diff -r 3a8d722fd3ff -r 16c4ea954511 ex/LList.ML
--- a/ex/LList.ML	Fri Nov 11 10:35:03 1994 +0100
+++ b/ex/LList.ML	Mon Nov 21 17:50:34 1994 +0100
@@ -23,7 +23,7 @@
 goalw LList.thy llist.defs "!!A B. A<=B ==> llist(A) <= llist(B)";
 by (rtac gfp_mono 1);
 by (REPEAT (ares_tac basic_monos 1));
-val llist_mono = result();
+qed "llist_mono";
 
 
 goal LList.thy "llist(A) = {Numb(0)} <+> (A <*> llist(A))";
@@ -31,7 +31,7 @@
 by (fast_tac (univ_cs addSIs (equalityI :: map rew llist.intrs)
                       addEs [rew llist.elim]) 1)
 end;
-val llist_unfold = result();
+qed "llist_unfold";
 
 
 (*** Type checking by coinduction, using list_Fun 
@@ -43,44 +43,44 @@
 be llist.coinduct 1;
 be (subsetD RS CollectD) 1;
 ba 1;
-val llist_coinduct = result();
+qed "llist_coinduct";
 
 goalw LList.thy [list_Fun_def, NIL_def] "NIL: list_Fun(A,X)";
 by (fast_tac set_cs 1);
-val list_Fun_NIL_I = result();
+qed "list_Fun_NIL_I";
 
 goalw LList.thy [list_Fun_def,CONS_def]
     "!!M N. [| M: A;  N: X |] ==> CONS(M,N) : list_Fun(A,X)";
 by (fast_tac set_cs 1);
-val list_Fun_CONS_I = result();
+qed "list_Fun_CONS_I";
 
 (*Utilise the "strong" part, i.e. gfp(f)*)
 goalw LList.thy (llist.defs @ [list_Fun_def])
     "!!M N. M: llist(A) ==> M : list_Fun(A, X Un llist(A))";
 by (etac (llist.mono RS gfp_fun_UnI2) 1);
-val list_Fun_llist_I = result();
+qed "list_Fun_llist_I";
 
 (*** LList_corec satisfies the desired recurion equation ***)
 
 (*A continuity result?*)
 goalw LList.thy [CONS_def] "CONS(M, UN x.f(x)) = (UN x. CONS(M, f(x)))";
 by (simp_tac (univ_ss addsimps [In1_UN1, Scons_UN1_y]) 1);
-val CONS_UN1 = result();
+qed "CONS_UN1";
 
 (*UNUSED; obsolete?
 goal Prod.thy "split(p, %x y.UN z.f(x,y,z)) = (UN z. split(p, %x y.f(x,y,z)))";
 by (simp_tac (prod_ss setloop (split_tac [expand_split])) 1);
-val split_UN1 = result();
+qed "split_UN1";
 
 goal Sum.thy "sum_case(s,f,%y.UN z.g(y,z)) = (UN z.sum_case(s,f,%y. g(y,z)))";
 by (simp_tac (sum_ss setloop (split_tac [expand_sum_case])) 1);
-val sum_case2_UN1 = result();
+qed "sum_case2_UN1";
 *)
 
 val prems = goalw LList.thy [CONS_def]
     "[| M<=M';  N<=N' |] ==> CONS(M,N) <= CONS(M',N')";
 by (REPEAT (resolve_tac ([In1_mono,Scons_mono]@prems) 1));
-val CONS_mono = result();
+qed "CONS_mono";
 
 val corec_fun_simps = [LList_corec_fun_def RS def_nat_rec_0,
 		       LList_corec_fun_def RS def_nat_rec_Suc];
@@ -95,7 +95,7 @@
 by (res_inst_tac [("n","k")] natE 1);
 by (ALLGOALS (asm_simp_tac corec_fun_ss));
 by (REPEAT (resolve_tac [allI, impI, subset_refl RS CONS_mono, UN1_upper] 1));
-val LList_corec_subset1 = result();
+qed "LList_corec_subset1";
 
 goalw LList.thy [LList_corec_def]
     "sum_case(%u.NIL, split(%z w. CONS(z, LList_corec(w,f))), f(a)) <= \
@@ -104,7 +104,7 @@
 by (safe_tac set_cs);
 by (ALLGOALS (res_inst_tac [("x","Suc(?k)")] UN1_I THEN' 
 	      asm_simp_tac corec_fun_ss));
-val LList_corec_subset2 = result();
+qed "LList_corec_subset2";
 
