diff -r 3a8d722fd3ff -r 16c4ea954511 Univ.ML
--- a/Univ.ML	Fri Nov 11 10:35:03 1994 +0100
+++ b/Univ.ML	Mon Nov 21 17:50:34 1994 +0100
@@ -17,7 +17,7 @@
 by (fast_tac (HOL_cs addSIs [prem1,prem2]) 1);
 by (cut_facts_tac [less_linear] 1);
 by (fast_tac (HOL_cs addSIs [prem1] addSDs [prem2]) 1);
-val Least_equality = result();
+qed "Least_equality";
 
 val [prem] = goal Univ.thy "P(k) ==> P(LEAST x.P(x))";
 by (rtac (prem RS rev_mp) 1);
@@ -28,7 +28,7 @@
 by (assume_tac 1);
 by (assume_tac 2);
 by (fast_tac HOL_cs 1);
-val LeastI = result();
+qed "LeastI";
 
 (*Proof is almost identical to the one above!*)
 val [prem] = goal Univ.thy "P(k) ==> (LEAST x.P(x)) <= k";
@@ -40,20 +40,20 @@
 by (assume_tac 1);
 by (rtac le_refl 2);
 by (fast_tac (HOL_cs addIs [less_imp_le,le_trans]) 1);
-val Least_le = result();
+qed "Least_le";
 
 val [prem] = goal Univ.thy "k < (LEAST x.P(x)) ==> ~P(k)";
 by (rtac notI 1);
 by (etac (rewrite_rule [le_def] Least_le RS notE) 1);
 by (rtac prem 1);
-val not_less_Least = result();
+qed "not_less_Least";
 
 
 (** apfst -- can be used in similar type definitions **)
 
 goalw Univ.thy [apfst_def] "apfst(f,<a,b>) = <f(a),b>";
 by (rtac split 1);
-val apfst = result();
+qed "apfst";
 
 val [major,minor] = goal Univ.thy
     "[| q = apfst(f,p);  !!x y. [| p = <x,y>;  q = <f(x),y> |] ==> R \
@@ -64,7 +64,7 @@
 by (rtac (major RS trans) 1);
 by (etac ssubst 1);
 by (rtac apfst 1);
-val apfstE = result();
+qed "apfstE";
 
 (** Push -- an injection, analogous to Cons on lists **)
 
@@ -72,37 +72,37 @@
 by (rtac (major RS fun_cong RS box_equals RS Suc_inject) 1);
 by (rtac nat_case_0 1);
 by (rtac nat_case_0 1);
-val Push_inject1 = result();
+qed "Push_inject1";
 
 val [major] = goalw Univ.thy [Push_def] "Push(i,f)=Push(j,g) ==> f=g";
 by (rtac (major RS fun_cong RS ext RS box_equals) 1);
 by (rtac (nat_case_Suc RS ext) 1);
 by (rtac (nat_case_Suc RS ext) 1);
-val Push_inject2 = result();
+qed "Push_inject2";
 
 val [major,minor] = goal Univ.thy
     "[| Push(i,f)=Push(j,g);  [| i=j;  f=g |] ==> P \
 \    |] ==> P";
 by (rtac ((major RS Push_inject2) RS ((major RS Push_inject1) RS minor)) 1);
-val Push_inject = result();
+qed "Push_inject";
 
 val [major] = goalw Univ.thy [Push_def] "Push(k,f)=(%z.0) ==> P";
 by (rtac (major RS fun_cong RS box_equals RS Suc_neq_Zero) 1);
 by (rtac nat_case_0 1);
 by (rtac refl 1);
-val Push_neq_K0 = result();
+qed "Push_neq_K0";
 
