src/HOLCF/Cont.ML

-(*  Title: 	HOLCF/cont.ML
+(*  Title:      HOLCF/cont.ML
     ID:         $Id$
-    Author: 	Franz Regensburger
+    Author:     Franz Regensburger
     Copyright   1993 Technische Universitaet Muenchen
 
 Lemmas for cont.thy 
 *)
 

 (* ------------------------------------------------------------------------ *)
 (* access to definition                                                     *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goalw "contlubI" 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)
-	]);
+        "! 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)
+        ]);
 
 qed_goalw "contlubE" Cont.thy [contlub]
-	" contlub(f)==>\
+        " 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)
-	]);
+        [
+        (cut_facts_tac prems 1),
+        (atac 1)
+        ]);
 
 
 qed_goalw "contI" Cont.thy [cont]
  "! Y. is_chain(Y) --> range(% i.f(Y(i))) <<| f(lub(range(Y))) ==> cont(f)"
 (fn prems =>
-	[
-	(cut_facts_tac prems 1),
-	(atac 1)
-	]);
+        [
+        (cut_facts_tac prems 1),
+        (atac 1)
+        ]);
 
 qed_goalw "contE" Cont.thy [cont]
  "cont(f) ==> ! Y. is_chain(Y) --> range(% i.f(Y(i))) <<| f(lub(range(Y)))"
 (fn prems =>
-	[
-	(cut_facts_tac prems 1),
-	(atac 1)
-	]);
+        [
+        (cut_facts_tac prems 1),
+        (atac 1)
+        ]);
 
 
 qed_goalw "monofunI" Cont.thy [monofun]
-	"! x y. x << y --> f(x) << f(y) ==> monofun(f)"
-(fn prems =>
-	[
-	(cut_facts_tac prems 1),
-	(atac 1)
-	]);
+        "! x y. x << y --> f(x) << f(y) ==> monofun(f)"
+(fn prems =>
+        [
+        (cut_facts_tac prems 1),
+        (atac 1)
+        ]);
 
 qed_goalw "monofunE" Cont.thy [monofun]
-	"monofun(f) ==> ! x y. x << y --> f(x) << f(y)"
-(fn prems =>
-	[
-	(cut_facts_tac prems 1),
-	(atac 1)
-	]);
+        "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)  <==> cont(f)                      *)
 (* ------------------------------------------------------------------------ *)

 (* ------------------------------------------------------------------------ *)
 (* monotone functions map chains to chains                                  *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goal "ch2ch_monofun" 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)
-	]);
+        "[| 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                       *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goal "ub2ub_monofun" 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)
-	]);
+        [
+        (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)  ==> cont(f)                     *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goalw "monocontlub2cont" Cont.thy [cont]
-	"[|monofun(f);contlub(f)|] ==> cont(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)
-	]);
+        "[|monofun(f);contlub(f)|] ==> cont(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                                        *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goal "binchain_cont" Cont.thy
 "[| cont(f); x << y |]  ==> range(%i. f(if i = 0 then x else y)) <<| f(y)"
 (fn prems => 
-	[
-	(cut_facts_tac prems 1),
-	(rtac subst 1), 
-	(etac (contE RS spec RS mp) 2),
-	(etac bin_chain 2),
-	(res_inst_tac [("y","y")] arg_cong 1),
-	(etac (lub_bin_chain RS thelubI) 1)
-	]);
+        [
+        (cut_facts_tac prems 1),
+        (rtac subst 1), 
+        (etac (contE 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: cont(f) ==> monofun(f) & contlub(f)                      *)
 (* part1:         cont(f) ==> monofun(f                                    *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goalw "cont2mono" Cont.thy [monofun]
-	"cont(f) ==> monofun(f)"
-(fn prems =>
-	[
-	(cut_facts_tac prems 1),
-	(strip_tac 1),
-	(res_inst_tac [("s","if 0 = 0 then x else y")] subst 1),
-	(rtac (binchain_cont RS is_ub_lub) 2),
-	(atac 2),
-	(atac 2),
-	(Simp_tac 1)
-	]);
+        "cont(f) ==> monofun(f)"
+(fn prems =>
+        [
+        (cut_facts_tac prems 1),
+        (strip_tac 1),
+        (res_inst_tac [("s","if 0 = 0 then x else y")] subst 1),
+        (rtac (binchain_cont RS is_ub_lub) 2),
+        (atac 2),
+        (atac 2),
+        (Simp_tac 1)
+        ]);
 
