
+	(rtac disjI1 1),
+	(hyp_subst_tac 1),
+	(rtac refl_less 1),
+	(rtac disjI2 1),
+	(rtac (chain_mono RS mp) 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* technical lemmas about lub and is_lub, use above results about @         *)
+(* ------------------------------------------------------------------------ *)
+
+val lubI = prove_goal Porder.thy "(? x. M <<| x) ==> M <<| lub(M)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (lub RS ssubst) 1),
+	(etac selectI2 1)
+	]);
+
+val lubE = prove_goal Porder.thy " M <<| lub(M) ==>  ? x. M <<| x"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac exI 1)
+	]);
+
+val lub_eq = prove_goal Porder.thy 
+	"(? x. M <<| x)  = M <<| lub(M)"
+(fn prems => 
+	[
+	(rtac (lub RS ssubst) 1),
+	(rtac (select_eq_Ex RS subst) 1),
+	(rtac refl 1)
+	]);
+
+
+val thelubI = prove_goal  Porder.thy " M <<| l ==> lub(M) = l"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1), 
+	(rtac unique_lub 1),
+	(rtac (lub RS ssubst) 1),
+	(etac selectI 1),
+	(atac 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* access to some definition as inference rule                              *)
+(* ------------------------------------------------------------------------ *)
+
+val is_lubE = prove_goalw  Porder.thy [is_lub]
+	"S <<| x  ==> S <| x & (! u. S <| u  --> x << u)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(atac 1)
+	]);
+
+val is_lubI = prove_goalw  Porder.thy [is_lub]
+	"S <| x & (! u. S <| u  --> x << u) ==> S <<| x"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(atac 1)
+	]);
+
+val is_chainE = prove_goalw Porder.thy [is_chain] 
+ "is_chain(F) ==> ! i. F(i) << F(Suc(i))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(atac 1)]);
+
+val is_chainI = prove_goalw Porder.thy [is_chain] 
+ "! i. F(i) << F(Suc(i)) ==> is_chain(F) "
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(atac 1)]);
+
+(* ------------------------------------------------------------------------ *)
+(* technical lemmas about (least) upper bounds of chains                    *)
+(* ------------------------------------------------------------------------ *)
+
+val ub_rangeE = prove_goalw  Porder.thy [is_ub]
+	"range(S) <| x  ==> ! i. S(i) << x"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(rtac mp 1),
+	(etac spec 1),
+	(rtac rangeI 1)
+	]);
+
+val ub_rangeI = prove_goalw Porder.thy [is_ub]
+	"! i. S(i) << x  ==> range(S) <| x"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(strip_tac 1),
+	(etac rangeE 1),
+	(hyp_subst_tac 1),
+	(etac spec 1)
+	]);
+
+val is_ub_lub = (is_lubE RS conjunct1 RS ub_rangeE RS spec);
+(* range(?S1) <<| ?x1 ==> ?S1(?x) << ?x1                                    *)
+
+val is_lub_lub = (is_lubE RS conjunct2 RS spec RS mp);
+(* [| ?S3 <<| ?x3; ?S3 <| ?x1 |] ==> ?x3 << ?x1                             *)
+
+(* ------------------------------------------------------------------------ *)
+(* Prototype lemmas for class pcpo                                          *)
+(* ------------------------------------------------------------------------ *)
+
+(* ------------------------------------------------------------------------ *)
+(* a technical argument about << on void                                    *)
+(* ------------------------------------------------------------------------ *)
+
+val less_void = prove_goal Porder.thy "(u1::void << u2) = (u1 = u2)"
+(fn prems =>
+	[
+	(rtac (inst_void_po RS ssubst) 1),
+	(rewrite_goals_tac [less_void_def]),
+	(rtac iffI 1),
+	(rtac injD 1),
+	(atac 2),
+	(rtac inj_inverseI 1),
+	(rtac Rep_Void_inverse 1),
+	(etac arg_cong 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* void is pointed. The least element is UU_void                            *)
+(* ------------------------------------------------------------------------ *)
+
+val minimal_void = prove_goal Porder.thy  	"UU_void << x"
+(fn prems =>
+	[
+	(rtac (inst_void_po RS ssubst) 1),
+	(rewrite_goals_tac [less_void_def]),
+	(simp_tac (HOL_ss addsimps [unique_void]) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* UU_void is the trivial lub of all chains in void                         *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_void = prove_goalw  Porder.thy [is_lub] "M <<| UU_void"
+(fn prems =>
+	[
+	(rtac conjI 1),
+	(rewrite_goals_tac [is_ub]),
+	(strip_tac 1),
+	(rtac (inst_void_po RS ssubst) 1),
+	(rewrite_goals_tac [less_void_def]),
+	(simp_tac (HOL_ss addsimps [unique_void]) 1),
+	(strip_tac 1),
+	(rtac minimal_void 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* lub(?M) = UU_void                                                        *)
+(* ------------------------------------------------------------------------ *)
+
+val thelub_void = (lub_void RS thelubI);
+
+(* ------------------------------------------------------------------------ *)
+(* void is a cpo wrt. countable chains                                      *)
+(* ------------------------------------------------------------------------ *)
+
+val cpo_void = prove_goal Porder.thy
+	"is_chain(S::nat=>void) ==> ? x. range(S) <<| x "
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("x","UU_void")] exI 1),
+	(rtac lub_void 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* end of prototype lemmas for class pcpo                                   *)
+(* ------------------------------------------------------------------------ *)
+
+
+(* ------------------------------------------------------------------------ *)
+(* the reverse law of anti--symmetrie of <<                                 *)
+(* ------------------------------------------------------------------------ *)
+
+val antisym_less_inverse = prove_goal Porder.thy "x=y ==> x << y & y << x"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac conjI 1),
+	((rtac subst 1) THEN (rtac refl_less 2) THEN (atac 1)),
+	((rtac subst 1) THEN (rtac refl_less 2) THEN (etac sym 1))
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* results about finite chains                                              *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_finch1 = prove_goalw Porder.thy [max_in_chain_def]
+	"[| is_chain(C) ; max_in_chain(i,C)|] ==> range(C) <<| C(i)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_lubI 1),
+	(rtac conjI 1),
+	(rtac ub_rangeI 1),
+	(rtac allI 1),
+	(res_inst_tac [("m","i")] nat_less_cases 1),
+	(rtac (antisym_less_inverse RS conjunct2) 1),
+	(etac (disjI1 RS less_or_eq_imp_le RS rev_mp) 1),
+	(etac spec 1),
+	(rtac (antisym_less_inverse RS conjunct2) 1),
+	(etac (disjI2 RS less_or_eq_imp_le RS rev_mp) 1),
+	(etac spec 1),
+	(etac (chain_mono RS mp) 1),
+	(atac 1),
+	(strip_tac 1),
+	(etac (ub_rangeE RS spec) 1)
+	]);	
+
+val lub_finch2 = prove_goalw Porder.thy [finite_chain_def]
+	"finite_chain(C) ==> range(C) <<| C(@ i. max_in_chain(i,C))"
+ (fn prems=>
+	[
+	(cut_facts_tac prems 1),
+	(rtac lub_finch1 1),
+	(etac conjunct1 1),
+	(rtac selectI2 1),
+	(etac conjunct2 1)
+	]);
+
+
+val bin_chain = prove_goal Porder.thy "x<<y ==> is_chain(%i. if(i=0,x,y))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_chainI 1),
+	(rtac allI 1),
+	(nat_ind_tac "i" 1),
+	(asm_simp_tac nat_ss 1),
+	(asm_simp_tac nat_ss 1),
+	(rtac refl_less 1)
+	]);
+
+val bin_chainmax = prove_goalw Porder.thy [max_in_chain_def,le_def]
+	"x<<y ==> max_in_chain(Suc(0),%i. if(i=0,x,y))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac allI 1),
+	(nat_ind_tac "j" 1),
+	(asm_simp_tac nat_ss 1),
+	(asm_simp_tac nat_ss 1)
+	]);
+
+val lub_bin_chain = prove_goal Porder.thy 
+	"x << y ==> range(%i. if(i = 0,x,y)) <<| y"
+(fn prems=>
+	[ (cut_facts_tac prems 1),
+	(res_inst_tac [("s","if(Suc(0) = 0,x,y)")] subst 1),
+	(rtac lub_finch1 2),
+	(etac bin_chain 2),
+	(etac bin_chainmax 2),
+	(simp_tac nat_ss  1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* the maximal element in a chain is its lub                                *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_chain_maxelem = prove_goal Porder.thy
+"[|is_chain(Y);? i.Y(i)=c;!i.Y(i)<<c|] ==> lub(range(Y)) = c"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac thelubI 1),
+	(rtac is_lubI 1),
+	(rtac conjI 1),
+	(etac ub_rangeI 1),
+	(strip_tac 1),
+	(res_inst_tac [("P","%i.Y(i)=c")] exE 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(etac (ub_rangeE RS spec) 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* the lub of a constant chain is the constant                              *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_const = prove_goal Porder.thy "range(%x.c) <<| c"
+ (fn prems =>
+	[
+	(rtac is_lubI 1),
+	(rtac conjI 1),
+	(rtac ub_rangeI 1),
+	(strip_tac 1),
+	(rtac refl_less 1),
+	(strip_tac 1),
+	(etac (ub_rangeE RS spec) 1)
+	]);
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Porder.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,71 @@
+(*  Title: 	HOLCF/porder.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Definition of class porder (partial order)
+
+The prototype theory for this class is void.thy 
+
+*)
+
+Porder = Void +
+
+(* Introduction of new class. The witness is type void. *)
+
+classes po < term
+
+(* default type is still term ! *)
+(* void is the prototype in po *)
+
+arities void :: po
+
+consts	"<<"	::	"['a,'a::po] => bool"	(infixl 55)
+
+	"<|"	::	"['a set,'a::po] => bool"	(infixl 55)
+	"<<|"	::	"['a set,'a::po] => bool"	(infixl 55)
+	lub	::	"'a set => 'a::po"
+	is_tord	::	"'a::po set => bool"
+	is_chain ::	"(nat=>'a::po) => bool"
+	max_in_chain :: "[nat,nat=>'a::po]=>bool"
+	finite_chain :: "(nat=>'a::po)=>bool"
+
+rules
+
+(* class axioms: justification is theory Void *)
+
+refl_less	"x << x"	
+				(* witness refl_less_void    *)
+
+antisym_less	"[|x<<y ; y<<x |] ==> x = y"	
+				(* witness antisym_less_void *)
+
+trans_less	"[|x<<y ; y<<z |] ==> x<<z"
+				(* witness trans_less_void   *)
+
+(* instance of << for the prototype void *)
+
+inst_void_po	"(op <<)::[void,void]=>bool = less_void"
+
+(* class definitions *)
+
+is_ub		"S  <| x == ! y.y:S --> y<<x"
+is_lub		"S <<| x == S <| x & (! u. S <| u  --> x << u)"
+
+lub		"lub(S) = (@x. S <<| x)"
+
+(* Arbitrary chains are total orders    *)                  
+is_tord		"is_tord(S) == ! x y. x:S & y:S --> (x<<y | y<<x)"
+
+
+(* Here we use countable chains and I prefer to code them as functions! *)
+is_chain	"is_chain(F) == (! i.F(i) << F(Suc(i)))"
+
+
+(* finite chains, needed for monotony of continouous functions *)
+
+max_in_chain_def "max_in_chain(i,C) == ! j. i <= j --> C(i) = C(j)" 
+
+finite_chain_def "finite_chain(C) == is_chain(C) & (? i. max_in_chain(i,C))"
+
+end 
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/ROOT.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,68 @@
+(*  Title:	HOLCF/ROOT
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright	1993 Technische Universitaet Muenchen
+
+ROOT file for the conservative extension of HOL by the LCF logic.
+Should be executed in subdirectory HOLCF.