 (*the recursion equation for LList_corec -- NOT SUITABLE FOR REWRITING!*)
 goal LList.thy
@@ -112,7 +112,7 @@
 \			     split(%z w. CONS(z, LList_corec(w,f))), f(a))";
 by (REPEAT (resolve_tac [equalityI, LList_corec_subset1, 
 			 LList_corec_subset2] 1));
-val LList_corec = result();
+qed "LList_corec";
 
 (*definitional version of same*)
 val [rew] = goal LList.thy
@@ -120,7 +120,7 @@
 \    h(a) = sum_case(%u.NIL, split(%z w. CONS(z, h(w))), f(a))";
 by (rewtac rew);
 by (rtac LList_corec 1);
-val def_LList_corec = result();
+qed "def_LList_corec";
 
 (*A typical use of co-induction to show membership in the gfp. 
   Bisimulation is  range(%x. LList_corec(x,f)) *)
@@ -131,7 +131,7 @@
 by (stac LList_corec 1);
 by (simp_tac (llist_ss addsimps [list_Fun_NIL_I, list_Fun_CONS_I, CollectI]
                        |> add_eqI) 1);
-val LList_corec_type = result();
+qed "LList_corec_type";
 
 (*Lemma for the proof of llist_corec*)
 goal LList.thy
@@ -143,7 +143,7 @@
 by (stac LList_corec 1);
 by (asm_simp_tac (llist_ss addsimps [list_Fun_NIL_I]) 1);
 by (fast_tac (set_cs addSIs [list_Fun_CONS_I]) 1);
-val LList_corec_type2 = result();
+qed "LList_corec_type2";
 
 
 (**** llist equality as a gfp; the bisimulation principle ****)
@@ -154,7 +154,7 @@
 by (fast_tac (univ_cs addSIs (equalityI :: map rew LListD.intrs)
                       addEs [rew LListD.elim]) 1)
 end;
-val LListD_unfold = result();
+qed "LListD_unfold";
 
 goal LList.thy "!M N. <M,N> : LListD(diag(A)) --> ntrunc(k,M) = ntrunc(k,N)";
 by (res_inst_tac [("n", "k")] less_induct 1);
@@ -167,7 +167,7 @@
 by (res_inst_tac [("n", "n'")] natE 1);
 by (asm_simp_tac (univ_ss addsimps [CONS_def, ntrunc_one_In1]) 1);
 by (asm_simp_tac (univ_ss addsimps [CONS_def, ntrunc_In1, ntrunc_Scons]) 1);
-val LListD_implies_ntrunc_equality = result();
+qed "LListD_implies_ntrunc_equality";
 
 (*The domain of the LListD relation*)
 goalw LList.thy (llist.defs @ [NIL_def, CONS_def])
@@ -177,7 +177,7 @@
 by (res_inst_tac [("P", "%x. fst``x <= ?B")] (LListD_unfold RS ssubst) 1);
 by (simp_tac fst_image_ss 1);
 by (fast_tac univ_cs 1);
-val fst_image_LListD = result();
+qed "fst_image_LListD";
 
 (*This inclusion justifies the use of coinduction to show M=N*)
 goal LList.thy "LListD(diag(A)) <= diag(llist(A))";
@@ -189,7 +189,7 @@
 	  ntrunc_equality) 1);
 by (assume_tac 1);
 by (etac (fst_imageI RS (fst_image_LListD RS subsetD)) 1);
-val LListD_subset_diag = result();
+qed "LListD_subset_diag";
 
 (** Coinduction, using LListD_Fun
     THE COINDUCTIVE DEFINITION PACKAGE COULD DO THIS!
@@ -200,25 +200,25 @@
 be LListD.coinduct 1;
 be (subsetD RS CollectD) 1;
 ba 1;
-val LListD_coinduct = result();
+qed "LListD_coinduct";
 
 goalw LList.thy [LListD_Fun_def,NIL_def] "<NIL,NIL> : LListD_Fun(r,s)";
 by (fast_tac set_cs 1);
-val LListD_Fun_NIL_I = result();
+qed "LListD_Fun_NIL_I";
 
 goalw LList.thy [LListD_Fun_def,CONS_def]
  "!!x. [| x:A;  <M,N>:s |] ==> <CONS(x,M), CONS(x,N)> : LListD_Fun(diag(A),s)";
 by (fast_tac univ_cs 1);
-val LListD_Fun_CONS_I = result();
+qed "LListD_Fun_CONS_I";
 
 (*Utilise the "strong" part, i.e. gfp(f)*)
 goalw LList.thy (LListD.defs @ [LListD_Fun_def])
     "!!M N. M: LListD(r) ==> M : LListD_Fun(r, X Un LListD(r))";
 by (etac (LListD.mono RS gfp_fun_UnI2) 1);
-val LListD_Fun_LListD_I = result();
+qed "LListD_Fun_LListD_I";
 