 (*** Isomorphisms ***)
 
 goal Univ.thy "inj(Rep_Node)";
 by (rtac inj_inverseI 1);	(*cannot combine by RS: multiple unifiers*)
 by (rtac Rep_Node_inverse 1);
-val inj_Rep_Node = result();
+qed "inj_Rep_Node";
 
 goal Univ.thy "inj_onto(Abs_Node,Node)";
 by (rtac inj_onto_inverseI 1);
 by (etac Abs_Node_inverse 1);
-val inj_onto_Abs_Node = result();
+qed "inj_onto_Abs_Node";
 
 val Abs_Node_inject = inj_onto_Abs_Node RS inj_ontoD;
 
@@ -111,12 +111,12 @@
 
 goalw Univ.thy [Node_def] "<%k. 0,a> : Node";
 by (fast_tac set_cs 1);
-val Node_K0_I = result();
+qed "Node_K0_I";
 
 goalw Univ.thy [Node_def,Push_def]
     "!!p. p: Node ==> apfst(Push(i), p) : Node";
 by (fast_tac (set_cs addSIs [apfst, nat_case_Suc RS trans]) 1);
-val Node_Push_I = result();
+qed "Node_Push_I";
 
 
 (*** Distinctness of constructors ***)
@@ -130,7 +130,7 @@
 by (REPEAT (eresolve_tac [imageE, Abs_Node_inject RS apfstE, 
 			  Pair_inject, sym RS Push_neq_K0] 1
      ORELSE resolve_tac [Node_K0_I, Rep_Node RS Node_Push_I] 1));
-val Scons_not_Atom = result();
+qed "Scons_not_Atom";
 val Atom_not_Scons = standard (Scons_not_Atom RS not_sym);
 
 val Scons_neq_Atom = standard (Scons_not_Atom RS notE);
@@ -144,20 +144,20 @@
 by (rtac injI 1);
 by (etac (singleton_inject RS Abs_Node_inject RS Pair_inject) 1);
 by (REPEAT (ares_tac [Node_K0_I] 1));
-val inj_Atom = result();
+qed "inj_Atom";
 val Atom_inject = inj_Atom RS injD;
 
 goalw Univ.thy [Leaf_def,o_def] "inj(Leaf)";
 by (rtac injI 1);
 by (etac (Atom_inject RS Inl_inject) 1);
-val inj_Leaf = result();
+qed "inj_Leaf";
 
 val Leaf_inject = inj_Leaf RS injD;
 
 goalw Univ.thy [Numb_def,o_def] "inj(Numb)";
 by (rtac injI 1);
 by (etac (Atom_inject RS Inr_inject) 1);
-val inj_Numb = result();
+qed "inj_Numb";
 
 val Numb_inject = inj_Numb RS injD;
 
@@ -175,7 +175,7 @@
 by (rtac (inj_Rep_Node RS injD) 1);
 by (etac trans 1);
 by (safe_tac (HOL_cs addSEs [Pair_inject,Push_inject,sym]));
-val Push_Node_inject = result();
+qed "Push_Node_inject";
 
 
 (** Injectiveness of Scons **)
@@ -184,38 +184,38 @@
 by (cut_facts_tac [major] 1);
 by (fast_tac (set_cs addSDs [Suc_inject]
 		     addSEs [Push_Node_inject, Zero_neq_Suc]) 1);
-val Scons_inject_lemma1 = result();
+qed "Scons_inject_lemma1";
 
 val [major] = goalw Univ.thy [Scons_def] "M$N <= M'$N' ==> N<=N'";
 by (cut_facts_tac [major] 1);
 by (fast_tac (set_cs addSDs [Suc_inject]
 		     addSEs [Push_Node_inject, Suc_neq_Zero]) 1);
-val Scons_inject_lemma2 = result();
+qed "Scons_inject_lemma2";
 
 val [major] = goal Univ.thy "M$N = M'$N' ==> M=M'";
 by (rtac (major RS equalityE) 1);
 by (REPEAT (ares_tac [equalityI, Scons_inject_lemma1] 1));
-val Scons_inject1 = result();
+qed "Scons_inject1";
 
 val [major] = goal Univ.thy "M$N = M'$N' ==> N=N'";
 by (rtac (major RS equalityE) 1);
 by (REPEAT (ares_tac [equalityI, Scons_inject_lemma2] 1));
-val Scons_inject2 = result();
+qed "Scons_inject2";
 
 val [major,minor] = goal Univ.thy
     "[| M$N = M'$N';  [| M=M';  N=N' |] ==> P \
 \    |] ==> P";
 by (rtac ((major RS Scons_inject2) RS ((major RS Scons_inject1) RS minor)) 1);
-val Scons_inject = result();
+qed "Scons_inject";
 