+*)
+
+val banner = "Higher-order Logic of Computable Functions";
+writeln banner;
+print_depth 1;
+
+structure Readthy = ReadthyFUN (structure ThySyn = ThySyn);
+Readthy.loaded_thys := !loaded_thys;
+open Readthy;
+
+use_thy "Holcfb";
+use_thy "Void";
+use_thy "Porder";
+use_thy "Pcpo";
+
+use_thy "Fun1";
+use_thy "Fun2";
+use_thy "Fun3";
+
+use_thy "Cont";
+
+use_thy "Cfun1";
+use_thy "Cfun2";
+use_thy "Cfun3";
+
+use_thy "Cprod1";
+use_thy "Cprod2";
+use_thy "Cprod3";
+
+use_thy "Sprod0";
+use_thy "Sprod1"; 
+use_thy "Sprod2"; 
+use_thy "Sprod3"; 
+
+use_thy "Ssum0";
+use_thy "Ssum1";
+use_thy "Ssum2";
+use_thy "Ssum3";
+
+use_thy "Lift1";
+use_thy "Lift2";
+use_thy "Lift3";
+
+use_thy "Fix";
+
+use_thy "ccc1";
+use_thy "One";
+use_thy "Tr1";
+use_thy "Tr2";
+
+use_thy "HOLCF";
+
+use_thy "Dnat";
+use_thy "Dnat2";
+use_thy "Stream";
+use_thy "Stream2";
+
+use "../Pure/install_pp.ML";
+print_depth 8;  
+
+val HOLCF_build_completed = ();	(*indicate successful build*)
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Sprod0.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,389 @@
+(*  Title: 	HOLCF/sprod0.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+Lemmas for theory sprod0.thy
+*)
+
+open Sprod0;
+
+(* ------------------------------------------------------------------------ *)
+(* A non-emptyness result for Sprod                                         *)
+(* ------------------------------------------------------------------------ *)
+
+val SprodI = prove_goalw Sprod0.thy [Sprod_def]
+	"Spair_Rep(a,b):Sprod"
+(fn prems =>
+	[
+	(EVERY1 [rtac CollectI, rtac exI,rtac exI, rtac refl])
+	]);
+
+
+val inj_onto_Abs_Sprod = prove_goal Sprod0.thy 
+	"inj_onto(Abs_Sprod,Sprod)"
+(fn prems =>
+	[
+	(rtac inj_onto_inverseI 1),
+	(etac Abs_Sprod_inverse 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* Strictness and definedness of Spair_Rep                                  *)
+(* ------------------------------------------------------------------------ *)
+
+
+val strict_Spair_Rep = prove_goalw Sprod0.thy [Spair_Rep_def]
+ "(a=UU | b=UU) ==> (Spair_Rep(a,b) = Spair_Rep(UU,UU))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac ext 1),
+	(rtac ext 1),
+	(rtac iffI 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val defined_Spair_Rep_rev = prove_goalw Sprod0.thy [Spair_Rep_def]
+ "(Spair_Rep(a,b) = Spair_Rep(UU,UU)) ==> (a=UU | b=UU)"
+ (fn prems =>
+	[
+	(res_inst_tac [("Q","a=UU|b=UU")] classical2 1),
+	(atac 1),
+	(rtac disjI1 1),
+	(rtac ((hd prems) RS fun_cong RS fun_cong RS iffD2 RS mp RS 
+	conjunct1 RS sym) 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* injectivity of Spair_Rep and Ispair                                      *)
+(* ------------------------------------------------------------------------ *)
+
+val inject_Spair_Rep = prove_goalw Sprod0.thy [Spair_Rep_def]
+"[|~aa=UU ; ~ba=UU ; Spair_Rep(a,b)=Spair_Rep(aa,ba) |] ==> a=aa & b=ba"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac ((nth_elem (2,prems)) RS fun_cong  RS fun_cong 
+		RS iffD1 RS mp) 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+
+val inject_Ispair =  prove_goalw Sprod0.thy [Ispair_def]
+	"[|~aa=UU ; ~ba=UU ; Ispair(a,b)=Ispair(aa,ba) |] ==> a=aa & b=ba"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac inject_Spair_Rep 1),
+	(atac 1),
+	(etac (inj_onto_Abs_Sprod  RS inj_ontoD) 1),
+	(rtac SprodI 1),
+	(rtac SprodI 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* strictness and definedness of Ispair                                     *)
+(* ------------------------------------------------------------------------ *)
+
+val strict_Ispair = prove_goalw Sprod0.thy [Ispair_def] 
+ "(a=UU | b=UU) ==> Ispair(a,b)=Ispair(UU,UU)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac (strict_Spair_Rep RS arg_cong) 1)
+	]);
+
+val strict_Ispair1 = prove_goalw Sprod0.thy [Ispair_def]
+	"Ispair(UU,b) = Ispair(UU,UU)"
+(fn prems =>
+	[
+	(rtac (strict_Spair_Rep RS arg_cong) 1),
+	(rtac disjI1 1),
+	(rtac refl 1)
+	]);
+
+val strict_Ispair2 = prove_goalw Sprod0.thy [Ispair_def]
+	"Ispair(a,UU) = Ispair(UU,UU)"
+(fn prems =>
+	[
+	(rtac (strict_Spair_Rep RS arg_cong) 1),
+	(rtac disjI2 1),
+	(rtac refl 1)
+	]);
+
+val strict_Ispair_rev = prove_goal Sprod0.thy 
+	"~Ispair(x,y)=Ispair(UU,UU) ==> ~x=UU & ~y=UU"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (de_morgan1 RS ssubst) 1),
+	(etac contrapos 1),
+	(etac strict_Ispair 1)
+	]);
+
+val defined_Ispair_rev = prove_goalw Sprod0.thy [Ispair_def]
+	"Ispair(a,b) = Ispair(UU,UU) ==> (a = UU | b = UU)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac defined_Spair_Rep_rev 1),
+	(rtac (inj_onto_Abs_Sprod  RS inj_ontoD) 1),
+	(atac 1),
+	(rtac SprodI 1),
+	(rtac SprodI 1)
+	]);
+
+val defined_Ispair = prove_goal Sprod0.thy  
+"[|~a=UU; ~b=UU|] ==> ~(Ispair(a,b) = Ispair(UU,UU))" 
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac contrapos 1),
+	(etac defined_Ispair_rev 2),
+	(rtac (de_morgan1 RS iffD1) 1),
+	(etac conjI 1),
+	(atac 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* Exhaustion of the strict product **                                      *)
+(* ------------------------------------------------------------------------ *)
+
+val Exh_Sprod = prove_goalw Sprod0.thy [Ispair_def]
+	"z=Ispair(UU,UU) | (? a b. z=Ispair(a,b) & ~a=UU & ~b=UU)"
+(fn prems =>
+	[
+	(rtac (rewrite_rule [Sprod_def] Rep_Sprod RS CollectE) 1),
+	(etac exE 1),
+	(etac exE 1),
+	(rtac (excluded_middle RS disjE) 1),
+	(rtac disjI2 1),
+	(rtac exI 1),
+	(rtac exI 1),
+	(rtac conjI 1),
+	(rtac (Rep_Sprod_inverse RS sym RS trans) 1),
+	(etac arg_cong 1),
+	(rtac (de_morgan1 RS ssubst) 1),
+	(atac 1),
+	(rtac disjI1 1),
+	(rtac (Rep_Sprod_inverse RS sym RS trans) 1),
+	(res_inst_tac [("f","Abs_Sprod")] arg_cong 1),
+	(etac trans 1),
+	(etac strict_Spair_Rep 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* general elimination rule for strict product                              *)
+(* ------------------------------------------------------------------------ *)
+
+val IsprodE = prove_goal Sprod0.thy
+"[|p=Ispair(UU,UU) ==> Q ;!!x y. [|p=Ispair(x,y); ~x=UU ; ~y=UU|] ==> Q|] ==> Q"
+(fn prems =>
+	[
+	(rtac (Exh_Sprod RS disjE) 1),
+	(etac (hd prems) 1),
+	(etac exE 1),
+	(etac exE 1),
+	(etac conjE 1),
+	(etac conjE 1),
+	(etac (hd (tl prems)) 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* some results about the selectors Isfst, Issnd                            *)
+(* ------------------------------------------------------------------------ *)
+
+val strict_Isfst = prove_goalw Sprod0.thy [Isfst_def] 
+	"p=Ispair(UU,UU)==>Isfst(p)=UU"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac  select_equality 1),
+	(rtac conjI 1),
+	(fast_tac HOL_cs  1),
+	(strip_tac 1),
+	(res_inst_tac [("P","Ispair(UU,UU) = Ispair(a,b)")] notE 1),
+	(rtac not_sym 1),
+	(rtac defined_Ispair 1),
+	(REPEAT (fast_tac HOL_cs  1))
+	]);
+
+
+val strict_Isfst1 =  prove_goal Sprod0.thy
+	"Isfst(Ispair(UU,y)) = UU"
+(fn prems =>
+	[
+	(rtac (strict_Ispair1 RS ssubst) 1),
+	(rtac strict_Isfst 1),
+	(rtac refl 1)
+	]);
+
+val strict_Isfst2 =  prove_goal Sprod0.thy
+	"Isfst(Ispair(x,UU)) = UU"
+(fn prems =>
+	[
+	(rtac (strict_Ispair2 RS ssubst) 1),
+	(rtac strict_Isfst 1),
+	(rtac refl 1)
+	]);
+
+
+val strict_Issnd = prove_goalw Sprod0.thy [Issnd_def] 
+	"p=Ispair(UU,UU)==>Issnd(p)=UU"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac  select_equality 1),
+	(rtac conjI 1),
+	(fast_tac HOL_cs  1),
+	(strip_tac 1),
+	(res_inst_tac [("P","Ispair(UU,UU) = Ispair(a,b)")] notE 1),
+	(rtac not_sym 1),
+	(rtac defined_Ispair 1),
+	(REPEAT (fast_tac HOL_cs  1))
+	]);
+
+val strict_Issnd1 =  prove_goal Sprod0.thy
+	"Issnd(Ispair(UU,y)) = UU"
+(fn prems =>
+	[
+	(rtac (strict_Ispair1 RS ssubst) 1),
+	(rtac strict_Issnd 1),
+	(rtac refl 1)
+	]);
+
+val strict_Issnd2 =  prove_goal Sprod0.thy
+	"Issnd(Ispair(x,UU)) = UU"
+(fn prems =>
+	[
+	(rtac (strict_Ispair2 RS ssubst) 1),
+	(rtac strict_Issnd 1),
+	(rtac refl 1)
+	]);
+
+val Isfst = prove_goalw Sprod0.thy [Isfst_def]
+	"[|~x=UU ;~y=UU |] ==> Isfst(Ispair(x,y)) = x"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac  select_equality 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(res_inst_tac [("P","Ispair(x,y) = Ispair(UU,UU)")] notE 1),
+	(etac defined_Ispair 1),
+	(atac 1),
+	(atac 1),
+	(strip_tac 1),
+	(rtac (inject_Ispair RS conjunct1) 1),
+	(fast_tac HOL_cs  3),
+	(fast_tac HOL_cs  1),
+	(fast_tac HOL_cs  1),
+	(fast_tac HOL_cs  1)
+	]);
+
+val Issnd = prove_goalw Sprod0.thy [Issnd_def]
+	"[|~x=UU ;~y=UU |] ==> Issnd(Ispair(x,y)) = y"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac  select_equality 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(res_inst_tac [("P","Ispair(x,y) = Ispair(UU,UU)")] notE 1),
+	(etac defined_Ispair 1),
+	(atac 1),
+	(atac 1),
+	(strip_tac 1),
+	(rtac (inject_Ispair RS conjunct2) 1),
+	(fast_tac HOL_cs  3),
+	(fast_tac HOL_cs  1),
+	(fast_tac HOL_cs  1),
+	(fast_tac HOL_cs  1)
+	]);
+
+val Isfst2 = prove_goal Sprod0.thy "~y=UU ==>Isfst(Ispair(x,y))=x"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1),
+	(etac Isfst 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(rtac strict_Isfst1 1)
+	]);
+
+val Issnd2 = prove_goal Sprod0.thy "~x=UU ==>Issnd(Ispair(x,y))=y"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("Q","y=UU")] (excluded_middle RS disjE) 1),
+	(etac Issnd 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(rtac strict_Issnd2 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* instantiate the simplifier                                               *)
+(* ------------------------------------------------------------------------ *)
+
+val Sprod_ss = 
+	HOL_ss 
+	addsimps [strict_Isfst1,strict_Isfst2,strict_Issnd1,strict_Issnd2,
+		 Isfst2,Issnd2];
+
+
+val defined_IsfstIssnd = prove_goal Sprod0.thy 
+	"~p=Ispair(UU,UU) ==> ~Isfst(p)=UU & ~Issnd(p)=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("p","p")] IsprodE 1),
+	(contr_tac 1),
+	(hyp_subst_tac 1),
+	(rtac conjI 1),
+	(asm_simp_tac Sprod_ss 1),
+	(asm_simp_tac Sprod_ss 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* Surjective pairing: equivalent to Exh_Sprod                              *)
+(* ------------------------------------------------------------------------ *)
+
+val surjective_pairing_Sprod = prove_goal Sprod0.thy 
+	"z = Ispair(Isfst(z))(Issnd(z))"
+(fn prems =>
+	[
+	(res_inst_tac [("z1","z")] (Exh_Sprod RS disjE) 1),
+	(asm_simp_tac Sprod_ss 1),
+	(etac exE 1),
+	(etac exE 1),
+	(asm_simp_tac Sprod_ss 1)
+	]);
+
+
+
+
+
+
+
+
+
+
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Sprod0.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,53 @@
+(*  Title: 	HOLCF/sprod0.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+Strict product
+*)
+
+Sprod0 = Cfun3 +
+
+(* new type for strict product *)
+
+types "**" 2        (infixr 20)
+
+arities "**" :: (pcpo,pcpo)term	
+
+consts
+  Sprod		:: "('a => 'b => bool)set"
+  Spair_Rep	:: "['a,'b] => ['a,'b] => bool"
+  Rep_Sprod	:: "('a ** 'b) => ('a => 'b => bool)"
+  Abs_Sprod	:: "('a => 'b => bool) => ('a ** 'b)"
+  Ispair	:: "['a,'b] => ('a ** 'b)"
+  Isfst		:: "('a ** 'b) => 'a"
+  Issnd		:: "('a ** 'b) => 'b"  
+
+rules
+
+  Spair_Rep_def		"Spair_Rep == (%a b. %x y.\
+\				(~a=UU & ~b=UU --> x=a  & y=b ))"
+
+  Sprod_def		"Sprod == {f. ? a b. f = Spair_Rep(a,b)}"
+
+  (*faking a type definition... *)
+  (* "**" is isomorphic to Sprod *)
+
+  Rep_Sprod		"Rep_Sprod(p):Sprod"		
+  Rep_Sprod_inverse	"Abs_Sprod(Rep_Sprod(p)) = p"	
+  Abs_Sprod_inverse	"f:Sprod ==> Rep_Sprod(Abs_Sprod(f)) = f"
+
+   (*defining the abstract constants*)