 
-(*This converse inclusion helps to strengthen llist_equalityI*)
+(*This converse inclusion helps to strengthen LList_equalityI*)
 goal LList.thy "diag(llist(A)) <= LListD(diag(A))";
 by (rtac subsetI 1);
 by (etac LListD_coinduct 1);
@@ -229,19 +229,19 @@
 by (ALLGOALS
     (asm_simp_tac (llist_ss addsimps [diagI, LListD_Fun_NIL_I,
 				      LListD_Fun_CONS_I])));
-val diag_subset_LListD = result();
+qed "diag_subset_LListD";
 
 goal LList.thy "LListD(diag(A)) = diag(llist(A))";
 by (REPEAT (resolve_tac [equalityI, LListD_subset_diag, 
 			 diag_subset_LListD] 1));
-val LListD_eq_diag = result();
+qed "LListD_eq_diag";
 
 goal LList.thy 
     "!!M N. M: llist(A) ==> <M,M> : LListD_Fun(diag(A), X Un diag(llist(A)))";
 by (rtac (LListD_eq_diag RS subst) 1);
 br LListD_Fun_LListD_I 1;
 by (asm_simp_tac (HOL_ss addsimps [LListD_eq_diag, diagI]) 1);
-val LListD_Fun_diag_I = result();
+qed "LListD_Fun_diag_I";
 
 
 (** To show two LLists are equal, exhibit a bisimulation! 
@@ -254,7 +254,7 @@
 by (etac LListD_coinduct 1);
 by (asm_simp_tac (HOL_ss addsimps [LListD_eq_diag]) 1);
 by (safe_tac prod_cs);
-val llist_equalityI = result();
+qed "LList_equalityI";
 
 
 (*** Finality of llist(A): Uniqueness of functions defined by corecursion ***)
@@ -267,7 +267,7 @@
 by (rtac ext 1);
 (*next step avoids an unknown (and flexflex pair) in simplification*)
 by (res_inst_tac [("A", "{u.True}"),
-		  ("r", "range(%u. <h1(u),h2(u)>)")] llist_equalityI 1);
+		  ("r", "range(%u. <h1(u),h2(u)>)")] LList_equalityI 1);
 by (rtac rangeI 1);
 by (safe_tac set_cs);
 by (stac prem1 1);
@@ -275,25 +275,25 @@
 by (simp_tac (llist_ss addsimps [LListD_Fun_NIL_I,
 				 CollectI RS LListD_Fun_CONS_I]
 	               |> add_eqI) 1);
-val LList_corec_unique = result();
+qed "LList_corec_unique";
 
 val [prem] = goal LList.thy
  "[| !!x. h(x) = sum_case(%u.NIL, split(%z w. CONS(z,h(w))), f(x)) |] \
 \ ==> h = (%x.LList_corec(x,f))";
 by (rtac (LList_corec RS (prem RS LList_corec_unique)) 1);
-val equals_LList_corec = result();
+qed "equals_LList_corec";
 
 
 (** Obsolete LList_corec_unique proof: complete induction, not coinduction **)
 
 goalw LList.thy [CONS_def] "ntrunc(Suc(0), CONS(M,N)) = {}";
 by (rtac ntrunc_one_In1 1);
-val ntrunc_one_CONS = result();
+qed "ntrunc_one_CONS";
 
 goalw LList.thy [CONS_def]
     "ntrunc(Suc(Suc(k)), CONS(M,N)) = CONS (ntrunc(k,M), ntrunc(k,N))";
 by (simp_tac (HOL_ss addsimps [ntrunc_Scons,ntrunc_In1]) 1);
-val ntrunc_CONS = result();
+qed "ntrunc_CONS";
 
 val [prem1,prem2] = goal LList.thy
  "[| !!x. h1(x) = sum_case(%u.NIL, split(%z w. CONS(z,h1(w))), f(x));  \
@@ -311,14 +311,14 @@
 by (res_inst_tac [("n", "xc")] natE 2);
 by (ALLGOALS(asm_simp_tac(nat_ss addsimps
             [ntrunc_0,ntrunc_one_CONS,ntrunc_CONS])));
-val LList_corec_unique = result();
+result();
 
 
 (*** Lconst -- defined directly using lfp, but equivalent to a LList_corec ***)
 
 goal LList.thy "mono(CONS(M))";
 by (REPEAT (ares_tac [monoI, subset_refl, CONS_mono] 1));
-val Lconst_fun_mono = result();
+qed "Lconst_fun_mono";
 