 (* ------------------------------------------------------------------------ *)
 (* right to left: cont(f) ==> monofun(f) & contlub(f)                      *)
 (* part2:         cont(f) ==>              contlub(f)                      *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goalw "cont2contlub" Cont.thy [contlub]
-	"cont(f) ==> contlub(f)"
-(fn prems =>
-	[
-	(cut_facts_tac prems 1),
-	(strip_tac 1),
-	(rtac (thelubI RS sym) 1),
-	(etac (contE RS spec RS mp) 1),
-	(atac 1)
-	]);
+        "cont(f) ==> contlub(f)"
+(fn prems =>
+        [
+        (cut_facts_tac prems 1),
+        (strip_tac 1),
+        (rtac (thelubI RS sym) 1),
+        (etac (contE RS spec RS mp) 1),
+        (atac 1)
+        ]);
 
 (* ------------------------------------------------------------------------ *)
 (* The following results are about a curried function that is monotone      *)
 (* in both arguments                                                        *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goal "ch2ch_MF2L" Cont.thy 
 "[|monofun(MF2); 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)
-	]);
+        [
+        (cut_facts_tac prems 1),
+        (etac (ch2ch_monofun RS ch2ch_fun) 1),
+        (atac 1)
+        ]);
 
 
 qed_goal "ch2ch_MF2R" Cont.thy 
 "[|monofun(MF2(f)); is_chain(Y)|] ==> is_chain(%i. MF2 f (Y i))"
 (fn prems =>
-	[
-	(cut_facts_tac prems 1),
-	(etac ch2ch_monofun 1),
-	(atac 1)
-	]);
+        [
+        (cut_facts_tac prems 1),
+        (etac ch2ch_monofun 1),
+        (atac 1)
+        ]);
 
 qed_goal "ch2ch_MF2LR" Cont.thy 
 "[|monofun(MF2); !f.monofun(MF2(f)); 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)
-	]);
+        [
+        (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)
+        ]);
 
 
 qed_goal "ch2ch_lubMF2R" 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)
-	]);
+\       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)
+        ]);
 
 
 qed_goal "ch2ch_lubMF2L" 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)
-	]);
+\       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)
+        ]);
 
 
 qed_goal "lub_MF2_mono" 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)
-	]);
+\       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)
+        ]);
 
 qed_goal "ex_lubMF2" 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 (ub_rangeI RSN (2,is_lub_thelub)) 1),
-	(etac ch2ch_lubMF2R 1),
-	(REPEAT (atac 1)),
-	(strip_tac 1),
-	(rtac lub_mono 1),
-	((rtac ch2ch_MF2R 1) THEN (etac spec 1)),
-	(atac 1),
-	(etac ch2ch_lubMF2L 1),
-	(REPEAT (atac 1)),
-	(strip_tac 1),
-	(rtac is_ub_thelub 1),
-	(etac ch2ch_MF2L 1),
-	(atac 1),
-	(rtac (ub_rangeI RSN (2,is_lub_thelub)) 1),
-	(etac ch2ch_lubMF2L 1),
-	(REPEAT (atac 1)),
-	(strip_tac 1),
-	(rtac lub_mono 1),
-	(etac ch2ch_MF2L 1),
-	(atac 1),
-	(etac ch2ch_lubMF2R 1),
-	(REPEAT (atac 1)),
-	(strip_tac 1),
-	(rtac is_ub_thelub 1),
-	((rtac ch2ch_MF2R 1) THEN (etac spec 1)),
-	(atac 1)
-	]);
+\       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 (ub_rangeI RSN (2,is_lub_thelub)) 1),
+        (etac ch2ch_lubMF2R 1),
+        (REPEAT (atac 1)),
+        (strip_tac 1),
+        (rtac lub_mono 1),
+        ((rtac ch2ch_MF2R 1) THEN (etac spec 1)),
+        (atac 1),
+        (etac ch2ch_lubMF2L 1),
+        (REPEAT (atac 1)),
+        (strip_tac 1),
+        (rtac is_ub_thelub 1),
+        (etac ch2ch_MF2L 1),
+        (atac 1),
+        (rtac (ub_rangeI RSN (2,is_lub_thelub)) 1),
+        (etac ch2ch_lubMF2L 1),
+        (REPEAT (atac 1)),
+        (strip_tac 1),
+        (rtac lub_mono 1),
+        (etac ch2ch_MF2L 1),
+        (atac 1),
+        (etac ch2ch_lubMF2R 1),
+        (REPEAT (atac 1)),
+        (strip_tac 1),
+        (rtac is_ub_thelub 1),
+        ((rtac ch2ch_MF2R 1) THEN (etac spec 1)),
+        (atac 1)
+        ]);
 