+
+  Ispair_def	"Ispair(a,b) == Abs_Sprod(Spair_Rep(a,b))"
+
+  Isfst_def	"Isfst(p) == @z.\
+\					(p=Ispair(UU,UU) --> z=UU)\
+\		&(! a b. ~a=UU & ~b=UU & p=Ispair(a,b)   --> z=a)"  
+
+  Issnd_def	"Issnd(p) == @z.\
+\					(p=Ispair(UU,UU) --> z=UU)\
+\		&(! a b. ~a=UU & ~b=UU & p=Ispair(a,b)   --> z=b)"  
+
+end
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Sprod1.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,204 @@
+(*  Title: 	HOLCF/sprod1.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+Lemmas for theory sprod1.thy
+*)
+
+open Sprod1;
+
+(* ------------------------------------------------------------------------ *)
+(* reduction properties for less_sprod                                      *)
+(* ------------------------------------------------------------------------ *)
+
+
+val less_sprod1a = prove_goalw Sprod1.thy [less_sprod_def]
+	"p1=Ispair(UU,UU) ==> less_sprod(p1,p2)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac eqTrueE 1),
+	(rtac select_equality 1),
+	(rtac conjI 1),
+	(fast_tac HOL_cs 1),
+	(strip_tac 1),
+	(contr_tac 1),
+	(dtac conjunct1 1),
+	(etac rev_mp 1),
+	(atac 1)
+	]);
+
+val less_sprod1b = prove_goalw Sprod1.thy [less_sprod_def]
+ "~p1=Ispair(UU,UU) ==> \
+\ less_sprod(p1,p2) = ( Isfst(p1) << Isfst(p2) & Issnd(p1) << Issnd(p2))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac select_equality 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(contr_tac 1),
+	(fast_tac HOL_cs 1),
+	(dtac conjunct2 1),
+	(etac rev_mp 1),
+	(atac 1)
+	]);
+
+val less_sprod2a = prove_goal Sprod1.thy
+	"less_sprod(Ispair(x,y),Ispair(UU,UU)) ==> x = UU | y = UU"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (excluded_middle RS disjE) 1),
+	(atac 2),
+	(rtac disjI1 1),
+	(rtac antisym_less 1),
+	(rtac minimal 2),
+	(res_inst_tac [("s","Isfst(Ispair(x,y))"),("t","x")] subst 1),
+	(rtac Isfst 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1),
+	(res_inst_tac [("s","Isfst(Ispair(UU,UU))"),("t","UU")] subst 1),
+	(simp_tac Sprod_ss 1),
+	(rtac (defined_Ispair RS less_sprod1b RS iffD1 RS conjunct1) 1),
+	(REPEAT (fast_tac HOL_cs 1))
+	]);
+
+val less_sprod2b = prove_goal Sprod1.thy
+ "less_sprod(p,Ispair(UU,UU)) ==> p = Ispair(UU,UU)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("p","p")] IsprodE 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(rtac strict_Ispair 1),
+	(etac less_sprod2a 1)
+	]);
+
+val less_sprod2c = prove_goal Sprod1.thy 
+ "[|less_sprod(Ispair(xa,ya),Ispair(x,y));\
+\~ xa = UU ; ~ ya = UU;~ x = UU ; ~ y = UU |] ==> xa << x & ya << y"
+(fn prems =>
+	[
+	(rtac conjI 1),
+	(res_inst_tac [("s","Isfst(Ispair(xa,ya))"),("t","xa")] subst 1),
+	(simp_tac (Sprod_ss addsimps prems)1),
+	(res_inst_tac [("s","Isfst(Ispair(x,y))"),("t","x")] subst 1),
+	(simp_tac (Sprod_ss addsimps prems)1),
+	(rtac (defined_Ispair RS less_sprod1b RS iffD1 RS conjunct1) 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1),
+	(simp_tac (Sprod_ss addsimps prems)1),
+	(res_inst_tac [("s","Issnd(Ispair(xa,ya))"),("t","ya")] subst 1),
+	(simp_tac (Sprod_ss addsimps prems)1),
+	(res_inst_tac [("s","Issnd(Ispair(x,y))"),("t","y")] subst 1),
+	(simp_tac (Sprod_ss addsimps prems)1),
+	(rtac (defined_Ispair RS less_sprod1b RS iffD1 RS conjunct2) 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1),
+	(simp_tac (Sprod_ss addsimps prems)1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* less_sprod is a partial order on Sprod                                   *)
+(* ------------------------------------------------------------------------ *)
+
+val refl_less_sprod = prove_goal Sprod1.thy "less_sprod(p,p)"
+(fn prems =>
+	[
+	(res_inst_tac [("p","p")] IsprodE 1),
+	(etac less_sprod1a 1),
+	(hyp_subst_tac 1),
+	(rtac (less_sprod1b RS ssubst) 1),
+	(rtac defined_Ispair 1),
+	(REPEAT (fast_tac (HOL_cs addIs [refl_less]) 1))
+	]);
+
+
+val antisym_less_sprod = prove_goal Sprod1.thy 
+ "[|less_sprod(p1,p2);less_sprod(p2,p1)|] ==> p1=p2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("p","p1")] IsprodE 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p2")] IsprodE 1),
+	(hyp_subst_tac 1),
+	(rtac refl 1),
+	(hyp_subst_tac 1),
+	(rtac (strict_Ispair RS sym) 1),
+	(etac less_sprod2a 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p2")] IsprodE 1),
+	(hyp_subst_tac 1),
+	(rtac (strict_Ispair) 1),
+	(etac less_sprod2a 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("x1","x"),("y1","xa"),("x","y"),("y","ya")] (arg_cong RS cong) 1),
+	(rtac antisym_less 1),
+	(asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct1]) 1),
+	(asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct1]) 1),
+	(rtac antisym_less 1),
+	(asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct2]) 1),
+	(asm_simp_tac (HOL_ss addsimps [less_sprod2c RS conjunct2]) 1)
+	]);
+
+val trans_less_sprod = prove_goal Sprod1.thy 
+ "[|less_sprod(p1,p2);less_sprod(p2,p3)|] ==> less_sprod(p1,p3)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("p","p1")] IsprodE 1),
+	(etac less_sprod1a 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p3")] IsprodE 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("s","p2"),("t","Ispair(UU,UU)")] subst 1),
+	(etac less_sprod2b 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("Q","p2=Ispair(UU,UU)")]  
+		(excluded_middle RS disjE) 1),
+	(rtac (defined_Ispair RS less_sprod1b RS ssubst) 1),
+	(atac 1),
+	(atac 1),
+	(rtac conjI 1),
+	(res_inst_tac [("y","Isfst(p2)")] trans_less 1),
+	(rtac conjunct1 1),
+	(rtac (less_sprod1b RS subst) 1),
+	(rtac defined_Ispair 1),
+	(atac 1),
+	(atac 1),
+	(atac 1),
+	(rtac conjunct1 1),
+	(rtac (less_sprod1b RS subst) 1),
+	(atac 1),
+	(atac 1),
+	(res_inst_tac [("y","Issnd(p2)")] trans_less 1),
+	(rtac conjunct2 1),
+	(rtac (less_sprod1b RS subst) 1),
+	(rtac defined_Ispair 1),
+	(atac 1),
+	(atac 1),
+	(atac 1),
+	(rtac conjunct2 1),
+	(rtac (less_sprod1b RS subst) 1),
+	(atac 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("s","Ispair(UU,UU)"),("t","Ispair(x,y)")] subst 1),
+	(etac (less_sprod2b RS sym) 1),
+	(atac 1)
+	]);
+
+
+
+
+
+
+
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Sprod1.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,22 @@
+(*  Title: 	HOLCF/sprod1.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+Partial ordering for the strict product
+*)
+
+Sprod1 = Sprod0 +
+
+consts
+  less_sprod	:: "[('a ** 'b),('a ** 'b)] => bool"	
+
+rules
+
+  less_sprod_def "less_sprod(p1,p2) == @z.\
+\	 ( p1=Ispair(UU,UU) --> z = True)\
+\	&(~p1=Ispair(UU,UU) --> z = (   Isfst(p1) << Isfst(p2) &\
+\					Issnd(p1) << Issnd(p2)))"
+
+end
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Sprod2.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,274 @@
+(*  Title: 	HOLCF/sprod2.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for sprod2.thy
+*)
+
+
+open Sprod2;
+
+(* ------------------------------------------------------------------------ *)
+(* access to less_sprod in class po                                         *)
+(* ------------------------------------------------------------------------ *)
+
+val less_sprod3a = prove_goal Sprod2.thy 
+	"p1=Ispair(UU,UU) ==> p1 << p2"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (inst_sprod_po RS ssubst) 1),
+	(etac less_sprod1a 1)
+	]);
+
+
+val less_sprod3b = prove_goal Sprod2.thy
+ "~p1=Ispair(UU,UU) ==>\
+\	(p1<<p2) = (Isfst(p1)<<Isfst(p2) & Issnd(p1)<<Issnd(p2))" 
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (inst_sprod_po RS ssubst) 1),
+	(etac less_sprod1b 1)
+	]);
+
+val less_sprod4b = prove_goal Sprod2.thy 
+	"p << Ispair(UU,UU) ==> p = Ispair(UU,UU)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac less_sprod2b 1),
+	(etac (inst_sprod_po RS subst) 1)
+	]);
+
+val less_sprod4a = (less_sprod4b RS defined_Ispair_rev);
+(* Ispair(?a,?b) << Ispair(UU,UU) ==> ?a = UU | ?b = UU *)
+
+val less_sprod4c = prove_goal Sprod2.thy
+ "[|Ispair(xa,ya)<<Ispair(x,y);~xa=UU;~ya=UU;~x=UU;~y=UU|] ==>\
+\		xa<<x & ya << y"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac less_sprod2c 1),
+	(etac (inst_sprod_po RS subst) 1),
+	(REPEAT (atac 1))
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* type sprod is pointed                                                    *)
+(* ------------------------------------------------------------------------ *)
+
+val minimal_sprod = prove_goal Sprod2.thy  "Ispair(UU,UU)<<p"
+(fn prems =>
+	[
+	(rtac less_sprod3a 1),
+	(rtac refl 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* Ispair is monotone in both arguments                                     *)
+(* ------------------------------------------------------------------------ *)
+
+val monofun_Ispair1 = prove_goalw Sprod2.thy [monofun] "monofun(Ispair)"
+(fn prems =>
+	[
+	(strip_tac 1),
+	(rtac (less_fun RS iffD2) 1),
+	(strip_tac 1),
+	(res_inst_tac [("Q",
+	" Ispair(y,xa) =Ispair(UU,UU)")] (excluded_middle RS disjE) 1),
+	(res_inst_tac [("Q",
+	" Ispair(x,xa) =Ispair(UU,UU)")] (excluded_middle RS disjE) 1),
+	(rtac (less_sprod3b RS iffD2) 1),
+	(atac 1),
+	(rtac conjI 1),
+	(rtac (Isfst RS ssubst) 1),
+	(etac (strict_Ispair_rev RS conjunct1) 1),
+	(etac (strict_Ispair_rev RS conjunct2) 1),
+	(rtac (Isfst RS ssubst) 1),
+	(etac (strict_Ispair_rev RS conjunct1) 1),
+	(etac (strict_Ispair_rev RS conjunct2) 1),
+	(atac 1),
+	(rtac (Issnd RS ssubst) 1),
+	(etac (strict_Ispair_rev RS conjunct1) 1),
+	(etac (strict_Ispair_rev RS conjunct2) 1),
+	(rtac (Issnd RS ssubst) 1),
+	(etac (strict_Ispair_rev RS conjunct1) 1),
+	(etac (strict_Ispair_rev RS conjunct2) 1),
+	(rtac refl_less 1),
+	(etac less_sprod3a 1),
+	(res_inst_tac [("Q",
+	" Ispair(x,xa) =Ispair(UU,UU)")] (excluded_middle RS disjE) 1),
+	(etac less_sprod3a 2),
+	(res_inst_tac [("P","Ispair(y,xa) = Ispair(UU,UU)")] notE 1),
+	(atac 2),
+	(rtac defined_Ispair 1),
+	(etac notUU_I 1),
+	(etac (strict_Ispair_rev RS  conjunct1) 1),
+	(etac (strict_Ispair_rev RS  conjunct2) 1)
+	]);
+
+
+val monofun_Ispair2 = prove_goalw Sprod2.thy [monofun] "monofun(Ispair(x))"
+(fn prems =>
+	[
+	(strip_tac 1),
+	(res_inst_tac [("Q",
+	" Ispair(x,y) =Ispair(UU,UU)")] (excluded_middle RS disjE) 1),
+	(res_inst_tac [("Q",
+	" Ispair(x,xa) =Ispair(UU,UU)")] (excluded_middle RS disjE) 1),
+	(rtac (less_sprod3b RS iffD2) 1),
+	(atac 1),
+	(rtac conjI 1),
+	(rtac (Isfst RS ssubst) 1),
+	(etac (strict_Ispair_rev RS conjunct1) 1),
+	(etac (strict_Ispair_rev RS conjunct2) 1),
+	(rtac (Isfst RS ssubst) 1),
+	(etac (strict_Ispair_rev RS conjunct1) 1),
+	(etac (strict_Ispair_rev RS conjunct2) 1),
+	(rtac refl_less 1),
+	(rtac (Issnd RS ssubst) 1),
+	(etac (strict_Ispair_rev RS conjunct1) 1),
+	(etac (strict_Ispair_rev RS conjunct2) 1),
+	(rtac (Issnd RS ssubst) 1),
+	(etac (strict_Ispair_rev RS conjunct1) 1),
+	(etac (strict_Ispair_rev RS conjunct2) 1),
+	(atac 1),
+	(etac less_sprod3a 1),
+	(res_inst_tac [("Q",
+	" Ispair(x,xa) =Ispair(UU,UU)")] (excluded_middle RS disjE) 1),
+	(etac less_sprod3a 2),
+	(res_inst_tac [("P","Ispair(x,y) = Ispair(UU,UU)")] notE 1),
+	(atac 2),
+	(rtac defined_Ispair 1),
+	(etac (strict_Ispair_rev RS  conjunct1) 1),
+	(etac notUU_I 1),
+	(etac (strict_Ispair_rev RS  conjunct2) 1)
+	]);
+
+val  monofun_Ispair = prove_goal Sprod2.thy 
+ "[|x1<<x2; y1<<y2|] ==> Ispair(x1,y1)<<Ispair(x2,y2)"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac trans_less 1),
+	(rtac (monofun_Ispair1 RS monofunE RS spec RS spec RS mp RS 
+	(less_fun RS iffD1 RS spec)) 1),
+	(rtac (monofun_Ispair2 RS monofunE RS spec RS spec RS mp) 2),
+	(atac 1),
+	(atac 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* Isfst and Issnd are monotone                                             *)