 (*rewrite rules*)
 goal Univ.thy "(Atom(a)=Atom(b)) = (a=b)";
 by (fast_tac (HOL_cs addSEs [Atom_inject]) 1);
-val Atom_Atom_eq = result();
+qed "Atom_Atom_eq";
 
 goal Univ.thy "(M$N = M'$N') = (M=M' & N=N')";
 by (fast_tac (HOL_cs addSEs [Scons_inject]) 1);
-val Scons_Scons_eq = result();
+qed "Scons_Scons_eq";
 
 (*** Distinctness involving Leaf and Numb ***)
 
@@ -223,7 +223,7 @@
 
 goalw Univ.thy [Leaf_def,o_def] "(M$N) ~= Leaf(a)";
 by (rtac Scons_not_Atom 1);
-val Scons_not_Leaf = result();
+qed "Scons_not_Leaf";
 val Leaf_not_Scons = standard (Scons_not_Leaf RS not_sym);
 
 val Scons_neq_Leaf = standard (Scons_not_Leaf RS notE);
@@ -233,7 +233,7 @@
 
 goalw Univ.thy [Numb_def,o_def] "(M$N) ~= Numb(k)";
 by (rtac Scons_not_Atom 1);
-val Scons_not_Numb = result();
+qed "Scons_not_Numb";
 val Numb_not_Scons = standard (Scons_not_Numb RS not_sym);
 
 val Scons_neq_Numb = standard (Scons_not_Numb RS notE);
@@ -243,7 +243,7 @@
 
 goalw Univ.thy [Leaf_def,Numb_def] "Leaf(a) ~= Numb(k)";
 by (simp_tac (HOL_ss addsimps [Atom_Atom_eq,Inl_not_Inr]) 1);
-val Leaf_not_Numb = result();
+qed "Leaf_not_Numb";
 val Numb_not_Leaf = standard (Leaf_not_Numb RS not_sym);
 
 val Leaf_neq_Numb = standard (Leaf_not_Numb RS notE);
@@ -261,14 +261,14 @@
 by (rtac Least_equality 1);
 by (rtac refl 1);
 by (etac less_zeroE 1);
-val ndepth_K0 = result();
+qed "ndepth_K0";
 
 goal Univ.thy "k < Suc(LEAST x. f(x)=0) --> nat_case(Suc(i), f, k) ~= 0";
 by (nat_ind_tac "k" 1);
 by (ALLGOALS (simp_tac nat_ss));
 by (rtac impI 1);
 by (etac not_less_Least 1);
-val ndepth_Push_lemma = result();
+qed "ndepth_Push_lemma";
 
 goalw Univ.thy [ndepth_def,Push_Node_def]
     "ndepth (Push_Node(i,n)) = Suc(ndepth(n))";
@@ -282,28 +282,28 @@
 by (rtac (nat_case_Suc RS trans) 1);
 by (etac LeastI 1);
 by (etac (ndepth_Push_lemma RS mp) 1);
-val ndepth_Push_Node = result();
+qed "ndepth_Push_Node";
 