 (* Lconst(M) = CONS(M,Lconst(M)) *)
 val Lconst = standard (Lconst_fun_mono RS (Lconst_def RS def_lfp_Tarski));
@@ -330,20 +330,20 @@
 by (safe_tac set_cs);
 by (res_inst_tac [("P", "%u. u: ?A")] (Lconst RS ssubst) 1);
 by (REPEAT (ares_tac [list_Fun_CONS_I, singletonI, UnI1] 1));
-val Lconst_type = result();
+qed "Lconst_type";
 
 goal LList.thy "Lconst(M) = LList_corec(M, %x.Inr(<x,x>))";
 by (rtac (equals_LList_corec RS fun_cong) 1);
 by (simp_tac sum_ss 1);
 by (rtac Lconst 1);
-val Lconst_eq_LList_corec = result();
+qed "Lconst_eq_LList_corec";
 
 (*Thus we could have used gfp in the definition of Lconst*)
 goal LList.thy "gfp(%N. CONS(M, N)) = LList_corec(M, %x.Inr(<x,x>))";
 by (rtac (equals_LList_corec RS fun_cong) 1);
 by (simp_tac sum_ss 1);
 by (rtac (Lconst_fun_mono RS gfp_Tarski) 1);
-val gfp_Lconst_eq_LList_corec = result();
+qed "gfp_Lconst_eq_LList_corec";
 
 
 (*** Isomorphisms ***)
@@ -351,19 +351,19 @@
 goal LList.thy "inj(Rep_llist)";
 by (rtac inj_inverseI 1);
 by (rtac Rep_llist_inverse 1);
-val inj_Rep_llist = result();
+qed "inj_Rep_llist";
 
 goal LList.thy "inj_onto(Abs_llist,llist(range(Leaf)))";
 by (rtac inj_onto_inverseI 1);
 by (etac Abs_llist_inverse 1);
-val inj_onto_Abs_llist = result();
+qed "inj_onto_Abs_llist";
 
 (** Distinctness of constructors **)
 
 goalw LList.thy [LNil_def,LCons_def] "~ LCons(x,xs) = LNil";
 by (rtac (CONS_not_NIL RS (inj_onto_Abs_llist RS inj_onto_contraD)) 1);
 by (REPEAT (resolve_tac (llist.intrs @ [rangeI, Rep_llist]) 1));
-val LCons_not_LNil = result();
+qed "LCons_not_LNil";
 
 val LNil_not_LCons = standard (LCons_not_LNil RS not_sym);
 
@@ -375,19 +375,19 @@
 goalw LList.thy [LNil_def]
     "Rep_llist(LNil) = NIL";
 by (rtac (llist.NIL_I RS Abs_llist_inverse) 1);
-val Rep_llist_LNil = result();
+qed "Rep_llist_LNil";
 
 goalw LList.thy [LCons_def]
     "Rep_llist(LCons(x,l)) = CONS(Leaf(x),Rep_llist(l))";
 by (REPEAT (resolve_tac [llist.CONS_I RS Abs_llist_inverse,
 			 rangeI, Rep_llist] 1));
-val Rep_llist_LCons = result();
+qed "Rep_llist_LCons";
 
 (** Injectiveness of CONS and LCons **)
 
 goalw LList.thy [CONS_def] "(CONS(M,N)=CONS(M',N')) = (M=M' & N=N')";
 by (fast_tac (HOL_cs addSEs [Scons_inject, make_elim In1_inject]) 1);
-val CONS_CONS_eq = result();
+qed "CONS_CONS_eq";
 
 val CONS_inject = standard (CONS_CONS_eq RS iffD1 RS conjE);
 
@@ -400,14 +400,14 @@
 
 goalw LList.thy [LCons_def] "(LCons(x,xs)=LCons(y,ys)) = (x=y & xs=ys)";
 by (fast_tac llist_cs 1);
-val LCons_LCons_eq = result();
+qed "LCons_LCons_eq";
 val LCons_inject = standard (LCons_LCons_eq RS iffD1 RS conjE);
 
 val [major] = goal LList.thy "CONS(M,N): llist(A) ==> M: A & N: llist(A)";
 by (rtac (major RS llist.elim) 1);
 by (etac CONS_neq_NIL 1);
 by (fast_tac llist_cs 1);
-val CONS_D = result();
+qed "CONS_D";
 