+(* ------------------------------------------------------------------------ *)
+
+val  monofun_Isfst = prove_goalw Sprod2.thy [monofun] "monofun(Isfst)"
+(fn prems =>
+	[
+	(strip_tac 1),
+	(res_inst_tac [("p","x")] IsprodE 1),
+	(hyp_subst_tac 1),
+	(rtac trans_less 1),
+	(rtac minimal 2),
+	(rtac (strict_Isfst1 RS ssubst) 1),
+	(rtac refl_less 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","y")] IsprodE 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("t","Isfst(Ispair(xa,ya))")] subst 1),
+	(rtac refl_less 2),
+	(etac (less_sprod4b RS sym RS arg_cong) 1),
+	(hyp_subst_tac 1),
+	(rtac (Isfst RS ssubst) 1),
+	(atac 1),
+	(atac 1),
+	(rtac (Isfst RS ssubst) 1),
+	(atac 1),
+	(atac 1),
+	(etac (less_sprod4c RS  conjunct1) 1),
+	(REPEAT (atac 1))
+	]);
+
+val monofun_Issnd = prove_goalw Sprod2.thy [monofun] "monofun(Issnd)"
+(fn prems =>
+	[
+	(strip_tac 1),
+	(res_inst_tac [("p","x")] IsprodE 1),
+	(hyp_subst_tac 1),
+	(rtac trans_less 1),
+	(rtac minimal 2),
+	(rtac (strict_Issnd1 RS ssubst) 1),
+	(rtac refl_less 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","y")] IsprodE 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("t","Issnd(Ispair(xa,ya))")] subst 1),
+	(rtac refl_less 2),
+	(etac (less_sprod4b RS sym RS arg_cong) 1),
+	(hyp_subst_tac 1),
+	(rtac (Issnd RS ssubst) 1),
+	(atac 1),
+	(atac 1),
+	(rtac (Issnd RS ssubst) 1),
+	(atac 1),
+	(atac 1),
+	(etac (less_sprod4c RS  conjunct2) 1),
+	(REPEAT (atac 1))
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* the type 'a ** 'b is a cpo                                               *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_sprod = prove_goal Sprod2.thy 
+"[|is_chain(S)|] ==> range(S) <<| \
+\ Ispair(lub(range(%i.Isfst(S(i)))),lub(range(%i.Issnd(S(i)))))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_lubI 1),
+	(rtac conjI 1),
+	(rtac ub_rangeI 1),
+	(rtac allI 1),
+	(res_inst_tac [("t","S(i)")] (surjective_pairing_Sprod RS ssubst) 1),
+	(rtac monofun_Ispair 1),
+	(rtac is_ub_thelub 1),
+	(etac (monofun_Isfst RS ch2ch_monofun) 1),
+	(rtac is_ub_thelub 1),
+	(etac (monofun_Issnd RS ch2ch_monofun) 1),
+	(strip_tac 1),
+	(res_inst_tac [("t","u")] (surjective_pairing_Sprod RS ssubst) 1),
+	(rtac monofun_Ispair 1),
+	(rtac is_lub_thelub 1),
+	(etac (monofun_Isfst RS ch2ch_monofun) 1),
+	(etac (monofun_Isfst RS ub2ub_monofun) 1),
+	(rtac is_lub_thelub 1),
+	(etac (monofun_Issnd RS ch2ch_monofun) 1),
+	(etac (monofun_Issnd RS ub2ub_monofun) 1)
+	]);
+
+val thelub_sprod = (lub_sprod RS thelubI);
+(* is_chain(?S1) ==> lub(range(?S1)) =                                     *)
+(* Ispair(lub(range(%i. Isfst(?S1(i)))),lub(range(%i. Issnd(?S1(i)))))     *)
+
+val cpo_sprod = prove_goal Sprod2.thy 
+	"is_chain(S::nat=>'a**'b)==>? x.range(S)<<| x"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac exI 1),
+	(etac lub_sprod 1)
+	]);
+
+
+
+
+
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Sprod2.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,24 @@
+(*  Title: 	HOLCF/sprod2.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Class Instance **::(pcpo,pcpo)po
+*)
+
+Sprod2 = Sprod1 + 
+
+arities "**" :: (pcpo,pcpo)po
+
+(* Witness for the above arity axiom is sprod1.ML *)
+
+rules
+
+(* instance of << for type ['a ** 'b]  *)
+
+inst_sprod_po	"(op <<)::['a ** 'b,'a ** 'b]=>bool = less_sprod"
+
+end
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Sprod3.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,695 @@
+(*  Title: 	HOLCF/sprod3.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for Sprod3.thy 
+*)
+
+open Sprod3;
+
+(* ------------------------------------------------------------------------ *)
+(* continuity of Ispair, Isfst, Issnd                                       *)
+(* ------------------------------------------------------------------------ *)
+
+val sprod3_lemma1 = prove_goal Sprod3.thy 
+"[| is_chain(Y);  x~= UU;  lub(range(Y))~= UU |] ==>\
+\ Ispair(lub(range(Y)),x) =\
+\ Ispair(lub(range(%i. Isfst(Ispair(Y(i),x)))),\
+\        lub(range(%i. Issnd(Ispair(Y(i),x)))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("f1","Ispair")] (arg_cong RS cong) 1),
+	(rtac lub_equal 1),
+	(atac 1),
+	(rtac (monofun_Isfst RS ch2ch_monofun) 1),
+	(rtac ch2ch_fun 1),
+	(rtac (monofun_Ispair1 RS ch2ch_monofun) 1),
+	(atac 1),
+	(rtac allI 1),
+	(asm_simp_tac Sprod_ss 1),
+	(rtac sym 1),
+	(rtac lub_chain_maxelem 1),
+	(rtac (monofun_Issnd RS ch2ch_monofun) 1),
+	(rtac ch2ch_fun 1),
+	(rtac (monofun_Ispair1 RS ch2ch_monofun) 1),
+	(atac 1),
+	(res_inst_tac [("P","%j.~Y(j)=UU")] exE 1),
+	(rtac (notall2ex RS iffD1) 1),
+	(res_inst_tac [("Q","lub(range(Y)) = UU")] contrapos 1),
+	(atac 1),
+	(rtac chain_UU_I_inverse 1),
+	(atac 1),
+	(rtac exI 1),
+	(etac Issnd2 1),
+	(rtac allI 1),
+	(res_inst_tac [("Q","Y(i)=UU")] (excluded_middle RS disjE) 1),
+	(asm_simp_tac Sprod_ss  1),
+	(rtac refl_less 1),
+	(res_inst_tac [("s","UU"),("t","Y(i)")] subst 1),
+	(etac sym 1),
+	(asm_simp_tac Sprod_ss  1),
+	(rtac minimal 1)
+	]);
+
+
+val sprod3_lemma2 = prove_goal Sprod3.thy 
+"[| is_chain(Y); ~ x = UU; lub(range(Y)) = UU |] ==>\
+\   Ispair(lub(range(Y)),x) =\
+\   Ispair(lub(range(%i. Isfst(Ispair(Y(i),x)))),\
+\          lub(range(%i. Issnd(Ispair(Y(i),x)))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("s","UU"),("t","lub(range(Y))")] ssubst 1),
+	(atac 1),
+	(rtac trans 1),
+	(rtac strict_Ispair1 1),
+	(rtac (strict_Ispair RS sym) 1),
+	(rtac disjI1 1),
+	(rtac chain_UU_I_inverse 1),
+	(rtac allI 1),
+	(asm_simp_tac Sprod_ss  1),
+	(etac (chain_UU_I RS spec) 1),
+	(atac 1)
+	]);
+
+
+val sprod3_lemma3 = prove_goal Sprod3.thy 
+"[| is_chain(Y); x = UU |] ==>\
+\          Ispair(lub(range(Y)),x) =\
+\          Ispair(lub(range(%i. Isfst(Ispair(Y(i),x)))),\
+\                  lub(range(%i. Issnd(Ispair(Y(i),x)))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("s","UU"),("t","x")] ssubst 1),
+	(atac 1),
+	(rtac trans 1),
+	(rtac strict_Ispair2 1),
+	(rtac (strict_Ispair RS sym) 1),
+	(rtac disjI1 1),
+	(rtac chain_UU_I_inverse 1),
+	(rtac allI 1),
+	(simp_tac Sprod_ss  1)
+	]);
+
+
+val contlub_Ispair1 = prove_goal Sprod3.thy "contlub(Ispair)"
+(fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac (expand_fun_eq RS iffD2) 1),
+	(strip_tac 1),
+	(rtac (lub_fun RS thelubI RS ssubst) 1),
+	(etac (monofun_Ispair1 RS ch2ch_monofun) 1),
+	(rtac trans 1),
+	(rtac (thelub_sprod RS sym) 2),
+	(rtac ch2ch_fun 2),
+	(etac (monofun_Ispair1 RS ch2ch_monofun) 2),
+	(res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1),
+	(res_inst_tac 
+		[("Q","lub(range(Y))=UU")] (excluded_middle RS disjE) 1),
+	(etac sprod3_lemma1 1),
+	(atac 1),
+	(atac 1),
+	(etac sprod3_lemma2 1),
+	(atac 1),
+	(atac 1),
+	(etac sprod3_lemma3 1),
+	(atac 1)
+	]);
+
+val sprod3_lemma4 = prove_goal Sprod3.thy 
+"[| is_chain(Y); ~ x = UU; ~ lub(range(Y)) = UU |] ==>\
+\         Ispair(x,lub(range(Y))) =\
+\         Ispair(lub(range(%i. Isfst(Ispair(x,Y(i))))),\
+\                lub(range(%i. Issnd(Ispair(x,Y(i))))))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("f1","Ispair")] (arg_cong RS cong) 1),
+	(rtac sym 1),
+	(rtac lub_chain_maxelem 1),
+	(rtac (monofun_Isfst RS ch2ch_monofun) 1),
+	(rtac (monofun_Ispair2 RS ch2ch_monofun) 1),
+	(atac 1),
+	(res_inst_tac [("P","%j.~Y(j)=UU")] exE 1),
+	(rtac (notall2ex RS iffD1) 1),
+	(res_inst_tac [("Q","lub(range(Y)) = UU")] contrapos 1),
+	(atac 1),
+	(rtac chain_UU_I_inverse 1),
+	(atac 1),
+	(rtac exI 1),
+	(etac Isfst2 1),
+	(rtac allI 1),
+	(res_inst_tac [("Q","Y(i)=UU")] (excluded_middle RS disjE) 1),
+	(asm_simp_tac Sprod_ss 1),
+	(rtac refl_less 1),
+	(res_inst_tac [("s","UU"),("t","Y(i)")] subst 1),
+	(etac sym 1),
+	(asm_simp_tac Sprod_ss  1),
+	(rtac minimal 1),
+	(rtac lub_equal 1),
+	(atac 1),
+	(rtac (monofun_Issnd RS ch2ch_monofun) 1),
+	(rtac (monofun_Ispair2 RS ch2ch_monofun) 1),
+	(atac 1),
+	(rtac allI 1),
+	(asm_simp_tac Sprod_ss 1)
+	]);
+
+val sprod3_lemma5 = prove_goal Sprod3.thy 
+"[| is_chain(Y); ~ x = UU; lub(range(Y)) = UU |] ==>\
+\         Ispair(x,lub(range(Y))) =\
+\         Ispair(lub(range(%i. Isfst(Ispair(x,Y(i))))),\
+\                lub(range(%i. Issnd(Ispair(x,Y(i))))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("s","UU"),("t","lub(range(Y))")] ssubst 1),
+	(atac 1),
+	(rtac trans 1),
+	(rtac strict_Ispair2 1),
+	(rtac (strict_Ispair RS sym) 1),
+	(rtac disjI2 1),
+	(rtac chain_UU_I_inverse 1),
+	(rtac allI 1),
+	(asm_simp_tac Sprod_ss  1),
+	(etac (chain_UU_I RS spec) 1),
+	(atac 1)
+	]);
+
+val sprod3_lemma6 = prove_goal Sprod3.thy 
+"[| is_chain(Y); x = UU |] ==>\
+\         Ispair(x,lub(range(Y))) =\
+\         Ispair(lub(range(%i. Isfst(Ispair(x,Y(i))))),\
+\                lub(range(%i. Issnd(Ispair(x,Y(i))))))"
+(fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("s","UU"),("t","x")] ssubst 1),
+	(atac 1),
+	(rtac trans 1),
+	(rtac strict_Ispair1 1),
+	(rtac (strict_Ispair RS sym) 1),
+	(rtac disjI1 1),
+	(rtac chain_UU_I_inverse 1),
+	(rtac allI 1),
+	(simp_tac Sprod_ss  1)
+	]);
+
+val contlub_Ispair2 = prove_goal Sprod3.thy "contlub(Ispair(x))"
+(fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac trans 1),
+	(rtac (thelub_sprod RS sym) 2),
+	(etac (monofun_Ispair2 RS ch2ch_monofun) 2),
+	(res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1),
+	(res_inst_tac [("Q","lub(range(Y))=UU")] 
+		(excluded_middle RS disjE) 1),
+	(etac sprod3_lemma4 1),
+	(atac 1),
+	(atac 1),
+	(etac sprod3_lemma5 1),
+	(atac 1),
+	(atac 1),
+	(etac sprod3_lemma6 1),
+	(atac 1)
+	]);
+
+
+val contX_Ispair1 = prove_goal Sprod3.thy "contX(Ispair)"
+(fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_Ispair1 1),
+	(rtac contlub_Ispair1 1)
+	]);
+
+
+val contX_Ispair2 = prove_goal Sprod3.thy "contX(Ispair(x))"
+(fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_Ispair2 1),
+	(rtac contlub_Ispair2 1)
+	]);
+
+val contlub_Isfst = prove_goal Sprod3.thy "contlub(Isfst)"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac (lub_sprod RS thelubI RS ssubst) 1),
+	(atac 1),
+	(res_inst_tac [("Q","lub(range(%i. Issnd(Y(i))))=UU")]	
+		(excluded_middle RS disjE) 1),
+	(asm_simp_tac Sprod_ss  1),
+	(res_inst_tac [("s","UU"),("t","lub(range(%i. Issnd(Y(i))))")]
+		ssubst 1),
+	(atac 1),
+	(rtac trans 1),
+	(asm_simp_tac Sprod_ss  1),
+	(rtac sym 1),
+	(rtac chain_UU_I_inverse 1),
+	(rtac allI 1),
+	(rtac strict_Isfst 1),
+	(rtac swap 1),
+	(etac (defined_IsfstIssnd RS conjunct2) 2),
+	(rtac notnotI 1),
+	(rtac (chain_UU_I RS spec) 1),
+	(rtac (monofun_Issnd RS ch2ch_monofun) 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+
+val contlub_Issnd = prove_goal Sprod3.thy "contlub(Issnd)"
+(fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac (lub_sprod RS thelubI RS ssubst) 1),
+	(atac 1),
+	(res_inst_tac [("Q","lub(range(%i. Isfst(Y(i))))=UU")]
+	 (excluded_middle RS disjE) 1),
+	(asm_simp_tac Sprod_ss  1),
+	(res_inst_tac [("s","UU"),("t","lub(range(%i. Isfst(Y(i))))")] 
+		ssubst 1),
+	(atac 1),
+	(asm_simp_tac Sprod_ss  1),
+	(rtac sym 1),
+	(rtac chain_UU_I_inverse 1),
+	(rtac allI 1),
+	(rtac strict_Issnd 1),
+	(rtac swap 1),
+	(etac (defined_IsfstIssnd RS conjunct1) 2),
+	(rtac notnotI 1),
+	(rtac (chain_UU_I RS spec) 1),
+	(rtac (monofun_Isfst RS ch2ch_monofun) 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+
+val contX_Isfst = prove_goal Sprod3.thy "contX(Isfst)"
+(fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_Isfst 1),
+	(rtac contlub_Isfst 1)
+	]);
+
+val contX_Issnd = prove_goal Sprod3.thy "contX(Issnd)"
+(fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_Issnd 1),
+	(rtac contlub_Issnd 1)
+	]);
+
+(* 