 
 (*** ntrunc applied to the various node sets ***)
 
 goalw Univ.thy [ntrunc_def] "ntrunc(0, M) = {}";
 by (safe_tac (set_cs addSIs [equalityI] addSEs [less_zeroE]));
-val ntrunc_0 = result();
+qed "ntrunc_0";
 
 goalw Univ.thy [Atom_def,ntrunc_def] "ntrunc(Suc(k), Atom(a)) = Atom(a)";
 by (safe_tac (set_cs addSIs [equalityI]));
 by (stac ndepth_K0 1);
 by (rtac zero_less_Suc 1);
-val ntrunc_Atom = result();
+qed "ntrunc_Atom";
 
 goalw Univ.thy [Leaf_def,o_def] "ntrunc(Suc(k), Leaf(a)) = Leaf(a)";
 by (rtac ntrunc_Atom 1);
-val ntrunc_Leaf = result();
+qed "ntrunc_Leaf";
 
 goalw Univ.thy [Numb_def,o_def] "ntrunc(Suc(k), Numb(i)) = Numb(i)";
 by (rtac ntrunc_Atom 1);
-val ntrunc_Numb = result();
+qed "ntrunc_Numb";
 
 goalw Univ.thy [Scons_def,ntrunc_def]
     "ntrunc(Suc(k), M$N) = ntrunc(k,M) $ ntrunc(k,N)";
@@ -312,7 +312,7 @@
 by (REPEAT (rtac Suc_less_SucD 1 THEN 
 	    rtac (ndepth_Push_Node RS subst) 1 THEN 
 	    assume_tac 1));
-val ntrunc_Scons = result();
+qed "ntrunc_Scons";
 
 (** Injection nodes **)
 
@@ -320,30 +320,30 @@
 by (simp_tac (univ_ss addsimps [ntrunc_Scons,ntrunc_0]) 1);
 by (rewtac Scons_def);
 by (safe_tac (set_cs addSIs [equalityI]));
-val ntrunc_one_In0 = result();
+qed "ntrunc_one_In0";
 
 goalw Univ.thy [In0_def]
     "ntrunc(Suc(Suc(k)), In0(M)) = In0 (ntrunc(Suc(k),M))";
 by (simp_tac (univ_ss addsimps [ntrunc_Scons,ntrunc_Numb]) 1);
-val ntrunc_In0 = result();
+qed "ntrunc_In0";
 
 goalw Univ.thy [In1_def] "ntrunc(Suc(0), In1(M)) = {}";
 by (simp_tac (univ_ss addsimps [ntrunc_Scons,ntrunc_0]) 1);
 by (rewtac Scons_def);
 by (safe_tac (set_cs addSIs [equalityI]));
-val ntrunc_one_In1 = result();
+qed "ntrunc_one_In1";
 
 goalw Univ.thy [In1_def]
     "ntrunc(Suc(Suc(k)), In1(M)) = In1 (ntrunc(Suc(k),M))";
 by (simp_tac (univ_ss addsimps [ntrunc_Scons,ntrunc_Numb]) 1);
-val ntrunc_In1 = result();
+qed "ntrunc_In1";
 
 
 (*** Cartesian Product ***)
 
 goalw Univ.thy [uprod_def] "!!M N. [| M:A;  N:B |] ==> (M$N) : A<*>B";
 by (REPEAT (ares_tac [singletonI,UN_I] 1));
-val uprodI = result();
+qed "uprodI";
 
 (*The general elimination rule*)
 val major::prems = goalw Univ.thy [uprod_def]
@@ -353,7 +353,7 @@
 by (cut_facts_tac [major] 1);
 by (REPEAT (eresolve_tac [asm_rl,singletonE,UN_E] 1
      ORELSE resolve_tac prems 1));
-val uprodE = result();
+qed "uprodE";
 
 (*Elimination of a pair -- introduces no eigenvariables*)
 val prems = goal Univ.thy
@@ -361,18 +361,18 @@
 \    |] ==> P";
 by (rtac uprodE 1);
 by (REPEAT (ares_tac prems 1 ORELSE eresolve_tac [Scons_inject,ssubst] 1));
-val uprodE2 = result();
+qed "uprodE2";
 