 
 (****** Reasoning about llist(A) ******)
@@ -424,7 +424,7 @@
 \               LListD_Fun(diag(A), (%u.<f(u),g(u)>)``llist(A) Un  \
 \                                   diag(llist(A)))		\
 \ |] ==> f(M) = g(M)";
-by (rtac llist_equalityI 1);
+by (rtac LList_equalityI 1);
 br (Mlist RS imageI) 1;
 by (rtac subsetI 1);
 by (etac imageE 1);
@@ -435,7 +435,7 @@
 br (gMlist RS LListD_Fun_diag_I) 1;
 by (etac ssubst 1);
 by (REPEAT (ares_tac [CONScase] 1));
-val llist_fun_equalityI = result();
+qed "LList_fun_equalityI";
 
 
 (*** The functional "Lmap" ***)
@@ -443,12 +443,12 @@
 goal LList.thy "Lmap(f,NIL) = NIL";
 by (rtac (Lmap_def RS def_LList_corec RS trans) 1);
 by (simp_tac List_case_ss 1);
-val Lmap_NIL = result();
+qed "Lmap_NIL";
 
 goal LList.thy "Lmap(f, CONS(M,N)) = CONS(f(M), Lmap(f,N))";
 by (rtac (Lmap_def RS def_LList_corec RS trans) 1);
 by (simp_tac List_case_ss 1);
-val Lmap_CONS = result();
+qed "Lmap_CONS";
 
 (*Another type-checking proof by coinduction*)
 val [major,minor] = goal LList.thy
@@ -459,34 +459,34 @@
 by (ALLGOALS (asm_simp_tac (HOL_ss addsimps [Lmap_NIL,Lmap_CONS])));
 by (REPEAT (ares_tac [list_Fun_NIL_I, list_Fun_CONS_I, 
 		      minor, imageI, UnI1] 1));
-val Lmap_type = result();
+qed "Lmap_type";
 
 (*This type checking rule synthesises a sufficiently large set for f*)
 val [major] = goal LList.thy  "M: llist(A) ==> Lmap(f,M): llist(f``A)";
 by (rtac (major RS Lmap_type) 1);
 by (etac imageI 1);
-val Lmap_type2 = result();
+qed "Lmap_type2";
 
 (** Two easy results about Lmap **)
 
 val [prem] = goalw LList.thy [o_def]
     "M: llist(A) ==> Lmap(f o g, M) = Lmap(f, Lmap(g, M))";
-by (rtac (prem RS imageI RS llist_equalityI) 1);
+by (rtac (prem RS imageI RS LList_equalityI) 1);
 by (safe_tac set_cs);
 by (etac llist.elim 1);
 by (ALLGOALS (asm_simp_tac (HOL_ss addsimps [Lmap_NIL,Lmap_CONS])));
 by (REPEAT (ares_tac [LListD_Fun_NIL_I, imageI, UnI1,
 		      rangeI RS LListD_Fun_CONS_I] 1));
-val Lmap_compose = result();
+qed "Lmap_compose";
 
 val [prem] = goal LList.thy "M: llist(A) ==> Lmap(%x.x, M) = M";
-by (rtac (prem RS imageI RS llist_equalityI) 1);
+by (rtac (prem RS imageI RS LList_equalityI) 1);
 by (safe_tac set_cs);
 by (etac llist.elim 1);
 by (ALLGOALS (asm_simp_tac (HOL_ss addsimps [Lmap_NIL,Lmap_CONS])));
 by (REPEAT (ares_tac [LListD_Fun_NIL_I, imageI RS UnI1,
 		      rangeI RS LListD_Fun_CONS_I] 1));
-val Lmap_ident = result();
+qed "Lmap_ident";
 
 
 (*** Lappend -- its two arguments cause some complications! ***)
@@ -494,19 +494,19 @@
 goalw LList.thy [Lappend_def] "Lappend(NIL,NIL) = NIL";
 by (rtac (LList_corec RS trans) 1);
 by (simp_tac List_case_ss 1);
-val Lappend_NIL_NIL = result();
+qed "Lappend_NIL_NIL";
 
 goalw LList.thy [Lappend_def]
     "Lappend(NIL,CONS(N,N')) = CONS(N, Lappend(NIL,N'))";
 by (rtac (LList_corec RS trans) 1);
 by (simp_tac List_case_ss 1);
-val Lappend_NIL_CONS = result();
+qed "Lappend_NIL_CONS";
 
 goalw LList.thy [Lappend_def]
     "Lappend(CONS(M,M'), N) = CONS(M, Lappend(M',N))";
 by (rtac (LList_corec RS trans) 1);
 by (simp_tac List_case_ss 1);
-val Lappend_CONS = result();
+qed "Lappend_CONS";
 
 val Lappend_ss = 
     List_case_ss addsimps [llist.NIL_I, Lappend_NIL_NIL, Lappend_NIL_CONS,
@@ -514,14 +514,14 @@
                  |> add_eqI;
 