+ -------------------------------------------------------------------------- 
+ more lemmas for Sprod3.thy 
+ 
+ -------------------------------------------------------------------------- 
+*)
+
+val spair_eq = prove_goal Sprod3.thy "[|x1=x2;y1=y2|] ==> x1##y1 = x2##y2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* convert all lemmas to the continuous versions                            *)
+(* ------------------------------------------------------------------------ *)
+
+val beta_cfun_sprod = prove_goalw Sprod3.thy [spair_def]
+	"(LAM x y.Ispair(x,y))[a][b] = Ispair(a,b)"
+ (fn prems =>
+	[
+	(rtac (beta_cfun RS ssubst) 1),
+	(contX_tac 1),
+	(rtac contX_Ispair2 1),
+	(rtac contX2contX_CF1L 1),
+	(rtac contX_Ispair1 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Ispair2 1),
+	(rtac refl 1)
+	]);
+
+val inject_spair = prove_goalw Sprod3.thy [spair_def]
+	"[|~aa=UU ; ~ba=UU ; (a##b)=(aa##ba) |] ==> a=aa & b=ba"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac inject_Ispair 1),
+	(atac 1),
+	(etac box_equals 1),
+	(rtac beta_cfun_sprod 1),
+	(rtac beta_cfun_sprod 1)
+	]);
+
+val inst_sprod_pcpo2 = prove_goalw Sprod3.thy [spair_def] "UU = (UU##UU)"
+ (fn prems =>
+	[
+	(rtac sym 1),
+	(rtac trans 1),
+	(rtac beta_cfun_sprod 1),
+	(rtac sym 1),
+	(rtac inst_sprod_pcpo 1)
+	]);
+
+val strict_spair = prove_goalw Sprod3.thy [spair_def] 
+	"(a=UU | b=UU) ==> (a##b)=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac trans 1),
+	(rtac beta_cfun_sprod 1),
+	(rtac trans 1),
+	(rtac (inst_sprod_pcpo RS sym) 2),
+	(etac strict_Ispair 1)
+	]);
+
+val strict_spair1 = prove_goalw Sprod3.thy [spair_def] "(UU##b) = UU"
+ (fn prems =>
+	[
+	(rtac (beta_cfun_sprod RS ssubst) 1),
+	(rtac trans 1),
+	(rtac (inst_sprod_pcpo RS sym) 2),
+	(rtac strict_Ispair1 1)
+	]);
+
+val strict_spair2 = prove_goalw Sprod3.thy [spair_def] "(a##UU) = UU"
+ (fn prems =>
+	[
+	(rtac (beta_cfun_sprod RS ssubst) 1),
+	(rtac trans 1),
+	(rtac (inst_sprod_pcpo RS sym) 2),
+	(rtac strict_Ispair2 1)
+	]);
+
+val strict_spair_rev = prove_goalw Sprod3.thy [spair_def]
+	"~(x##y)=UU ==> ~x=UU & ~y=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac strict_Ispair_rev 1),
+	(rtac (beta_cfun_sprod RS subst) 1),
+	(rtac (inst_sprod_pcpo RS subst) 1),
+	(atac 1)
+	]);
+
+val defined_spair_rev = prove_goalw Sprod3.thy [spair_def]
+ "(a##b) = UU ==> (a = UU | b = UU)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac defined_Ispair_rev 1),
+	(rtac (beta_cfun_sprod RS subst) 1),
+	(rtac (inst_sprod_pcpo RS subst) 1),
+	(atac 1)
+	]);
+
+val defined_spair = prove_goalw Sprod3.thy [spair_def]
+	"[|~a=UU; ~b=UU|] ==> ~(a##b) = UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (beta_cfun_sprod RS ssubst) 1),
+	(rtac (inst_sprod_pcpo RS ssubst) 1),
+	(etac defined_Ispair 1),
+	(atac 1)
+	]);
+
+val Exh_Sprod2 = prove_goalw Sprod3.thy [spair_def]
+	"z=UU | (? a b. z=(a##b) & ~a=UU & ~b=UU)"
+ (fn prems =>
+	[
+	(rtac (Exh_Sprod RS disjE) 1),
+	(rtac disjI1 1),
+	(rtac (inst_sprod_pcpo RS ssubst) 1),
+	(atac 1),
+	(rtac disjI2 1),
+	(etac exE 1),
+	(etac exE 1),
+	(rtac exI 1),
+	(rtac exI 1),
+	(rtac conjI 1),
+	(rtac (beta_cfun_sprod RS ssubst) 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+
+val sprodE =  prove_goalw Sprod3.thy [spair_def]
+"[|p=UU ==> Q;!!x y. [|p=(x##y);~x=UU ; ~y=UU|] ==> Q|] ==> Q"
+(fn prems =>
+	[
+	(rtac IsprodE 1),
+	(resolve_tac prems 1),
+	(rtac (inst_sprod_pcpo RS ssubst) 1),
+	(atac 1),
+	(resolve_tac prems 1),
+	(atac 2),
+	(atac 2),
+	(rtac (beta_cfun_sprod RS ssubst) 1),
+	(atac 1)
+	]);
+
+
+val strict_sfst = prove_goalw Sprod3.thy [sfst_def] 
+	"p=UU==>sfst[p]=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Isfst 1),
+	(rtac strict_Isfst 1),
+	(rtac (inst_sprod_pcpo RS subst) 1),
+	(atac 1)
+	]);
+
+val strict_sfst1 = prove_goalw Sprod3.thy [sfst_def,spair_def] 
+	"sfst[UU##y] = UU"
+ (fn prems =>
+	[
+	(rtac (beta_cfun_sprod RS ssubst) 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Isfst 1),
+	(rtac strict_Isfst1 1)
+	]);
+ 
+val strict_sfst2 = prove_goalw Sprod3.thy [sfst_def,spair_def] 
+	"sfst[x##UU] = UU"
+ (fn prems =>
+	[
+	(rtac (beta_cfun_sprod RS ssubst) 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Isfst 1),
+	(rtac strict_Isfst2 1)
+	]);
+
+val strict_ssnd = prove_goalw Sprod3.thy [ssnd_def] 
+	"p=UU==>ssnd[p]=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Issnd 1),
+	(rtac strict_Issnd 1),
+	(rtac (inst_sprod_pcpo RS subst) 1),
+	(atac 1)
+	]);
+
+val strict_ssnd1 = prove_goalw Sprod3.thy [ssnd_def,spair_def] 
+	"ssnd[UU##y] = UU"
+ (fn prems =>
+	[
+	(rtac (beta_cfun_sprod RS ssubst) 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Issnd 1),
+	(rtac strict_Issnd1 1)
+	]);
+
+val strict_ssnd2 = prove_goalw Sprod3.thy [ssnd_def,spair_def] 
+	"ssnd[x##UU] = UU"
+ (fn prems =>
+	[
+	(rtac (beta_cfun_sprod RS ssubst) 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Issnd 1),
+	(rtac strict_Issnd2 1)
+	]);
+
+val sfst2 = prove_goalw Sprod3.thy [sfst_def,spair_def] 
+	"~y=UU ==>sfst[x##y]=x"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (beta_cfun_sprod RS ssubst) 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Isfst 1),
+	(etac Isfst2 1)
+	]);
+
+val ssnd2 = prove_goalw Sprod3.thy [ssnd_def,spair_def] 
+	"~x=UU ==>ssnd[x##y]=y"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (beta_cfun_sprod RS ssubst) 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Issnd 1),
+	(etac Issnd2 1)
+	]);
+
+
+val defined_sfstssnd = prove_goalw Sprod3.thy [sfst_def,ssnd_def,spair_def]
+	"~p=UU ==> ~sfst[p]=UU & ~ssnd[p]=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Issnd 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Isfst 1),
+	(rtac defined_IsfstIssnd 1),
+	(rtac (inst_sprod_pcpo RS subst) 1),
+	(atac 1)
+	]);
+ 
+
+val surjective_pairing_Sprod2 = prove_goalw Sprod3.thy 
+	[sfst_def,ssnd_def,spair_def] "(sfst[p] ## ssnd[p]) = p"
+ (fn prems =>
+	[
+	(rtac (beta_cfun_sprod RS ssubst) 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Issnd 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Isfst 1),
+	(rtac (surjective_pairing_Sprod RS sym) 1)
+	]);
+
+
+val less_sprod5b = prove_goalw Sprod3.thy [sfst_def,ssnd_def,spair_def]
+ "~p1=UU ==> (p1<<p2) = (sfst[p1]<<sfst[p2] & ssnd[p1]<<ssnd[p2])"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Issnd 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Issnd 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Isfst 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(rtac contX_Isfst 1),
+	(rtac less_sprod3b 1),
+	(rtac (inst_sprod_pcpo RS subst) 1),
+	(atac 1)
+	]);
+
+ 
+val less_sprod5c = prove_goalw Sprod3.thy [sfst_def,ssnd_def,spair_def]
+ "[|xa##ya<<x##y;~xa=UU;~ya=UU;~x=UU;~y=UU|] ==>xa<<x & ya << y"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac less_sprod4c 1),
+	(REPEAT (atac 2)),
+	(rtac (beta_cfun_sprod RS subst) 1),
+	(rtac (beta_cfun_sprod RS subst) 1),
+	(atac 1)
+	]);
+
+val lub_sprod2 = prove_goalw Sprod3.thy [sfst_def,ssnd_def,spair_def]
+"[|is_chain(S)|] ==> range(S) <<| \
+\ (lub(range(%i.sfst[S(i)])) ## lub(range(%i.ssnd[S(i)])))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (beta_cfun_sprod RS ssubst) 1),
+	(rtac (beta_cfun RS ext RS ssubst) 1),
+	(rtac contX_Issnd 1),
+	(rtac (beta_cfun RS ext RS ssubst) 1),
+	(rtac contX_Isfst 1),
+	(rtac lub_sprod 1),
+	(resolve_tac prems 1)
+	]);
+
+
+val thelub_sprod2 = (lub_sprod2 RS thelubI);
+(* is_chain(?S1) ==> lub(range(?S1)) =                                    *) 
+(*     (lub(range(%i. sfst[?S1(i)]))## lub(range(%i. ssnd[?S1(i)])))        *)
+
+
+
+val ssplit1 = prove_goalw Sprod3.thy [ssplit_def]
+	"ssplit[f][UU]=UU"
+ (fn prems =>
+	[
+	(rtac (beta_cfun RS ssubst) 1),
+	(contX_tacR 1),
+	(rtac (strictify1 RS ssubst) 1),
+	(rtac refl 1)
+	]);
+
+val ssplit2 = prove_goalw Sprod3.thy [ssplit_def]
+	"[|~x=UU;~y=UU|] ==> ssplit[f][x##y]=f[x][y]"
+ (fn prems =>
+	[
+	(rtac (beta_cfun RS ssubst) 1),
+	(contX_tacR 1),
+	(rtac (strictify2 RS ssubst) 1),
+	(rtac defined_spair 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(contX_tacR 1),
+	(rtac (sfst2 RS ssubst) 1),
+	(resolve_tac prems 1),
+	(rtac (ssnd2 RS ssubst) 1),
+	(resolve_tac prems 1),
+	(rtac refl 1)
+	]);
+
+
+val ssplit3 = prove_goalw Sprod3.thy [ssplit_def]
+  "ssplit[spair][z]=z"
+ (fn prems =>
+	[
+	(rtac (beta_cfun RS ssubst) 1),
+	(contX_tacR 1),
+	(res_inst_tac [("Q","z=UU")] classical2 1),
+	(hyp_subst_tac 1),
+	(rtac strictify1 1),
+	(rtac trans 1),
+	(rtac strictify2 1),
+	(atac 1),
+	(rtac (beta_cfun RS ssubst) 1),
+	(contX_tacR 1),
+	(rtac surjective_pairing_Sprod2 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* install simplifier for Sprod                                             *)
+(* ------------------------------------------------------------------------ *)
+
+val Sprod_rews = [strict_spair1,strict_spair2,strict_sfst1,strict_sfst2,
+		strict_ssnd1,strict_ssnd2,sfst2,ssnd2,
+		ssplit1,ssplit2];
+
+val Sprod_ss = Cfun_ss addsimps Sprod_rews;
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Sprod3.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,39 @@
+(*  Title: 	HOLCF/sprod3.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Class instance of  ** for class pcpo
+*)
+
+Sprod3 = Sprod2 +
+
+arities "**" :: (pcpo,pcpo)pcpo			(* Witness sprod2.ML *)
+
+consts  
+	"@spair"     :: "'a => 'b => ('a**'b)" ("_##_" [101,100] 100)
+	"cop @spair" :: "'a -> 'b -> ('a**'b)" ("spair")
+					(* continuous strict pairing *)
+	sfst         :: "('a**'b)->'a"
+	ssnd         :: "('a**'b)->'b"
+	ssplit       :: "('a->'b->'c)->('a**'b)->'c"
+
+rules 
+
+inst_sprod_pcpo	"UU::'a**'b = Ispair(UU,UU)"
+spair_def	"spair  == (LAM x y.Ispair(x,y))"
+sfst_def	"sfst   == (LAM p.Isfst(p))"
+ssnd_def	"ssnd   == (LAM p.Issnd(p))"	
+ssplit_def	"ssplit == (LAM f. strictify[LAM p.f[sfst[p]][ssnd[p]]])"
+
+end
+
+ML
+
+(* ----------------------------------------------------------------------*)
+(* parse translations for the above mixfix                               *)
+(* ----------------------------------------------------------------------*)
+
+val parse_translation = [("@spair",mk_cinfixtr "@spair")];
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Ssum0.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,394 @@
+(*  Title: 	HOLCF/ssum0.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+Lemmas for theory ssum0.thy 
+*)
+
+open Ssum0;
+
+(* ------------------------------------------------------------------------ *)
+(* A non-emptyness result for Sssum                                         *)
+(* ------------------------------------------------------------------------ *)
+
+val SsumIl = prove_goalw Ssum0.thy [Ssum_def] "Sinl_Rep(a):Ssum"
+ (fn prems =>
+	[
+	(rtac CollectI 1),
+	(rtac disjI1 1),
+	(rtac exI 1),
+	(rtac refl 1)
+	]);
+
+val SsumIr = prove_goalw Ssum0.thy [Ssum_def] "Sinr_Rep(a):Ssum"
+ (fn prems =>
+	[
+	(rtac CollectI 1),
+	(rtac disjI2 1),
+	(rtac exI 1),
+	(rtac refl 1)
+	]);
+
+val inj_onto_Abs_Ssum = prove_goal Ssum0.thy "inj_onto(Abs_Ssum,Ssum)"
+(fn prems =>
+	[
+	(rtac inj_onto_inverseI 1),
+	(etac Abs_Ssum_inverse 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* Strictness of Sinr_Rep, Sinl_Rep and Isinl, Isinr                        *)
+(* ------------------------------------------------------------------------ *)
+
+val strict_SinlSinr_Rep = prove_goalw Ssum0.thy [Sinr_Rep_def,Sinl_Rep_def]
+ "Sinl_Rep(UU) = Sinr_Rep(UU)"
+ (fn prems =>
+	[
+	(rtac ext 1),
+	(rtac ext 1),
+	(rtac ext 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val strict_IsinlIsinr = prove_goalw Ssum0.thy [Isinl_def,Isinr_def]
+ "Isinl(UU) = Isinr(UU)"