 
 (*** Disjoint Sum ***)
 
 goalw Univ.thy [usum_def] "!!M. M:A ==> In0(M) : A<+>B";
 by (fast_tac set_cs 1);
-val usum_In0I = result();
+qed "usum_In0I";
 
 goalw Univ.thy [usum_def] "!!N. N:B ==> In1(N) : A<+>B";
 by (fast_tac set_cs 1);
-val usum_In1I = result();
+qed "usum_In1I";
 
 val major::prems = goalw Univ.thy [usum_def]
     "[| u : A<+>B;  \
@@ -382,7 +382,7 @@
 by (rtac (major RS UnE) 1);
 by (REPEAT (rtac refl 1 
      ORELSE eresolve_tac (prems@[imageE,ssubst]) 1));
-val usumE = result();
+qed "usumE";
 
 
 (** Injection **)
@@ -390,7 +390,7 @@
 goalw Univ.thy [In0_def,In1_def] "In0(M) ~= In1(N)";
 by (rtac notI 1);
 by (etac (Scons_inject1 RS Numb_inject RS Zero_neq_Suc) 1);
-val In0_not_In1 = result();
+qed "In0_not_In1";
 
 val In1_not_In0 = standard (In0_not_In1 RS not_sym);
 val In0_neq_In1 = standard (In0_not_In1 RS notE);
@@ -398,24 +398,24 @@
 
 val [major] = goalw Univ.thy [In0_def] "In0(M) = In0(N) ==>  M=N";
 by (rtac (major RS Scons_inject2) 1);
-val In0_inject = result();
+qed "In0_inject";
 
 val [major] = goalw Univ.thy [In1_def] "In1(M) = In1(N) ==>  M=N";
 by (rtac (major RS Scons_inject2) 1);
-val In1_inject = result();
+qed "In1_inject";
 
 
 (*** proving equality of sets and functions using ntrunc ***)
 
 goalw Univ.thy [ntrunc_def] "ntrunc(k,M) <= M";
 by (fast_tac set_cs 1);
-val ntrunc_subsetI = result();
+qed "ntrunc_subsetI";
 
 val [major] = goalw Univ.thy [ntrunc_def]
     "(!!k. ntrunc(k,M) <= N) ==> M<=N";
 by (fast_tac (set_cs addIs [less_add_Suc1, less_add_Suc2, 
 			    major RS subsetD]) 1);
-val ntrunc_subsetD = result();
+qed "ntrunc_subsetD";
 
 (*A generalized form of the take-lemma*)
 val [major] = goal Univ.thy "(!!k. ntrunc(k,M) = ntrunc(k,N)) ==> M=N";
@@ -424,81 +424,81 @@
 by (ALLGOALS (rtac (ntrunc_subsetI RSN (2, subset_trans))));
 by (rtac (major RS equalityD1) 1);
 by (rtac (major RS equalityD2) 1);
-val ntrunc_equality = result();
+qed "ntrunc_equality";
 
 val [major] = goalw Univ.thy [o_def]
     "[| !!k. (ntrunc(k) o h1) = (ntrunc(k) o h2) |] ==> h1=h2";
 by (rtac (ntrunc_equality RS ext) 1);
 by (rtac (major RS fun_cong) 1);
-val ntrunc_o_equality = result();
+qed "ntrunc_o_equality";
 
 (*** Monotonicity ***)
 
 goalw Univ.thy [uprod_def] "!!A B. [| A<=A';  B<=B' |] ==> A<*>B <= A'<*>B'";
 by (fast_tac set_cs 1);
-val uprod_mono = result();
+qed "uprod_mono";
 
 goalw Univ.thy [usum_def] "!!A B. [| A<=A';  B<=B' |] ==> A<+>B <= A'<+>B'";
 by (fast_tac set_cs 1);
-val usum_mono = result();
+qed "usum_mono";
 
 goalw Univ.thy [Scons_def] "!!M N. [| M<=M';  N<=N' |] ==> M$N <= M'$N'";
 by (fast_tac set_cs 1);
-val Scons_mono = result();
+qed "Scons_mono";
 
 goalw Univ.thy [In0_def] "!!M N. M<=N ==> In0(M) <= In0(N)";
 by (REPEAT (ares_tac [subset_refl,Scons_mono] 1));
-val In0_mono = result();
+qed "In0_mono";
 
 goalw Univ.thy [In1_def] "!!M N. M<=N ==> In1(M) <= In1(N)";
 by (REPEAT (ares_tac [subset_refl,Scons_mono] 1));
-val In1_mono = result();
+qed "In1_mono";
 
