src/HOLCF/Pcpo.ML

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

 (* ------------------------------------------------------------------------ *)
 (* in pcpo's everthing equal to THE lub has lub properties for every chain  *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goal "thelubE"  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)
-	]);
+        "[| 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                                                    *)
 (* ------------------------------------------------------------------------ *)
 

 (* ------------------------------------------------------------------------ *)
 (* the << relation between two chains is preserved by their lubs            *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goal "lub_mono" Pcpo.thy 
-	"[|is_chain(C1::(nat=>'a::pcpo));is_chain(C2); ! k. C1(k) << C2(k)|]\
+        "[|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)
-	]);
+        [
+        (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            *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goal "lub_equal" 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)
-	]);
+\       ==> 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                          *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goal "lub_mono2" 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 1),
-	(rtac is_ub_thelub 1),
-	(resolve_tac prems 1)
-	]);
+        [
+        (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 1),
+        (rtac is_ub_thelub 1),
+        (resolve_tac prems 1)
+        ]);
 
 qed_goal "lub_equal2" 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)
-	]);
+        [
+        (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)
+        ]);
 
 qed_goal "lub_mono3" 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)
-	]);
+        [
+        (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                                                  *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goal "eq_UU_iff" 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)
-	]);
+        [
+        (rtac iffI 1),
+        (hyp_subst_tac 1),
+        (rtac refl_less 1),
+        (rtac antisym_less 1),
+        (atac 1),
+        (rtac minimal 1)
+        ]);
 
 qed_goal "UU_I" Pcpo.thy "x << UU ==> x = UU"
  (fn prems =>
-	[
-	(rtac (eq_UU_iff RS ssubst) 1),
-	(resolve_tac prems 1)
-	]);
+        [
+        (rtac (eq_UU_iff RS ssubst) 1),
+        (resolve_tac prems 1)
+        ]);
 
 qed_goal "not_less2not_eq" 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)
-	]);
+        [
+        (cut_facts_tac prems 1),
+        (rtac classical3 1),
+        (atac 1),
+        (hyp_subst_tac 1),
+        (rtac refl_less 1)
+        ]);
 
 qed_goal "chain_UU_I" 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),
-	(etac subst 1),
-	(etac is_ub_thelub 1)
-	]);
+        "[|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),
+        (etac subst 1),
+        (etac is_ub_thelub 1)
+        ]);
 
 
 qed_goal "chain_UU_I_inverse" 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 exI 1),
-	(etac spec 1),
-	(rtac allI 1),
-	(rtac (antisym_less_inverse RS conjunct1) 1),
-	(etac spec 1)
-	]);
+        "!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 exI 1),
+        (etac spec 1),
+        (rtac allI 1),
+        (rtac (antisym_less_inverse RS conjunct1) 1),
+        (etac spec 1)
+        ]);
 
 qed_goal "chain_UU_I_inverse2" 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)
-	]);
+        "~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)
+        ]);
 
 
 qed_goal "notUU_I" 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)
-	]);
+        [
+        (cut_facts_tac prems 1),
+        (etac contrapos 1),
+        (rtac UU_I 1),
+        (hyp_subst_tac 1),
+        (atac 1)
+        ]);
 
 
 qed_goal "chain_mono2" 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)
-	]);
+        [
+        (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                                                       *)
 (* ------------------------------------------------------------------------ *)
 
 qed_goal "unique_void2" 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)
-	]);
-
-
+        [
+        (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)
+        ]);
+
+