+ (fn prems =>
+	[
+	(rtac (strict_SinlSinr_Rep RS arg_cong) 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* distinctness of  Sinl_Rep, Sinr_Rep and Isinl, Isinr                     *)
+(* ------------------------------------------------------------------------ *)
+
+val noteq_SinlSinr_Rep = prove_goalw Ssum0.thy [Sinl_Rep_def,Sinr_Rep_def]
+	"(Sinl_Rep(a) = Sinr_Rep(b)) ==> a=UU & b=UU"
+ (fn prems =>
+	[
+	(rtac conjI 1),
+	(res_inst_tac [("Q","a=UU")] classical2 1),
+	(atac 1),
+	(rtac ((hd prems) RS fun_cong RS fun_cong RS fun_cong RS iffD2 
+	RS mp RS conjunct1 RS sym) 1),
+	(fast_tac HOL_cs 1),
+	(atac 1),
+	(res_inst_tac [("Q","b=UU")] classical2 1),
+	(atac 1),
+	(rtac ((hd prems) RS fun_cong RS fun_cong RS fun_cong RS iffD1 
+	RS mp RS conjunct1 RS sym) 1),
+	(fast_tac HOL_cs 1),
+	(atac 1)
+	]);
+
+
+val noteq_IsinlIsinr = prove_goalw Ssum0.thy [Isinl_def,Isinr_def]
+	"Isinl(a)=Isinr(b) ==> a=UU & b=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac noteq_SinlSinr_Rep 1),
+	(etac (inj_onto_Abs_Ssum  RS inj_ontoD) 1),
+	(rtac SsumIl 1),
+	(rtac SsumIr 1)
+	]);
+
+
+
+(* ------------------------------------------------------------------------ *)
+(* injectivity of Sinl_Rep, Sinr_Rep and Isinl, Isinr                       *)
+(* ------------------------------------------------------------------------ *)
+
+val inject_Sinl_Rep1 = prove_goalw Ssum0.thy [Sinl_Rep_def]
+ "(Sinl_Rep(a) = Sinl_Rep(UU)) ==> a=UU"
+ (fn prems =>
+	[
+	(res_inst_tac [("Q","a=UU")] classical2 1),
+	(atac 1),
+	(rtac ((hd prems) RS fun_cong RS fun_cong RS fun_cong 
+	RS iffD2 RS mp RS conjunct1 RS sym) 1),
+	(fast_tac HOL_cs 1),
+	(atac 1)
+	]);
+
+val inject_Sinr_Rep1 = prove_goalw Ssum0.thy [Sinr_Rep_def]
+ "(Sinr_Rep(b) = Sinr_Rep(UU)) ==> b=UU"
+ (fn prems =>
+	[
+	(res_inst_tac [("Q","b=UU")] classical2 1),
+	(atac 1),
+	(rtac ((hd prems) RS fun_cong RS fun_cong RS fun_cong 
+	RS iffD2 RS mp RS conjunct1 RS sym) 1),
+	(fast_tac HOL_cs 1),
+	(atac 1)
+	]);
+
+val inject_Sinl_Rep2 = prove_goalw Ssum0.thy [Sinl_Rep_def]
+"[|~a1=UU ; ~a2=UU ; Sinl_Rep(a1)=Sinl_Rep(a2) |] ==> a1=a2"
+ (fn prems =>
+	[
+	(rtac ((nth_elem (2,prems)) RS fun_cong  RS fun_cong RS fun_cong 
+	RS iffD1 RS mp RS conjunct1) 1),
+	(fast_tac HOL_cs 1),
+	(resolve_tac prems 1)
+	]);
+
+val inject_Sinr_Rep2 = prove_goalw Ssum0.thy [Sinr_Rep_def]
+"[|~b1=UU ; ~b2=UU ; Sinr_Rep(b1)=Sinr_Rep(b2) |] ==> b1=b2"
+ (fn prems =>
+	[
+	(rtac ((nth_elem (2,prems)) RS fun_cong  RS fun_cong RS fun_cong 
+	RS iffD1 RS mp RS conjunct1) 1),
+	(fast_tac HOL_cs 1),
+	(resolve_tac prems 1)
+	]);
+
+val inject_Sinl_Rep = prove_goal Ssum0.thy 
+	"Sinl_Rep(a1)=Sinl_Rep(a2) ==> a1=a2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("Q","a1=UU")] classical2 1),
+	(hyp_subst_tac 1),
+	(rtac (inject_Sinl_Rep1 RS sym) 1),
+	(etac sym 1),
+	(res_inst_tac [("Q","a2=UU")] classical2 1),
+	(hyp_subst_tac 1),
+	(etac inject_Sinl_Rep1 1),
+	(etac inject_Sinl_Rep2 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+val inject_Sinr_Rep = prove_goal Ssum0.thy 
+	"Sinr_Rep(b1)=Sinr_Rep(b2) ==> b1=b2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("Q","b1=UU")] classical2 1),
+	(hyp_subst_tac 1),
+	(rtac (inject_Sinr_Rep1 RS sym) 1),
+	(etac sym 1),
+	(res_inst_tac [("Q","b2=UU")] classical2 1),
+	(hyp_subst_tac 1),
+	(etac inject_Sinr_Rep1 1),
+	(etac inject_Sinr_Rep2 1),
+	(atac 1),
+	(atac 1)
+	]);
+
+val inject_Isinl = prove_goalw Ssum0.thy [Isinl_def]
+"Isinl(a1)=Isinl(a2)==> a1=a2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac inject_Sinl_Rep 1),
+	(etac (inj_onto_Abs_Ssum  RS inj_ontoD) 1),
+	(rtac SsumIl 1),
+	(rtac SsumIl 1)
+	]);
+
+val inject_Isinr = prove_goalw Ssum0.thy [Isinr_def]
+"Isinr(b1)=Isinr(b2) ==> b1=b2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac inject_Sinr_Rep 1),
+	(etac (inj_onto_Abs_Ssum  RS inj_ontoD) 1),
+	(rtac SsumIr 1),
+	(rtac SsumIr 1)
+	]);
+
+val inject_Isinl_rev = prove_goal Ssum0.thy  
+"~a1=a2 ==> ~Isinl(a1) = Isinl(a2)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac contrapos 1),
+	(etac inject_Isinl 2),
+	(atac 1)
+	]);
+
+val inject_Isinr_rev = prove_goal Ssum0.thy  
+"~b1=b2 ==> ~Isinr(b1) = Isinr(b2)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac contrapos 1),
+	(etac inject_Isinr 2),
+	(atac 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* Exhaustion of the strict sum ++                                          *)
+(* choice of the bottom representation is arbitrary                         *)
+(* ------------------------------------------------------------------------ *)
+
+val Exh_Ssum = prove_goalw Ssum0.thy [Isinl_def,Isinr_def]
+	"z=Isinl(UU) | (? a. z=Isinl(a) & ~a=UU) | (? b. z=Isinr(b) & ~b=UU)"
+ (fn prems =>
+	[
+	(rtac (rewrite_rule [Ssum_def] Rep_Ssum RS CollectE) 1),
+	(etac disjE 1),
+	(etac exE 1),
+	(res_inst_tac [("Q","z= Abs_Ssum(Sinl_Rep(UU))")] classical2 1),
+	(etac disjI1 1),
+	(rtac disjI2 1),
+	(rtac disjI1 1),
+	(rtac exI 1),
+	(rtac conjI 1),
+	(rtac (Rep_Ssum_inverse RS sym RS trans) 1),
+	(etac arg_cong 1),
+	(res_inst_tac [("Q","Sinl_Rep(a)=Sinl_Rep(UU)")] contrapos 1),
+	(etac arg_cong 2),
+	(etac contrapos 1),
+	(rtac (Rep_Ssum_inverse RS sym RS trans) 1),
+	(rtac trans 1),
+	(etac arg_cong 1),
+	(etac arg_cong 1),
+	(etac exE 1),
+	(res_inst_tac [("Q","z= Abs_Ssum(Sinl_Rep(UU))")] classical2 1),
+	(etac disjI1 1),
+	(rtac disjI2 1),
+	(rtac disjI2 1),
+	(rtac exI 1),
+	(rtac conjI 1),
+	(rtac (Rep_Ssum_inverse RS sym RS trans) 1),
+	(etac arg_cong 1),
+	(res_inst_tac [("Q","Sinr_Rep(b)=Sinl_Rep(UU)")] contrapos 1),
+	(hyp_subst_tac 2),
+	(rtac (strict_SinlSinr_Rep RS sym) 2),
+	(etac contrapos 1),
+	(rtac (Rep_Ssum_inverse RS sym RS trans) 1),
+	(rtac trans 1),
+	(etac arg_cong 1),
+	(etac arg_cong 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* elimination rules for the strict sum ++                                  *)
+(* ------------------------------------------------------------------------ *)
+
+val IssumE = prove_goal Ssum0.thy
+	"[|p=Isinl(UU) ==> Q ;\
+\	!!x.[|p=Isinl(x); ~x=UU |] ==> Q;\
+\	!!y.[|p=Isinr(y); ~y=UU |] ==> Q|] ==> Q"
+ (fn prems =>
+	[
+	(rtac (Exh_Ssum RS disjE) 1),
+	(etac disjE 2),
+	(eresolve_tac prems 1),
+	(etac exE 1),
+	(etac conjE 1),
+	(eresolve_tac prems 1),
+	(atac 1),
+	(etac exE 1),
+	(etac conjE 1),
+	(eresolve_tac prems 1),
+	(atac 1)
+	]);
+
+val IssumE2 = prove_goal Ssum0.thy 
+"[| !!x. [| p = Isinl(x) |] ==> Q;   !!y. [| p = Isinr(y) |] ==> Q |] ==>Q"
+ (fn prems =>
+	[
+	(rtac IssumE 1),
+	(eresolve_tac prems 1), 
+	(eresolve_tac prems 1), 
+	(eresolve_tac prems 1)
+	]);
+
+
+
+
+(* ------------------------------------------------------------------------ *)
+(* rewrites for Iwhen                                                       *)
+(* ------------------------------------------------------------------------ *)
+
+val Iwhen1 = prove_goalw Ssum0.thy [Iwhen_def]
+	"Iwhen(f)(g)(Isinl(UU)) = UU"
+ (fn prems =>
+	[
+	(rtac  select_equality 1),
+	(rtac conjI 1),
+	(fast_tac HOL_cs  1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(res_inst_tac [("P","a=UU")] notE 1),
+	(fast_tac HOL_cs  1),
+	(rtac inject_Isinl 1),
+	(rtac sym 1),
+	(fast_tac HOL_cs  1),
+	(strip_tac 1),
+	(res_inst_tac [("P","b=UU")] notE 1),
+	(fast_tac HOL_cs  1),
+	(rtac inject_Isinr 1),
+	(rtac sym 1),
+	(rtac (strict_IsinlIsinr RS subst) 1),
+	(fast_tac HOL_cs  1),
+	(fast_tac HOL_cs  1)
+	]);
+
+
+val Iwhen2 = prove_goalw Ssum0.thy [Iwhen_def]
+	"~x=UU ==> Iwhen(f)(g)(Isinl(x)) = f[x]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac  select_equality 1),
+	(fast_tac HOL_cs  2),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(res_inst_tac [("P","x=UU")] notE 1),
+	(atac 1),
+	(rtac inject_Isinl 1),
+	(atac 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(rtac cfun_arg_cong 1),
+	(rtac inject_Isinl 1),
+	(fast_tac HOL_cs  1),
+	(strip_tac 1),
+	(res_inst_tac [("P","Isinl(x) = Isinr(b)")] notE 1),
+	(fast_tac HOL_cs  2),
+	(rtac contrapos 1),
+	(etac noteq_IsinlIsinr 2),
+	(fast_tac HOL_cs  1)
+	]);
+
+val Iwhen3 = prove_goalw Ssum0.thy [Iwhen_def]
+	"~y=UU ==> Iwhen(f)(g)(Isinr(y)) = g[y]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac  select_equality 1),
+	(fast_tac HOL_cs  2),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(res_inst_tac [("P","y=UU")] notE 1),
+	(atac 1),
+	(rtac inject_Isinr 1),
+	(rtac (strict_IsinlIsinr RS subst) 1),
+	(atac 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(res_inst_tac [("P","Isinr(y) = Isinl(a)")] notE 1),
+	(fast_tac HOL_cs  2),
+	(rtac contrapos 1),
+	(etac (sym RS noteq_IsinlIsinr) 2),
+	(fast_tac HOL_cs  1),
+	(strip_tac 1),
+	(rtac cfun_arg_cong 1),
+	(rtac inject_Isinr 1),
+	(fast_tac HOL_cs  1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* instantiate the simplifier                                               *)
+(* ------------------------------------------------------------------------ *)
+
+val Ssum_ss = Cfun_ss addsimps 
+		[(strict_IsinlIsinr RS sym),Iwhen1,Iwhen2,Iwhen3];
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Ssum0.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,54 @@
+(*  Title: 	HOLCF/ssum0.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+Strict sum
+*)
+
+Ssum0 = Cfun3 +
+
+(* new type for strict sum *)
+
+types "++" 2        (infixr 10)
+
+arities "++" :: (pcpo,pcpo)term	
+
+consts
+  Ssum		:: "(['a,'b,bool]=>bool)set"
+  Sinl_Rep	:: "['a,'a,'b,bool]=>bool"
+  Sinr_Rep	:: "['b,'a,'b,bool]=>bool"
+  Rep_Ssum	:: "('a ++ 'b) => (['a,'b,bool]=>bool)"
+  Abs_Ssum	:: "(['a,'b,bool]=>bool) => ('a ++ 'b)"
+  Isinl		:: "'a => ('a ++ 'b)"
+  Isinr		:: "'b => ('a ++ 'b)"
+  Iwhen		:: "('a->'c)=>('b->'c)=>('a ++ 'b)=> 'c"
+
+rules
+
+  Sinl_Rep_def		"Sinl_Rep == (%a.%x y p.\
+\				(~a=UU --> x=a  & p))"
+
+  Sinr_Rep_def		"Sinr_Rep == (%b.%x y p.\
+\				(~b=UU --> y=b  & ~p))"
+
+  Ssum_def		"Ssum =={f.(? a.f=Sinl_Rep(a))|(? b.f=Sinr_Rep(b))}"
+
+  (*faking a type definition... *)
+  (* "++" is isomorphic to Ssum *)
+
+  Rep_Ssum		"Rep_Ssum(p):Ssum"		
+  Rep_Ssum_inverse	"Abs_Ssum(Rep_Ssum(p)) = p"	
+  Abs_Ssum_inverse	"f:Ssum ==> Rep_Ssum(Abs_Ssum(f)) = f"
+
+   (*defining the abstract constants*)
+  Isinl_def	"Isinl(a) == Abs_Ssum(Sinl_Rep(a))"
+  Isinr_def	"Isinr(b) == Abs_Ssum(Sinr_Rep(b))"
+
+  Iwhen_def	"Iwhen(f)(g)(s) == @z.\
+\				    (s=Isinl(UU) --> z=UU)\
+\			&(!a. ~a=UU & s=Isinl(a) --> z=f[a])\  
+\			&(!b. ~b=UU & s=Isinr(b) --> z=g[b])"  
+
+end
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Ssum1.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,353 @@
+(*  Title: 	HOLCF/ssum1.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+Lemmas for theory ssum1.thy
+*)
+
+open Ssum1;
+
+local 
+
+fun eq_left s1 s2 = 
+	(
+	(res_inst_tac [("s",s1),("t",s2)] (inject_Isinl RS subst) 1)
+	THEN 	(rtac trans 1)
+	THEN 	(atac 2)
+	THEN 	(etac sym 1));
+
+fun eq_right s1 s2 = 
+	(
+	(res_inst_tac [("s",s1),("t",s2)] (inject_Isinr RS subst) 1)
+	THEN 	(rtac trans 1)
+	THEN 	(atac 2)
+	THEN 	(etac sym 1));
+
+fun UU_left s1 = 
+	(
+	(res_inst_tac [("t",s1)](noteq_IsinlIsinr RS conjunct1 RS ssubst)1)
+	THEN (rtac trans 1)
+	THEN (atac 2)
+	THEN (etac sym 1));
+
+fun UU_right s1 = 
+	(
+	(res_inst_tac [("t",s1)](noteq_IsinlIsinr RS conjunct2 RS ssubst)1)
+	THEN (rtac trans 1)
+	THEN (atac 2)
+	THEN (etac sym 1))
+
+in
+
+val less_ssum1a = prove_goalw Ssum1.thy [less_ssum_def]
+"[|s1=Isinl(x); s2=Isinl(y)|] ==> less_ssum(s1,s2) = (x << y)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac  select_equality 1),
+	(dtac conjunct1 2),
+	(dtac spec 2),
+	(dtac spec 2),
+	(etac mp 2),