 goal LList.thy "!!M. M: llist(A) ==> Lappend(NIL,M) = M";
-by (etac llist_fun_equalityI 1);
+by (etac LList_fun_equalityI 1);
 by (ALLGOALS (asm_simp_tac Lappend_ss));
-val Lappend_NIL = result();
+qed "Lappend_NIL";
 
 goal LList.thy "!!M. M: llist(A) ==> Lappend(M,NIL) = M";
-by (etac llist_fun_equalityI 1);
+by (etac LList_fun_equalityI 1);
 by (ALLGOALS (asm_simp_tac Lappend_ss));
-val Lappend_NIL2 = result();
+qed "Lappend_NIL2";
 
 (** Alternative type-checking proofs for Lappend **)
 
@@ -550,7 +550,7 @@
 by (asm_simp_tac (Lappend_ss addsimps [Lappend_NIL, list_Fun_llist_I]) 1);
 by (asm_simp_tac Lappend_ss 1);
 by (fast_tac (set_cs addSIs [list_Fun_CONS_I]) 1);
-val Lappend_type = result();
+qed "Lappend_type";
 
 (**** Lazy lists as the type 'a llist -- strongly typed versions of above ****)
 
@@ -565,12 +565,12 @@
 
 goalw LList.thy [llist_case_def,LNil_def]  "llist_case(c, d, LNil) = c";
 by (simp_tac Rep_llist_ss 1);
-val llist_case_LNil = result();
+qed "llist_case_LNil";
 
 goalw LList.thy [llist_case_def,LCons_def]
     "llist_case(c, d, LCons(M,N)) = d(M,N)";
 by (simp_tac Rep_llist_ss 1);
-val llist_case_LCons = result();
+qed "llist_case_LCons";
 
 (*Elimination is case analysis, not induction.*)
 val [prem1,prem2] = goalw LList.thy [NIL_def,CONS_def]
@@ -585,7 +585,7 @@
 by (asm_simp_tac (HOL_ss addsimps [Rep_llist_LCons]) 1);
 by (etac (Abs_llist_inverse RS ssubst) 1);
 by (rtac refl 1);
-val llistE = result();
+qed "llistE";
 
 (** llist_corec: corecursion for 'a llist **)
 
@@ -599,7 +599,7 @@
 by (asm_simp_tac (llist_ss addsimps [LList_corec_type2,Abs_llist_inverse]) 1);
 (*FIXME: correct case splits usd to be found automatically:
 by (ASM_SIMP_TAC(llist_ss addsimps [LList_corec_type2,Abs_llist_inverse]) 1);*)
-val llist_corec = result();
+qed "llist_corec";
 
 (*definitional version of same*)
 val [rew] = goal LList.thy
@@ -607,7 +607,7 @@
 \    h(a) = sum_case(%u.LNil, split(%z w. LCons(z, h(w))), f(a))";
 by (rewtac rew);
 by (rtac llist_corec 1);
-val def_llist_corec = result();
+qed "def_llist_corec";
 
 (**** Proofs about type 'a llist functions ****)
 
@@ -619,13 +619,13 @@
 by (stac llist_unfold 1);
 by (simp_tac (HOL_ss addsimps [NIL_def, CONS_def]) 1);
 by (fast_tac univ_cs 1);
-val LListD_Fun_subset_Sigma_llist = result();
+qed "LListD_Fun_subset_Sigma_llist";
 
 goal LList.thy
     "prod_fun(Rep_llist,Rep_llist) `` r <= \
 \    Sigma(llist(range(Leaf)), %x.llist(range(Leaf)))";
 by (fast_tac (prod_cs addIs [Rep_llist]) 1);
-val subset_Sigma_llist = result();
+qed "subset_Sigma_llist";
 
 val [prem] = goal LList.thy
     "r <= Sigma(llist(range(Leaf)), %x.llist(range(Leaf))) ==> \
@@ -634,7 +634,7 @@
 by (rtac (prem RS subsetD RS SigmaE2) 1);
 by (assume_tac 1);
 by (asm_simp_tac (HOL_ss addsimps [o_def,prod_fun,Abs_llist_inverse]) 1);
-val prod_fun_lemma = result();
+qed "prod_fun_lemma";
 
 goal LList.thy
     "prod_fun(Rep_llist, Rep_llist) `` range(%x. <x, x>) = \
@@ -642,7 +642,7 @@
 br equalityI 1;
 by (fast_tac (univ_cs addIs [Rep_llist]) 1);
 by (fast_tac (univ_cs addSEs [Abs_llist_inverse RS subst]) 1);
-val prod_fun_range_eq_diag = result();
+qed "prod_fun_range_eq_diag";
 