 
 qed_goal "diag_lubMF2_1" Cont.thy 
 "[|monofun(MF2::('a::po=>'b::po=>'c::pcpo));\
 \  !f.monofun(MF2(f)::('b::po=>'c::pcpo));\
 \  is_chain(FY);is_chain(TY)|] ==>\
 \ lub(range(%i. lub(range(%j. MF2(FY(j))(TY(i)))))) =\
 \ lub(range(%i. MF2(FY(i))(TY(i))))"
  (fn prems =>
-	[
-	(cut_facts_tac prems 1),
-	(rtac antisym_less 1),
-	(rtac (ub_rangeI RSN (2,is_lub_thelub)) 1),
-	(etac ch2ch_lubMF2L 1),
-	(REPEAT (atac 1)),
-	(strip_tac 1 ),
-	(rtac lub_mono3 1),
-	(etac ch2ch_MF2L 1),
-	(REPEAT (atac 1)),
-	(etac ch2ch_MF2LR 1),
-	(REPEAT (atac 1)),
-	(rtac allI 1),
-	(res_inst_tac [("m","i"),("n","ia")] nat_less_cases 1),
-	(res_inst_tac [("x","ia")] exI 1),
-	(rtac (chain_mono RS mp) 1),
-	(etac allE 1),
-	(etac ch2ch_MF2R 1),
-	(REPEAT (atac 1)),
-	(hyp_subst_tac 1),
-	(res_inst_tac [("x","ia")] exI 1),
-	(rtac refl_less 1),
-	(res_inst_tac [("x","i")] exI 1),
-	(rtac (chain_mono RS mp) 1),
-	(etac ch2ch_MF2L 1),
-	(REPEAT (atac 1)),
-	(rtac lub_mono 1),
-	(etac ch2ch_MF2LR 1),
-	(REPEAT(atac 1)),
-	(etac ch2ch_lubMF2L 1),
-	(REPEAT (atac 1)),
-	(strip_tac 1 ),
-	(rtac is_ub_thelub 1),
-	(etac ch2ch_MF2L 1),
-	(atac 1)
-	]);
+        [
+        (cut_facts_tac prems 1),
+        (rtac antisym_less 1),
+        (rtac (ub_rangeI RSN (2,is_lub_thelub)) 1),
+        (etac ch2ch_lubMF2L 1),
+        (REPEAT (atac 1)),
+        (strip_tac 1 ),
+        (rtac lub_mono3 1),
+        (etac ch2ch_MF2L 1),
+        (REPEAT (atac 1)),
+        (etac ch2ch_MF2LR 1),
+        (REPEAT (atac 1)),
+        (rtac allI 1),
+        (res_inst_tac [("m","i"),("n","ia")] nat_less_cases 1),
+        (res_inst_tac [("x","ia")] exI 1),
+        (rtac (chain_mono RS mp) 1),
+        (etac allE 1),
+        (etac ch2ch_MF2R 1),
+        (REPEAT (atac 1)),
+        (hyp_subst_tac 1),
+        (res_inst_tac [("x","ia")] exI 1),
+        (rtac refl_less 1),
+        (res_inst_tac [("x","i")] exI 1),
+        (rtac (chain_mono RS mp) 1),
+        (etac ch2ch_MF2L 1),
+        (REPEAT (atac 1)),
+        (rtac lub_mono 1),
+        (etac ch2ch_MF2LR 1),
+        (REPEAT(atac 1)),
+        (etac ch2ch_lubMF2L 1),
+        (REPEAT (atac 1)),
+        (strip_tac 1 ),
+        (rtac is_ub_thelub 1),
+        (etac ch2ch_MF2L 1),
+        (atac 1)
+        ]);
 