+	(fast_tac HOL_cs 2),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(eq_left "x" "u"),
+	(eq_left "y" "xa"),
+	(rtac refl 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(UU_left "x"),
+	(UU_right "v"),
+	(simp_tac Cfun_ss 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(eq_left "x" "u"),
+	(UU_left "y"),
+	(rtac iffI 1),
+	(etac UU_I 1),
+	(res_inst_tac [("s","x"),("t","UU")] subst 1),
+	(atac 1),
+	(rtac refl_less 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(UU_left "x"),
+	(UU_right "v"),
+	(simp_tac Cfun_ss 1)
+	]);
+
+
+val less_ssum1b = prove_goalw Ssum1.thy [less_ssum_def]
+"[|s1=Isinr(x); s2=Isinr(y)|] ==> less_ssum(s1,s2) = (x << y)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac  select_equality 1),
+	(dtac conjunct2 2),
+	(dtac conjunct1 2),
+	(dtac spec 2),
+	(dtac spec 2),
+	(etac mp 2),
+	(fast_tac HOL_cs 2),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(UU_right "x"),
+	(UU_left "u"),
+	(simp_tac Cfun_ss 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(eq_right "x" "v"),
+	(eq_right "y" "ya"),
+	(rtac refl 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(UU_right "x"),
+	(UU_left "u"),
+	(simp_tac Cfun_ss 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(eq_right "x" "v"),
+	(UU_right "y"),
+	(rtac iffI 1),
+	(etac UU_I 1),
+	(res_inst_tac [("s","UU"),("t","x")] subst 1),
+	(etac sym 1),
+	(rtac refl_less 1)
+	]);
+
+
+val less_ssum1c = prove_goalw Ssum1.thy [less_ssum_def]
+"[|s1=Isinl(x); s2=Isinr(y)|] ==> less_ssum(s1,s2) = (x = UU)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac  select_equality 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(eq_left  "x" "u"),
+	(UU_left "xa"),
+	(rtac iffI 1),
+	(res_inst_tac [("s","x"),("t","UU")] subst 1),
+	(atac 1),
+	(rtac refl_less 1),
+	(etac UU_I 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(UU_left "x"),
+	(UU_right "v"),
+	(simp_tac Cfun_ss 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(eq_left  "x" "u"),
+	(rtac refl 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(UU_left "x"),
+	(UU_right "v"),
+	(simp_tac Cfun_ss 1),
+	(dtac conjunct2 1),
+	(dtac conjunct2 1),
+	(dtac conjunct1 1),
+	(dtac spec 1),
+	(dtac spec 1),
+	(etac mp 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+
+val less_ssum1d = prove_goalw Ssum1.thy [less_ssum_def]
+"[|s1=Isinr(x); s2=Isinl(y)|] ==> less_ssum(s1,s2) = (x = UU)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac  select_equality 1),
+	(dtac conjunct2 2),
+	(dtac conjunct2 2),
+	(dtac conjunct2 2),
+	(dtac spec 2),
+	(dtac spec 2),
+	(etac mp 2),
+	(fast_tac HOL_cs 2),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(UU_right "x"),
+	(UU_left "u"),
+	(simp_tac Cfun_ss 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(UU_right "ya"),
+	(eq_right "x" "v"),
+	(rtac iffI 1),
+	(etac UU_I 2),
+	(res_inst_tac [("s","UU"),("t","x")] subst 1),
+	(etac sym 1),
+	(rtac refl_less 1),
+	(rtac conjI 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(UU_right "x"),
+	(UU_left "u"),
+	(simp_tac HOL_ss 1),
+	(strip_tac 1),
+	(etac conjE 1),
+	(eq_right "x" "v"),
+	(rtac refl 1)
+	])
+end;
+
+
+(* ------------------------------------------------------------------------ *)
+(* optimize lemmas about less_ssum                                          *)
+(* ------------------------------------------------------------------------ *)
+
+val less_ssum2a = prove_goal Ssum1.thy 
+	"less_ssum(Isinl(x),Isinl(y)) = (x << y)"
+ (fn prems =>
+	[
+	(rtac less_ssum1a 1),
+	(rtac refl 1),
+	(rtac refl 1)
+	]);
+
+val less_ssum2b = prove_goal Ssum1.thy 
+	"less_ssum(Isinr(x),Isinr(y)) = (x << y)"
+ (fn prems =>
+	[
+	(rtac less_ssum1b 1),
+	(rtac refl 1),
+	(rtac refl 1)
+	]);
+
+val less_ssum2c = prove_goal Ssum1.thy 
+	"less_ssum(Isinl(x),Isinr(y)) = (x = UU)"
+ (fn prems =>
+	[
+	(rtac less_ssum1c 1),
+	(rtac refl 1),
+	(rtac refl 1)
+	]);
+
+val less_ssum2d = prove_goal Ssum1.thy 
+	"less_ssum(Isinr(x),Isinl(y)) = (x = UU)"
+ (fn prems =>
+	[
+	(rtac less_ssum1d 1),
+	(rtac refl 1),
+	(rtac refl 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* less_ssum is a partial order on ++                                     *)
+(* ------------------------------------------------------------------------ *)
+
+val refl_less_ssum = prove_goal Ssum1.thy "less_ssum(p,p)"
+ (fn prems =>
+	[
+	(res_inst_tac [("p","p")] IssumE2 1),
+	(hyp_subst_tac 1),
+	(rtac (less_ssum2a RS iffD2) 1),
+	(rtac refl_less 1),
+	(hyp_subst_tac 1),
+	(rtac (less_ssum2b RS iffD2) 1),
+	(rtac refl_less 1)
+	]);
+
+val antisym_less_ssum = prove_goal Ssum1.thy 
+ "[|less_ssum(p1,p2);less_ssum(p2,p1)|] ==> p1=p2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("p","p1")] IssumE2 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p2")] IssumE2 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("f","Isinl")] arg_cong 1),
+	(rtac antisym_less 1),
+	(etac (less_ssum2a RS iffD1) 1),
+	(etac (less_ssum2a RS iffD1) 1),
+	(hyp_subst_tac 1),
+	(etac (less_ssum2d RS iffD1 RS ssubst) 1),
+	(etac (less_ssum2c RS iffD1 RS ssubst) 1),
+	(rtac strict_IsinlIsinr 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p2")] IssumE2 1),
+	(hyp_subst_tac 1),
+	(etac (less_ssum2c RS iffD1 RS ssubst) 1),
+	(etac (less_ssum2d RS iffD1 RS ssubst) 1),
+	(rtac (strict_IsinlIsinr RS sym) 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("f","Isinr")] arg_cong 1),
+	(rtac antisym_less 1),
+	(etac (less_ssum2b RS iffD1) 1),
+	(etac (less_ssum2b RS iffD1) 1)
+	]);
+
+val trans_less_ssum = prove_goal Ssum1.thy 
+ "[|less_ssum(p1,p2);less_ssum(p2,p3)|] ==> less_ssum(p1,p3)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("p","p1")] IssumE2 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p3")] IssumE2 1),
+	(hyp_subst_tac 1),
+	(rtac (less_ssum2a RS iffD2) 1),
+	(res_inst_tac [("p","p2")] IssumE2 1),
+	(hyp_subst_tac 1),
+	(rtac trans_less 1),
+	(etac (less_ssum2a RS iffD1) 1),
+	(etac (less_ssum2a RS iffD1) 1),
+	(hyp_subst_tac 1),
+	(etac (less_ssum2c RS iffD1 RS ssubst) 1),
+	(rtac minimal 1),
+	(hyp_subst_tac 1),
+	(rtac (less_ssum2c RS iffD2) 1),
+	(res_inst_tac [("p","p2")] IssumE2 1),
+	(hyp_subst_tac 1),
+	(rtac UU_I 1),
+	(rtac trans_less 1),
+	(etac (less_ssum2a RS iffD1) 1),
+	(rtac (antisym_less_inverse RS conjunct1) 1),
+	(etac (less_ssum2c RS iffD1) 1),
+	(hyp_subst_tac 1),
+	(etac (less_ssum2c RS iffD1) 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","p3")] IssumE2 1),
+	(hyp_subst_tac 1),
+	(rtac (less_ssum2d RS iffD2) 1),
+	(res_inst_tac [("p","p2")] IssumE2 1),
+	(hyp_subst_tac 1),
+	(etac (less_ssum2d RS iffD1) 1),
+	(hyp_subst_tac 1),
+	(rtac UU_I 1),
+	(rtac trans_less 1),
+	(etac (less_ssum2b RS iffD1) 1),
+	(rtac (antisym_less_inverse RS conjunct1) 1),
+	(etac (less_ssum2d RS iffD1) 1),
+	(hyp_subst_tac 1),
+	(rtac (less_ssum2b RS iffD2) 1),
+	(res_inst_tac [("p","p2")] IssumE2 1),
+	(hyp_subst_tac 1),
+	(etac (less_ssum2d RS iffD1 RS ssubst) 1),
+	(rtac minimal 1),
+	(hyp_subst_tac 1),
+	(rtac trans_less 1),
+	(etac (less_ssum2b RS iffD1) 1),
+	(etac (less_ssum2b RS iffD1) 1)
+	]);
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Ssum1.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,25 @@
+(*  Title: 	HOLCF/ssum1.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+Partial ordering for the strict sum ++
+*)
+
+Ssum1 = Ssum0 +
+
+consts
+
+  less_ssum	:: "[('a ++ 'b),('a ++ 'b)] => bool"	
+
+rules
+
+  less_ssum_def "less_ssum(s1,s2) == (@z.\
+\	 (! u x.s1=Isinl(u) & s2=Isinl(x) --> z = (u << x))\
+\	&(! v y.s1=Isinr(v) & s2=Isinr(y) --> z = (v << y))\
+\	&(! u y.s1=Isinl(u) & s2=Isinr(y) --> z = (u = UU))\
+\	&(! v x.s1=Isinr(v) & s2=Isinl(x) --> z = (v = UU)))"
+
+end
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Ssum2.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,419 @@
+(*  Title: 	HOLCF/ssum2.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for ssum2.thy
+*)
+
+open Ssum2;
+
+(* ------------------------------------------------------------------------ *)
+(* access to less_ssum in class po                                          *)
+(* ------------------------------------------------------------------------ *)
+
+val less_ssum3a = prove_goal Ssum2.thy 
+	"(Isinl(x) << Isinl(y)) = (x << y)"
+ (fn prems =>
+	[
+	(rtac (inst_ssum_po RS ssubst) 1),
+	(rtac less_ssum2a 1)
+	]);
+
+val less_ssum3b = prove_goal Ssum2.thy 
+	"(Isinr(x) << Isinr(y)) = (x << y)"
+ (fn prems =>
+	[
+	(rtac (inst_ssum_po RS ssubst) 1),
+	(rtac less_ssum2b 1)
+	]);
+
+val less_ssum3c = prove_goal Ssum2.thy 
+	"(Isinl(x) << Isinr(y)) = (x = UU)"
+ (fn prems =>
+	[
+	(rtac (inst_ssum_po RS ssubst) 1),
+	(rtac less_ssum2c 1)
+	]);
+
+val less_ssum3d = prove_goal Ssum2.thy 
+	"(Isinr(x) << Isinl(y)) = (x = UU)"
+ (fn prems =>
+	[
+	(rtac (inst_ssum_po RS ssubst) 1),
+	(rtac less_ssum2d 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* type ssum ++ is pointed                                                  *)
+(* ------------------------------------------------------------------------ *)
+
+val minimal_ssum = prove_goal Ssum2.thy "Isinl(UU) << s"
+ (fn prems =>
+	[
+	(res_inst_tac [("p","s")] IssumE2 1),
+	(hyp_subst_tac 1),
+	(rtac (less_ssum3a RS iffD2) 1),
+	(rtac minimal 1),
+	(hyp_subst_tac 1),
+	(rtac (strict_IsinlIsinr RS ssubst) 1),
+	(rtac (less_ssum3b RS iffD2) 1),
+	(rtac minimal 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* Isinl, Isinr are monotone                                                *)
+(* ------------------------------------------------------------------------ *)
+
+val monofun_Isinl = prove_goalw Ssum2.thy [monofun] "monofun(Isinl)"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(etac (less_ssum3a RS iffD2) 1)
+	]);
+
+val monofun_Isinr = prove_goalw Ssum2.thy [monofun] "monofun(Isinr)"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(etac (less_ssum3b RS iffD2) 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* Iwhen is monotone in all arguments                                       *)
+(* ------------------------------------------------------------------------ *)
+
+
+val monofun_Iwhen1 = prove_goalw Ssum2.thy [monofun] "monofun(Iwhen)"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(rtac (less_fun RS iffD2) 1),
+	(strip_tac 1),
+	(rtac (less_fun RS iffD2) 1),
+	(strip_tac 1),
+	(res_inst_tac [("p","xb")] IssumE 1),
+	(hyp_subst_tac 1),
+	(asm_simp_tac Ssum_ss 1),
+	(asm_simp_tac Ssum_ss 1),
+	(etac monofun_cfun_fun 1),
+	(asm_simp_tac Ssum_ss 1)
+	]);
+
+val monofun_Iwhen2 = prove_goalw Ssum2.thy [monofun] "monofun(Iwhen(f))"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(rtac (less_fun RS iffD2) 1),
+	(strip_tac 1),
+	(res_inst_tac [("p","xa")] IssumE 1),
+	(hyp_subst_tac 1),
+	(asm_simp_tac Ssum_ss 1),
+	(asm_simp_tac Ssum_ss 1),
+	(asm_simp_tac Ssum_ss 1),
+	(etac monofun_cfun_fun 1)
+	]);
+
+val monofun_Iwhen3 = prove_goalw Ssum2.thy [monofun] "monofun(Iwhen(f)(g))"
+ (fn prems =>
+	[
+	(strip_tac 1),
+	(res_inst_tac [("p","x")] IssumE 1),
+	(hyp_subst_tac 1),
+	(asm_simp_tac Ssum_ss 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","y")] IssumE 1),
+	(hyp_subst_tac 1),
+	(asm_simp_tac Ssum_ss 1),
+	(res_inst_tac  [("P","xa=UU")] notE 1),
+	(atac 1),
+	(rtac UU_I 1),
+	(rtac (less_ssum3a  RS iffD1) 1),
+	(atac 1),
+	(hyp_subst_tac 1),
+	(asm_simp_tac Ssum_ss 1),
+	(rtac monofun_cfun_arg 1),
+	(etac (less_ssum3a  RS iffD1) 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("s","UU"),("t","xa")] subst 1),
+	(etac (less_ssum3c  RS iffD1 RS sym) 1),
+	(asm_simp_tac Ssum_ss 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("p","y")] IssumE 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("s","UU"),("t","ya")] subst 1),