 (** To show two llists are equal, exhibit a bisimulation! 
       [also admits true equality] **)
@@ -651,7 +651,7 @@
 by (rtac (inj_Rep_llist RS injD) 1);
 by (res_inst_tac [("r", "prod_fun(Rep_llist,Rep_llist)``r"),
 		  ("A", "range(Leaf)")] 
-	llist_equalityI 1);
+	LList_equalityI 1);
 by (rtac (prem1 RS prod_fun_imageI) 1);
 by (rtac (prem2 RS image_mono RS subset_trans) 1);
 by (rtac (image_compose RS subst) 1);
@@ -661,18 +661,18 @@
 by (rtac (LListD_Fun_subset_Sigma_llist RS prod_fun_lemma) 1);
 by (rtac (subset_Sigma_llist RS Un_least) 1);
 by (rtac diag_subset_Sigma 1);
-val llist_equalityI = result();
+qed "llist_equalityI";
 
 (** Rules to prove the 2nd premise of llist_equalityI **)
 goalw LList.thy [llistD_Fun_def,LNil_def] "<LNil,LNil> : llistD_Fun(r)";
 by (rtac (LListD_Fun_NIL_I RS prod_fun_imageI) 1);
-val llistD_Fun_LNil_I = result();
+qed "llistD_Fun_LNil_I";
 
 val [prem] = goalw LList.thy [llistD_Fun_def,LCons_def]
     "<l1,l2>:r ==> <LCons(x,l1), LCons(x,l2)> : llistD_Fun(r)";
 by (rtac (rangeI RS LListD_Fun_CONS_I RS prod_fun_imageI) 1);
 by (rtac (prem RS prod_fun_imageI) 1);
-val llistD_Fun_LCons_I = result();
+qed "llistD_Fun_LCons_I";
 
 (*Utilise the "strong" part, i.e. gfp(f)*)
 goalw LList.thy [llistD_Fun_def]
@@ -682,7 +682,7 @@
 by (rtac (image_Un RS ssubst) 1);
 by (stac prod_fun_range_eq_diag 1);
 br (Rep_llist RS LListD_Fun_diag_I) 1;
-val llistD_Fun_range_I = result();
+qed "llistD_Fun_range_I";
 
 (*A special case of list_equality for functions over lazy lists*)
 val [prem1,prem2] = goal LList.thy
@@ -701,7 +701,7 @@
 by (rtac llistD_Fun_range_I 1);
 by (etac ssubst 1);
 by (rtac prem2 1);
-val llist_fun_equalityI = result();
+qed "llist_fun_equalityI";
 
 (*simpset for llist bisimulations*)
 val llistD_simps = [llist_case_LNil, llist_case_LCons, 
@@ -715,12 +715,12 @@
 goal LList.thy "lmap(f,LNil) = LNil";
 by (rtac (lmap_def RS def_llist_corec RS trans) 1);
 by (simp_tac llistD_ss 1);
-val lmap_LNil = result();
+qed "lmap_LNil";
 
 goal LList.thy "lmap(f, LCons(M,N)) = LCons(f(M), lmap(f,N))";
 by (rtac (lmap_def RS def_llist_corec RS trans) 1);
 by (simp_tac llistD_ss 1);
-val lmap_LCons = result();
+qed "lmap_LCons";
 
 
 (** Two easy results about lmap **)
@@ -728,12 +728,12 @@
 goal LList.thy "lmap(f o g, l) = lmap(f, lmap(g, l))";
 by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
 by (ALLGOALS (simp_tac (llistD_ss addsimps [lmap_LNil, lmap_LCons])));
-val lmap_compose = result();
+qed "lmap_compose";
 
 goal LList.thy "lmap(%x.x, l) = l";
 by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
 by (ALLGOALS (simp_tac (llistD_ss addsimps [lmap_LNil, lmap_LCons])));
-val lmap_ident = result();
+qed "lmap_ident";
 