 qed_goal "diag_lubMF2_2" Cont.thy 
 "[|monofun(MF2::('a::po=>'b::po=>'c::pcpo));\
 \  !f.monofun(MF2(f)::('b::po=>'c::pcpo));\
 \  is_chain(FY);is_chain(TY)|] ==>\
 \ lub(range(%j. lub(range(%i. MF2(FY(j))(TY(i)))))) =\
 \ lub(range(%i. MF2(FY(i))(TY(i))))"
  (fn prems =>
-	[
-	(cut_facts_tac prems 1),
-	(rtac trans 1),
-	(rtac ex_lubMF2 1),
-	(REPEAT (atac 1)),
-	(etac diag_lubMF2_1 1),
-	(REPEAT (atac 1))
-	]);
+        [
+        (cut_facts_tac prems 1),
+        (rtac trans 1),
+        (rtac ex_lubMF2 1),
+        (REPEAT (atac 1)),
+        (etac diag_lubMF2_1 1),
+        (REPEAT (atac 1))
+        ]);
 
 
 
 
 (* ------------------------------------------------------------------------ *)

 
 qed_goal "contlub_CF2" Cont.thy 
 "[|cont(CF2);!f.cont(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 cont2contlub RS contlubE RS spec RS mp RS ssubst) 1),
-	(atac 1),
-	(rtac (thelub_fun RS ssubst) 1),
-	(rtac ((hd prems) RS cont2mono RS ch2ch_monofun) 1),
-	(atac 1),
-	(rtac trans 1),
-	(rtac (((hd (tl prems)) RS spec RS cont2contlub) RS contlubE RS                spec RS mp RS ext RS arg_cong RS arg_cong) 1),
-	(atac 1),
-	(rtac diag_lubMF2_2 1),
-	(etac cont2mono 1),
-	(rtac allI 1),
-	(etac allE 1),
-	(etac cont2mono 1),
-	(REPEAT (atac 1))
-	]);
+        [
+        (cut_facts_tac prems 1),
+        (rtac ((hd prems) RS cont2contlub RS contlubE RS spec RS mp RS ssubst) 1),
+        (atac 1),
+        (rtac (thelub_fun RS ssubst) 1),
+        (rtac ((hd prems) RS cont2mono RS ch2ch_monofun) 1),
+        (atac 1),
+        (rtac trans 1),
+        (rtac (((hd (tl prems)) RS spec RS cont2contlub) RS contlubE RS                spec RS mp RS ext RS arg_cong RS arg_cong) 1),
+        (atac 1),
+        (rtac diag_lubMF2_2 1),
+        (etac cont2mono 1),
+        (rtac allI 1),
+        (etac allE 1),
+        (etac cont2mono 1),
+        (REPEAT (atac 1))
+        ]);
 