+	(etac (less_ssum3d  RS iffD1 RS sym) 1),
+	(asm_simp_tac Ssum_ss 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("s","UU"),("t","ya")] subst 1),
+	(etac (less_ssum3d  RS iffD1 RS sym) 1),
+	(asm_simp_tac Ssum_ss 1),
+	(hyp_subst_tac 1),
+	(asm_simp_tac Ssum_ss 1),
+	(rtac monofun_cfun_arg 1),
+	(etac (less_ssum3b  RS iffD1) 1)
+	]);
+
+
+
+
+(* ------------------------------------------------------------------------ *)
+(* some kind of exhaustion rules for chains in 'a ++ 'b                     *)
+(* ------------------------------------------------------------------------ *)
+
+
+val ssum_lemma1 = prove_goal Ssum2.thy 
+"[|~(!i.? x.Y(i::nat)=Isinl(x))|] ==> (? i.! x.~Y(i)=Isinl(x))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val ssum_lemma2 = prove_goal Ssum2.thy 
+"[|(? i.!x.~(Y::nat => 'a++'b)(i::nat)=Isinl(x::'a))|] ==>\
+\   (? i y. (Y::nat => 'a++'b)(i::nat)=Isinr(y::'b) & ~y=UU)"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac exE 1),
+	(res_inst_tac [("p","Y(i)")] IssumE 1),
+	(dtac spec 1),
+	(contr_tac 1),
+	(dtac spec 1),
+	(contr_tac 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+
+val ssum_lemma3 = prove_goal Ssum2.thy 
+"[|is_chain(Y);(? i x. Y(i)=Isinr(x) & ~x=UU)|] ==> (!i.? y.Y(i)=Isinr(y))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(etac exE 1),
+	(etac exE 1),
+	(rtac allI 1),
+	(res_inst_tac [("p","Y(ia)")] IssumE 1),
+	(rtac exI 1),
+	(rtac trans 1),
+	(rtac strict_IsinlIsinr 2),
+	(atac 1),
+	(etac exI 2),
+	(etac conjE 1),
+	(res_inst_tac [("m","i"),("n","ia")] nat_less_cases 1),
+	(hyp_subst_tac 2),
+	(etac exI 2),
+	(res_inst_tac [("P","x=UU")] notE 1),
+	(atac 1),
+	(rtac (less_ssum3d RS iffD1) 1),
+	(res_inst_tac [("s","Y(i)"),("t","Isinr(x)")] subst 1),
+	(atac 1),
+	(res_inst_tac [("s","Y(ia)"),("t","Isinl(xa)")] subst 1),
+	(atac 1),
+	(etac (chain_mono RS mp) 1),
+	(atac 1),
+	(res_inst_tac [("P","xa=UU")] notE 1),
+	(atac 1),
+	(rtac (less_ssum3c RS iffD1) 1),
+	(res_inst_tac [("s","Y(i)"),("t","Isinr(x)")] subst 1),
+	(atac 1),
+	(res_inst_tac [("s","Y(ia)"),("t","Isinl(xa)")] subst 1),
+	(atac 1),
+	(etac (chain_mono RS mp) 1),
+	(atac 1)
+	]);
+
+val ssum_lemma4 = prove_goal Ssum2.thy 
+"is_chain(Y) ==> (!i.? x.Y(i)=Isinl(x))|(!i.? y.Y(i)=Isinr(y))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac classical2 1),
+	(etac disjI1 1),
+	(rtac disjI2 1),
+	(etac ssum_lemma3 1),
+	(rtac ssum_lemma2 1),
+	(etac ssum_lemma1 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* restricted surjectivity of Isinl                                         *)
+(* ------------------------------------------------------------------------ *)
+
+val ssum_lemma5 = prove_goal Ssum2.thy 
+"z=Isinl(x)==> Isinl((Iwhen (LAM x.x) (LAM y.UU))(z)) = z"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("Q","x=UU")] classical2 1),
+	(asm_simp_tac Ssum_ss 1),
+	(asm_simp_tac Ssum_ss 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* restricted surjectivity of Isinr                                         *)
+(* ------------------------------------------------------------------------ *)
+
+val ssum_lemma6 = prove_goal Ssum2.thy 
+"z=Isinr(x)==> Isinr((Iwhen (LAM y.UU) (LAM x.x))(z)) = z"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(hyp_subst_tac 1),
+	(res_inst_tac [("Q","x=UU")] classical2 1),
+	(asm_simp_tac Ssum_ss 1),
+	(asm_simp_tac Ssum_ss 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* technical lemmas                                                         *)
+(* ------------------------------------------------------------------------ *)
+
+val ssum_lemma7 = prove_goal Ssum2.thy 
+"[|Isinl(x) << z; ~x=UU|] ==> ? y.z=Isinl(y) & ~y=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("p","z")] IssumE 1),
+	(hyp_subst_tac 1),
+	(etac notE 1),
+	(rtac antisym_less 1),
+	(etac (less_ssum3a RS iffD1) 1),
+	(rtac minimal 1),
+	(fast_tac HOL_cs 1),
+	(hyp_subst_tac 1),
+	(rtac notE 1),
+	(etac (less_ssum3c RS iffD1) 2),
+	(atac 1)
+	]);
+
+val ssum_lemma8 = prove_goal Ssum2.thy 
+"[|Isinr(x) << z; ~x=UU|] ==> ? y.z=Isinr(y) & ~y=UU"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("p","z")] IssumE 1),
+	(hyp_subst_tac 1),
+	(etac notE 1),
+	(etac (less_ssum3d RS iffD1) 1),
+	(hyp_subst_tac 1),
+	(rtac notE 1),
+	(etac (less_ssum3d RS iffD1) 2),
+	(atac 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+(* ------------------------------------------------------------------------ *)
+(* the type 'a ++ 'b is a cpo in three steps                                *)
+(* ------------------------------------------------------------------------ *)
+
+val lub_ssum1a = prove_goal Ssum2.thy 
+"[|is_chain(Y);(!i.? x.Y(i)=Isinl(x))|] ==>\
+\ range(Y) <<|\
+\ Isinl(lub(range(%i.(Iwhen (LAM x.x) (LAM y.UU))(Y(i)))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_lubI 1),
+	(rtac conjI 1),
+	(rtac ub_rangeI 1),
+	(rtac allI 1),
+	(etac allE 1),
+	(etac exE 1),
+	(res_inst_tac [("t","Y(i)")] (ssum_lemma5 RS subst) 1),
+	(atac 1),
+	(rtac (monofun_Isinl RS monofunE RS spec RS spec RS mp) 1),
+	(rtac is_ub_thelub 1),
+	(etac (monofun_Iwhen3 RS ch2ch_monofun) 1),
+	(strip_tac 1),
+	(res_inst_tac [("p","u")] IssumE2 1),
+	(res_inst_tac [("t","u")] (ssum_lemma5 RS subst) 1),
+	(atac 1),
+	(rtac (monofun_Isinl RS monofunE RS spec RS spec RS mp) 1),
+	(rtac is_lub_thelub 1),
+	(etac (monofun_Iwhen3 RS ch2ch_monofun) 1),
+	(etac (monofun_Iwhen3 RS ub2ub_monofun) 1),
+	(hyp_subst_tac 1),
+	(rtac (less_ssum3c RS iffD2) 1),
+	(rtac chain_UU_I_inverse 1),
+	(rtac allI 1),
+	(res_inst_tac [("p","Y(i)")] IssumE 1),
+	(asm_simp_tac Ssum_ss 1),
+	(asm_simp_tac Ssum_ss 2),
+	(etac notE 1),
+	(rtac (less_ssum3c RS iffD1) 1),
+	(res_inst_tac [("t","Isinl(x)")] subst 1),
+	(atac 1),
+	(etac (ub_rangeE RS spec) 1)
+	]);
+
+
+val lub_ssum1b = prove_goal Ssum2.thy 
+"[|is_chain(Y);(!i.? x.Y(i)=Isinr(x))|] ==>\
+\ range(Y) <<|\
+\ Isinr(lub(range(%i.(Iwhen (LAM y.UU) (LAM x.x))(Y(i)))))"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac is_lubI 1),
+	(rtac conjI 1),
+	(rtac ub_rangeI 1),
+	(rtac allI 1),
+	(etac allE 1),
+	(etac exE 1),
+	(res_inst_tac [("t","Y(i)")] (ssum_lemma6 RS subst) 1),
+	(atac 1),
+	(rtac (monofun_Isinr RS monofunE RS spec RS spec RS mp) 1),
+	(rtac is_ub_thelub 1),
+	(etac (monofun_Iwhen3 RS ch2ch_monofun) 1),
+	(strip_tac 1),
+	(res_inst_tac [("p","u")] IssumE2 1),
+	(hyp_subst_tac 1),
+	(rtac (less_ssum3d RS iffD2) 1),
+	(rtac chain_UU_I_inverse 1),
+	(rtac allI 1),
+	(res_inst_tac [("p","Y(i)")] IssumE 1),
+	(asm_simp_tac Ssum_ss 1),
+	(asm_simp_tac Ssum_ss 1),
+	(etac notE 1),
+	(rtac (less_ssum3d RS iffD1) 1),
+	(res_inst_tac [("t","Isinr(y)")] subst 1),
+	(atac 1),
+	(etac (ub_rangeE RS spec) 1),
+	(res_inst_tac [("t","u")] (ssum_lemma6 RS subst) 1),
+	(atac 1),
+	(rtac (monofun_Isinr RS monofunE RS spec RS spec RS mp) 1),
+	(rtac is_lub_thelub 1),
+	(etac (monofun_Iwhen3 RS ch2ch_monofun) 1),
+	(etac (monofun_Iwhen3 RS ub2ub_monofun) 1)
+	]);
+
+
+val thelub_ssum1a = lub_ssum1a RS thelubI;
+(* [| is_chain(?Y1); ! i. ? x. ?Y1(i) = Isinl(x) |] ==>                     *)
+(* lub(range(?Y1)) = Isinl(lub(range(%i. Iwhen(LAM x. x,LAM y. UU,?Y1(i)))))*)
+
+val thelub_ssum1b = lub_ssum1b RS thelubI;
+(* [| is_chain(?Y1); ! i. ? x. ?Y1(i) = Isinr(x) |] ==>                     *)
+(* lub(range(?Y1)) = Isinr(lub(range(%i. Iwhen(LAM y. UU,LAM x. x,?Y1(i)))))*)
+
+val cpo_ssum = prove_goal Ssum2.thy 
+	"is_chain(Y::nat=>'a ++'b) ==> ? x.range(Y) <<|x"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac (ssum_lemma4 RS disjE) 1),
+	(atac 1),
+	(rtac exI 1),
+	(etac lub_ssum1a 1),
+	(atac 1),
+	(rtac exI 1),
+	(etac lub_ssum1b 1),
+	(atac 1)
+	]);
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Ssum2.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,23 @@
+(*  Title: 	HOLCF/ssum2.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Class Instance ++::(pcpo,pcpo)po
+*)
+
+Ssum2 = Ssum1 + 
+
+arities "++" :: (pcpo,pcpo)po
+(* Witness for the above arity axiom is ssum1.ML *)
+
+rules
+
+(* instance of << for type ['a ++ 'b]  *)
+
+inst_ssum_po	"(op <<)::['a ++ 'b,'a ++ 'b]=>bool = less_ssum"
+
+end
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Ssum3.ML	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,728 @@
+(*  Title: 	HOLCF/ssum3.ML
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Lemmas for ssum3.thy
+*)
+
+open Ssum3;
+
+(* ------------------------------------------------------------------------ *)
+(* continuity for Isinl and Isinr                                           *)
+(* ------------------------------------------------------------------------ *)
+
+
+val contlub_Isinl = prove_goal Ssum3.thy "contlub(Isinl)"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac trans 1),
+	(rtac (thelub_ssum1a RS sym) 2),
+	(rtac allI 3),
+	(rtac exI 3),
+	(rtac refl 3),
+	(etac (monofun_Isinl RS ch2ch_monofun) 2),
+	(res_inst_tac [("Q","lub(range(Y))=UU")] classical2 1),
+	(res_inst_tac [("s","UU"),("t","lub(range(Y))")] ssubst 1),
+	(atac 1),
+	(res_inst_tac [("f","Isinl")] arg_cong  1),
+	(rtac (chain_UU_I_inverse RS sym) 1),
+	(rtac allI 1),
+	(res_inst_tac [("s","UU"),("t","Y(i)")] ssubst 1),
+	(etac (chain_UU_I RS spec ) 1),
+	(atac 1),
+	(rtac Iwhen1 1),
+	(res_inst_tac [("f","Isinl")] arg_cong  1),
+	(rtac lub_equal 1),
+	(atac 1),
+	(rtac (monofun_Iwhen3 RS ch2ch_monofun) 1),
+	(etac (monofun_Isinl RS ch2ch_monofun) 1),
+	(rtac allI 1),
+	(res_inst_tac [("Q","Y(k)=UU")] classical2 1),
+	(asm_simp_tac Ssum_ss 1),
+	(asm_simp_tac Ssum_ss 1)
+	]);
+
+val contlub_Isinr = prove_goal Ssum3.thy "contlub(Isinr)"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac trans 1),
+	(rtac (thelub_ssum1b RS sym) 2),
+	(rtac allI 3),
+	(rtac exI 3),
+	(rtac refl 3),
+	(etac (monofun_Isinr RS ch2ch_monofun) 2),
+	(res_inst_tac [("Q","lub(range(Y))=UU")] classical2 1),
+	(res_inst_tac [("s","UU"),("t","lub(range(Y))")] ssubst 1),
+	(atac 1),
+	((rtac arg_cong 1) THEN (rtac (chain_UU_I_inverse RS sym) 1)),
+	(rtac allI 1),
+	(res_inst_tac [("s","UU"),("t","Y(i)")] ssubst 1),
+	(etac (chain_UU_I RS spec ) 1),
+	(atac 1),
+	(rtac (strict_IsinlIsinr RS subst) 1),
+	(rtac Iwhen1 1),
+	((rtac arg_cong 1) THEN (rtac lub_equal 1)),
+	(atac 1),
+	(rtac (monofun_Iwhen3 RS ch2ch_monofun) 1),
+	(etac (monofun_Isinr RS ch2ch_monofun) 1),
+	(rtac allI 1),
+	(res_inst_tac [("Q","Y(k)=UU")] classical2 1),
+	(asm_simp_tac Ssum_ss 1),
+	(asm_simp_tac Ssum_ss 1)
+	]);
+
+val contX_Isinl = prove_goal Ssum3.thy "contX(Isinl)"
+ (fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_Isinl 1),
+	(rtac contlub_Isinl 1)
+	]);
+
+val contX_Isinr = prove_goal Ssum3.thy "contX(Isinr)"
+ (fn prems =>
+	[
+	(rtac monocontlub2contX 1),
+	(rtac monofun_Isinr 1),
+	(rtac contlub_Isinr 1)
+	]);
+
+
+(* ------------------------------------------------------------------------ *)
+(* continuity for Iwhen in the firts two arguments                          *)
+(* ------------------------------------------------------------------------ *)
+
+val contlub_Iwhen1 = prove_goal Ssum3.thy "contlub(Iwhen)"
+ (fn prems =>
+	[
+	(rtac contlubI 1),
+	(strip_tac 1),
+	(rtac trans 1),
+	(rtac (thelub_fun RS sym) 2),
+	(etac (monofun_Iwhen1 RS ch2ch_monofun) 2),
+	(rtac (expand_fun_eq RS iffD2) 1),
+	(strip_tac 1),
+	(rtac trans 1),
+	(rtac (thelub_fun RS sym) 2),
+	(rtac ch2ch_fun 2),
+	(etac (monofun_Iwhen1 RS ch2ch_monofun) 2),
+	(rtac (expand_fun_eq RS iffD2) 1),
+	(strip_tac 1),
+	(res_inst_tac [("p","xa")] IssumE 1),
+	(asm_simp_tac Ssum_ss 1),
+	(rtac (lub_const RS thelubI RS sym) 1),
+	(asm_simp_tac Ssum_ss 1),
+	(etac contlub_cfun_fun 1),
+	(asm_simp_tac Ssum_ss 1),
+	(rtac (lub_const