 
 (*** iterates -- llist_fun_equalityI cannot be used! ***)
@@ -741,7 +741,7 @@
 goal LList.thy "iterates(f,x) = LCons(x, iterates(f,f(x)))";
 by (rtac (iterates_def RS def_llist_corec RS trans) 1);
 by (simp_tac sum_ss 1);
-val iterates = result();
+qed "iterates";
 
 goal LList.thy "lmap(f, iterates(f,x)) = iterates(f,f(x))";
 by (res_inst_tac [("r", "range(%u.<lmap(f,iterates(f,u)),iterates(f,f(u))>)")] 
@@ -751,12 +751,12 @@
 by (res_inst_tac [("x1", "f(u)")] (iterates RS ssubst) 1);
 by (res_inst_tac [("x1", "u")] (iterates RS ssubst) 1);
 by (simp_tac (llistD_ss addsimps [lmap_LCons]) 1);
-val lmap_iterates = result();
+qed "lmap_iterates";
 
 goal LList.thy "iterates(f,x) = LCons(x, lmap(f, iterates(f,x)))";
 br (lmap_iterates RS ssubst) 1;
 br iterates 1;
-val iterates_lmap = result();
+qed "iterates_lmap";
 
 (*** A rather complex proof about iterates -- cf Andy Pitts ***)
 
@@ -767,12 +767,12 @@
 \    LCons(nat_rec(n, b, %m. f), nat_rec(n, l, %m. lmap(f)))";
 by (nat_ind_tac "n" 1);
 by (ALLGOALS (asm_simp_tac (nat_ss addsimps [lmap_LCons])));
-val fun_power_lmap = result();
+qed "fun_power_lmap";
 
 goal Nat.thy "nat_rec(n, g(x), %m. g) = nat_rec(Suc(n), x, %m. g)";
 by (nat_ind_tac "n" 1);
 by (ALLGOALS (asm_simp_tac nat_ss));
-val fun_power_Suc = result();
+qed "fun_power_Suc";
 
 val Pair_cong = read_instantiate_sg (sign_of Prod.thy)
  [("f","Pair")] (standard(refl RS cong RS cong));
@@ -798,7 +798,7 @@
 by (stac fun_power_Suc 1);
 br (UN1_I RS UnI1) 1;
 br rangeI 1;
-val iterates_equality = result();
+qed "iterates_equality";
 
 
 (*** lappend -- its two arguments cause some complications! ***)
@@ -806,31 +806,31 @@
 goalw LList.thy [lappend_def] "lappend(LNil,LNil) = LNil";
 by (rtac (llist_corec RS trans) 1);
 by (simp_tac llistD_ss 1);
-val lappend_LNil_LNil = result();
+qed "lappend_LNil_LNil";
 
 goalw LList.thy [lappend_def]
     "lappend(LNil,LCons(l,l')) = LCons(l, lappend(LNil,l'))";
 by (rtac (llist_corec RS trans) 1);
 by (simp_tac llistD_ss 1);
-val lappend_LNil_LCons = result();
+qed "lappend_LNil_LCons";
 
 goalw LList.thy [lappend_def]
     "lappend(LCons(l,l'), N) = LCons(l, lappend(l',N))";
 by (rtac (llist_corec RS trans) 1);
 by (simp_tac llistD_ss 1);
-val lappend_LCons = result();
+qed "lappend_LCons";
 
 goal LList.thy "lappend(LNil,l) = l";
 by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
 by (ALLGOALS 
     (simp_tac (llistD_ss addsimps [lappend_LNil_LNil, lappend_LNil_LCons])));
-val lappend_LNil = result();
+qed "lappend_LNil";
 
 goal LList.thy "lappend(l,LNil) = l";
 by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
 by (ALLGOALS 
     (simp_tac (llistD_ss addsimps [lappend_LNil_LNil, lappend_LCons])));
-val lappend_LNil2 = result();
+qed "lappend_LNil2";
 
 (*The infinite first argument blocks the second*)
 goal LList.thy "lappend(iterates(f,x), N) = iterates(f,x)";
@@ -840,7 +840,7 @@
 by (safe_tac set_cs);
 by (stac iterates 1);
 by (simp_tac (llistD_ss addsimps [lappend_LCons]) 1);
-val lappend_iterates = result();
+qed "lappend_iterates";
 
 (** Two proofs that lmap distributes over lappend **)
 
@@ -870,11 +870,11 @@
 by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
 by (simp_tac (llistD_ss addsimps [lappend_LNil, lmap_LNil])1);
 by (simp_tac (llistD_ss addsimps [lappend_LCons, lmap_LCons]) 1);
-val lmap_lappend_distrib = result();
+qed "lmap_lappend_distrib";
 
 (*Without strong coinduction, three case analyses might be needed*)
 goal LList.thy "lappend(lappend(l1,l2) ,l3) = lappend(l1, lappend(l2,l3))";
 by (res_inst_tac [("l","l1")] llist_fun_equalityI 1);
 by (simp_tac (llistD_ss addsimps [lappend_LNil])1);
 by (simp_tac (llistD_ss addsimps [lappend_LCons]) 1);
-val lappend_assoc = result();
+qed "lappend_assoc";