 (* ------------------------------------------------------------------------ *)
 (* The following results are about application for functions in 'a=>'b      *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goal "monofun_fun_fun" Cont.thy 
-	"f1 << f2 ==> f1(x) << f2(x)"
-(fn prems =>
-	[
-	(cut_facts_tac prems 1),
-	(etac (less_fun RS iffD1 RS spec) 1)
-	]);
+        "f1 << f2 ==> f1(x) << f2(x)"
+(fn prems =>
+        [
+        (cut_facts_tac prems 1),
+        (etac (less_fun RS iffD1 RS spec) 1)
+        ]);
 
 qed_goal "monofun_fun_arg" 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)
-	]);
+        "[|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)
+        ]);
 
 qed_goal "monofun_fun" 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)
-	]);
+        [
+        (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                                                               *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goal "mono2mono_MF1L" 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)
-	]);
+        "[|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)
+        ]);
 
 qed_goal "cont2cont_CF1L" Cont.thy 
-	"[|cont(c1)|] ==> cont(%x. c1 x y)"
-(fn prems =>
-	[
-	(cut_facts_tac prems 1),
-	(rtac monocontlub2cont 1),
-	(etac (cont2mono RS mono2mono_MF1L) 1),
-	(rtac contlubI 1),
-	(strip_tac 1),
-	(rtac ((hd prems) RS cont2contlub RS 
-		contlubE RS spec RS mp RS ssubst) 1),
-	(atac 1),
-	(rtac (thelub_fun RS ssubst) 1),
-	(rtac ch2ch_monofun 1),
-	(etac cont2mono 1),
-	(atac 1),
-	(rtac refl 1)
-	]);
+        "[|cont(c1)|] ==> cont(%x. c1 x y)"
+(fn prems =>
+        [
+        (cut_facts_tac prems 1),
+        (rtac monocontlub2cont 1),
+        (etac (cont2mono RS mono2mono_MF1L) 1),
+        (rtac contlubI 1),
+        (strip_tac 1),
+        (rtac ((hd prems) RS cont2contlub RS 
+                contlubE RS spec RS mp RS ssubst) 1),
+        (atac 1),
+        (rtac (thelub_fun RS ssubst) 1),
+        (rtac ch2ch_monofun 1),
+        (etac cont2mono 1),
+        (atac 1),
+        (rtac refl 1)
+        ]);
 
 (*********  Note "(%x.%y.c1 x y) = c1" ***********)
 
 qed_goal "mono2mono_MF1L_rev" 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)
-	]);
+        "!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)
+        ]);
 
 qed_goal "cont2cont_CF1L_rev" Cont.thy
-	"!y.cont(%x.c1 x y) ==> cont(c1)"
-(fn prems =>
-	[
-	(cut_facts_tac prems 1),
-	(rtac monocontlub2cont 1),
-	(rtac (cont2mono 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 (cont2mono RS allI RS mono2mono_MF1L_rev RS ch2ch_monofun) 1),
-	(etac spec 1),
-	(atac 1),
-	(rtac 
-	((hd prems) RS spec RS cont2contlub RS contlubE RS spec RS mp) 1),
-	(atac 1)
-	]);
+        "!y.cont(%x.c1 x y) ==> cont(c1)"
+(fn prems =>
+        [
+        (cut_facts_tac prems 1),
+        (rtac monocontlub2cont 1),
+        (rtac (cont2mono 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 (cont2mono RS allI RS mono2mono_MF1L_rev RS ch2ch_monofun) 1),
+        (etac spec 1),
+        (atac 1),
+        (rtac 
+        ((hd prems) RS spec RS cont2contlub RS contlubE RS spec RS mp) 1),
+        (atac 1)
+        ]);
 
 
 (* ------------------------------------------------------------------------ *)
 (* What D.A.Schmidt calls continuity of abstraction                         *)
 (* never used here                                                          *)

 
 qed_goal "contlub_abstraction" Cont.thy
 "[|is_chain(Y::nat=>'a);!y.cont(%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 (cont2contlub RS contlubE RS spec RS mp) 2),
-	(atac 3),
-	(etac cont2cont_CF1L_rev 2),
-	(rtac ext 1), 
-	(rtac (cont2contlub RS contlubE RS spec RS mp RS sym) 1),
-	(etac spec 1),
-	(atac 1)
-	]);
+        [
+        (cut_facts_tac prems 1),
+        (rtac trans 1),
+        (rtac (cont2contlub RS contlubE RS spec RS mp) 2),
+        (atac 3),
+        (etac cont2cont_CF1L_rev 2),
+        (rtac ext 1), 
+        (rtac (cont2contlub RS contlubE RS spec RS mp RS sym) 1),
+        (etac spec 1),
+        (atac 1)
+        ]);
 