 
 (*** Split and Case ***)
 
 goalw Univ.thy [Split_def] "Split(c, M$N) = c(M,N)";
 by (fast_tac (set_cs addIs [select_equality] addEs [Scons_inject]) 1);
-val Split = result();
+qed "Split";
 
 goalw Univ.thy [Case_def] "Case(c, d, In0(M)) = c(M)";
 by (fast_tac (set_cs addIs [select_equality] 
 		     addEs [make_elim In0_inject, In0_neq_In1]) 1);
-val Case_In0 = result();
+qed "Case_In0";
 
 goalw Univ.thy [Case_def] "Case(c, d, In1(N)) = d(N)";
 by (fast_tac (set_cs addIs [select_equality] 
 		     addEs [make_elim In1_inject, In1_neq_In0]) 1);
-val Case_In1 = result();
+qed "Case_In1";
 
 (**** UN x. B(x) rules ****)
 
 goalw Univ.thy [ntrunc_def] "ntrunc(k, UN x.f(x)) = (UN x. ntrunc(k, f(x)))";
 by (fast_tac (set_cs addIs [equalityI]) 1);
-val ntrunc_UN1 = result();
+qed "ntrunc_UN1";
 
 goalw Univ.thy [Scons_def] "(UN x.f(x)) $ M = (UN x. f(x) $ M)";
 by (fast_tac (set_cs addIs [equalityI]) 1);
-val Scons_UN1_x = result();
+qed "Scons_UN1_x";
 
 goalw Univ.thy [Scons_def] "M $ (UN x.f(x)) = (UN x. M $ f(x))";
 by (fast_tac (set_cs addIs [equalityI]) 1);
-val Scons_UN1_y = result();
+qed "Scons_UN1_y";
 
 goalw Univ.thy [In0_def] "In0(UN x.f(x)) = (UN x. In0(f(x)))";
 br Scons_UN1_y 1;
-val In0_UN1 = result();
+qed "In0_UN1";
 
 goalw Univ.thy [In1_def] "In1(UN x.f(x)) = (UN x. In1(f(x)))";
 br Scons_UN1_y 1;
-val In1_UN1 = result();
+qed "In1_UN1";
 
 
 (*** Equality : the diagonal relation ***)
 
 goalw Univ.thy [diag_def] "!!a A. [| a=b;  a:A |] ==> <a,b> : diag(A)";
 by (fast_tac set_cs 1);
-val diag_eqI = result();
+qed "diag_eqI";
 
 val diagI = refl RS diag_eqI |> standard;
 
@@ -509,14 +509,14 @@
 \    |] ==> P";
 by (rtac (major RS UN_E) 1);
 by (REPEAT (eresolve_tac [asm_rl,singletonE] 1 ORELSE resolve_tac prems 1));
-val diagE = result();
+qed "diagE";
 
 (*** Equality for Cartesian Product ***)
 
 goalw Univ.thy [dprod_def]
     "!!r s. [| <M,M'>:r;  <N,N'>:s |] ==> <M$N, M'$N'> : r<**>s";
 by (fast_tac prod_cs 1);
-val dprodI = result();
+qed "dprodI";
 
 (*The general elimination rule*)
 val major::prems = goalw Univ.thy [dprod_def]
@@ -526,18 +526,18 @@
 by (cut_facts_tac [major] 1);
 by (REPEAT_FIRST (eresolve_tac [asm_rl, UN_E, mem_splitE, singletonE]));
 by (REPEAT (ares_tac prems 1 ORELSE hyp_subst_tac 1));
-val dprodE = result();
+qed "dprodE";
 
 
 (*** Equality for Disjoint Sum ***)
 
 goalw Univ.thy [dsum_def]  "!!r. <M,M'>:r ==> <In0(M), In0(M')> : r<++>s";
 by (fast_tac prod_cs 1);
-val dsum_In0I = result();
+qed "dsum_In0I";
 
 goalw Univ.thy [dsum_def]  "!!r. <N,N'>:s ==> <In1(N), In1(N')> : r<++>s";
 by (fast_tac prod_cs 1);
-val dsum_In1I = result();
+qed "dsum_In1I";
 
 val major::prems = goalw Univ.thy [dsum_def]
     "[| w : r<++>s;  \
@@ -547,7 +547,7 @@
 by (cut_facts_tac [major] 1);
 by (REPEAT_FIRST (eresolve_tac [asm_rl, UN_E, UnE, mem_splitE, singletonE]));
 by (DEPTH_SOLVE (ares_tac prems 1 ORELSE hyp_subst_tac 1));
-val dsumE = result();
+qed "dsumE";
 
 
 val univ_cs =
@@ -560,22 +560,22 @@
 
 goal Univ.thy "!!r s. [| r<=r';  s<=s' |] ==> r<**>s <= r'<**>s'";
 by (fast_tac univ_cs 1);
-val dprod_mono = result();
+qed "dprod_mono";
 
 goal Univ.thy "!!r s. [| r<=r';  s<=s' |] ==> r<++>s <= r'<++>s'";
 by (fast_tac univ_cs 1);
-val dsum_mono = result();
+qed "dsum_mono";
 
 
 (*** Bounding theorems ***)
 
 goal Univ.thy "diag(A) <= Sigma(A,%x.A)";
 by (fast_tac univ_cs 1);
-val diag_subset_Sigma = result();
+qed "diag_subset_Sigma";
 
 goal Univ.thy "(Sigma(A,%x.B) <**> Sigma(C,%x.D)) <= Sigma(A<*>C, %z. B<*>D)";
 by (fast_tac univ_cs 1);
-val dprod_Sigma = result();
+qed "dprod_Sigma";
 
 val dprod_subset_Sigma = [dprod_mono, dprod_Sigma] MRS subset_trans |>standard;
 
@@ -585,11 +585,11 @@
 by (safe_tac univ_cs);
 by (stac Split 1);
 by (fast_tac univ_cs 1);
-val dprod_subset_Sigma2 = result();
+qed "dprod_subset_Sigma2";
 
 goal Univ.thy "(Sigma(A,%x.B) <++> Sigma(C,%x.D)) <= Sigma(A<+>C, %z. B<+>D)";
 by (fast_tac univ_cs 1);
-val dsum_Sigma = result();
+qed "dsum_Sigma";
 
 val dsum_subset_Sigma = [dsum_mono, dsum_Sigma] MRS subset_trans |> standard;
 
@@ -598,18 +598,18 @@
 
 goal Univ.thy "fst `` diag(A) = A";
 by (fast_tac (prod_cs addIs [equalityI, diagI] addSEs [diagE]) 1);
-val fst_image_diag = result();
+qed "fst_image_diag";
 
 goal Univ.thy "fst `` (r<**>s) = (fst``r) <*> (fst``s)";
 by (fast_tac (prod_cs addIs [equalityI, uprodI, dprodI]
                      addSEs [uprodE, dprodE]) 1);
-val fst_image_dprod = result();
+qed "fst_image_dprod";
 
 goal Univ.thy "fst `` (r<++>s) = (fst``r) <+> (fst``s)";
 by (fast_tac (prod_cs addIs [equalityI, usum_In0I, usum_In1I, 
 			     dsum_In0I, dsum_In1I]
                      addSEs [usumE, dsumE]) 1);
-val fst_image_dsum = result();
+qed "fst_image_dsum";
 
 val fst_image_simps = [fst_image_diag, fst_image_dprod, fst_image_dsum];
 val fst_image_ss = univ_ss addsimps fst_image_simps;