 
 qed_goal "mono2mono_app" 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)
-	]);
+\        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)
+        ]);
 
 
 qed_goal "cont2contlub_app" Cont.thy 
 "[|cont(ft);!x.cont(ft(x));cont(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),
-	(etac cont2contlub 1),
-	(atac 1),
-	(rtac contlub_CF2 1),
-	(REPEAT (atac 1)),
-	(etac (cont2mono RS ch2ch_monofun) 1),
-	(atac 1)
-	]);
+        [
+        (cut_facts_tac prems 1),
+        (rtac contlubI 1),
+        (strip_tac 1),
+        (res_inst_tac [("f3","tt")] (contlubE RS spec RS mp RS ssubst) 1),
+        (etac cont2contlub 1),
+        (atac 1),
+        (rtac contlub_CF2 1),
+        (REPEAT (atac 1)),
+        (etac (cont2mono RS ch2ch_monofun) 1),
+        (atac 1)
+        ]);
 
 
 qed_goal "cont2cont_app" Cont.thy 
 "[|cont(ft);!x.cont(ft(x));cont(tt)|] ==>\
-\	 cont(%x.(ft(x))(tt(x)))"
- (fn prems =>
-	[
-	(rtac monocontlub2cont 1),
-	(rtac mono2mono_app 1),
-	(rtac cont2mono 1),
-	(resolve_tac prems 1),
-	(strip_tac 1),
-	(rtac cont2mono 1),
-	(cut_facts_tac prems 1),
-	(etac spec 1),
-	(rtac cont2mono 1),
-	(resolve_tac prems 1),
-	(rtac cont2contlub_app 1),
-	(resolve_tac prems 1),
-	(resolve_tac prems 1),
-	(resolve_tac prems 1)
-	]);
+\        cont(%x.(ft(x))(tt(x)))"
+ (fn prems =>
+        [
+        (rtac monocontlub2cont 1),
+        (rtac mono2mono_app 1),
+        (rtac cont2mono 1),
+        (resolve_tac prems 1),
+        (strip_tac 1),
+        (rtac cont2mono 1),
+        (cut_facts_tac prems 1),
+        (etac spec 1),
+        (rtac cont2mono 1),
+        (resolve_tac prems 1),
+        (rtac cont2contlub_app 1),
+        (resolve_tac prems 1),
+        (resolve_tac prems 1),
+        (resolve_tac prems 1)
+        ]);
 
 
 val cont2cont_app2 = (allI RSN (2,cont2cont_app));
 (*  [| cont ?ft; !!x. cont (?ft x); cont ?tt |] ==> *)
 (*        cont (%x. ?ft x (?tt x))                    *)

 (* The identity function is continuous                                      *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goal "cont_id" Cont.thy "cont(% x.x)"
  (fn prems =>
-	[
-	(rtac contI 1),
-	(strip_tac 1),
-	(etac thelubE 1),
-	(rtac refl 1)
-	]);
+        [
+        (rtac contI 1),
+        (strip_tac 1),
+        (etac thelubE 1),
+        (rtac refl 1)
+        ]);
 
 
 
 (* ------------------------------------------------------------------------ *)
 (* constant functions are continuous                                        *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goalw "cont_const" Cont.thy [cont] "cont(%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)
-	]);
+        [
+        (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)
+        ]);
 
 
 qed_goal "cont2cont_app3" Cont.thy 
  "[|cont(f);cont(t) |] ==> cont(%x. f(t(x)))"
  (fn prems =>
-	[
-	(cut_facts_tac prems 1),
-	(rtac cont2cont_app2 1),
-	(rtac cont_const 1),
-	(atac 1),
-	(atac 1)
-	]);
-
+        [
+        (cut_facts_tac prems 1),
+        (rtac cont2cont_app2 1),
+        (rtac cont_const 1),
+        (atac 1),
+        (atac 1)
+        ]);
+