src/ZF/mono.ML

--- a/src/ZF/mono.ML	Wed Dec 07 12:34:47 1994 +0100
+++ b/src/ZF/mono.ML	Wed Dec 07 13:12:04 1994 +0100
@@ -12,121 +12,121 @@
   would have to be single-valued*)
 goal ZF.thy "!!A B. A<=B ==> Replace(A,P) <= Replace(B,P)";
 by (fast_tac (ZF_cs addSEs [ReplaceE]) 1);
-val Replace_mono = result();
+qed "Replace_mono";
 
 goal ZF.thy "!!A B. A<=B ==> {f(x). x:A} <= {f(x). x:B}";
 by (fast_tac ZF_cs 1);
-val RepFun_mono = result();
+qed "RepFun_mono";
 
 goal ZF.thy "!!A B. A<=B ==> Pow(A) <= Pow(B)";
 by (fast_tac ZF_cs 1);
-val Pow_mono = result();
+qed "Pow_mono";
 
 goal ZF.thy "!!A B. A<=B ==> Union(A) <= Union(B)";
 by (fast_tac ZF_cs 1);
-val Union_mono = result();
+qed "Union_mono";
 
 val prems = goal ZF.thy
     "[| A<=C;  !!x. x:A ==> B(x)<=D(x) \
 \    |] ==> (UN x:A. B(x)) <= (UN x:C. D(x))";
 by (fast_tac (ZF_cs addIs (prems RL [subsetD])) 1);
-val UN_mono = result();
+qed "UN_mono";
 
 (*Intersection is ANTI-monotonic.  There are TWO premises! *)
 goal ZF.thy "!!A B. [| A<=B;  a:A |] ==> Inter(B) <= Inter(A)";
 by (fast_tac ZF_cs 1);
-val Inter_anti_mono = result();
+qed "Inter_anti_mono";
 
 goal ZF.thy "!!C D. C<=D ==> cons(a,C) <= cons(a,D)";
 by (fast_tac ZF_cs 1);
-val cons_mono = result();
+qed "cons_mono";
 
 goal ZF.thy "!!A B C D. [| A<=C;  B<=D |] ==> A Un B <= C Un D";
 by (fast_tac ZF_cs 1);
-val Un_mono = result();
+qed "Un_mono";
 
 goal ZF.thy "!!A B C D. [| A<=C;  B<=D |] ==> A Int B <= C Int D";
 by (fast_tac ZF_cs 1);
-val Int_mono = result();
+qed "Int_mono";
 
 goal ZF.thy "!!A B C D. [| A<=C;  D<=B |] ==> A-B <= C-D";
 by (fast_tac ZF_cs 1);
-val Diff_mono = result();
+qed "Diff_mono";
 
 (** Standard products, sums and function spaces **)
 
 goal ZF.thy "!!A B C D. [| A<=C;  ALL x:A. B(x) <= D(x) |] ==> \
 \                       Sigma(A,B) <= Sigma(C,D)";
 by (fast_tac ZF_cs 1);
-val Sigma_mono_lemma = result();
+qed "Sigma_mono_lemma";
 val Sigma_mono = ballI RSN (2,Sigma_mono_lemma);
 
 goalw Sum.thy sum_defs "!!A B C D. [| A<=C;  B<=D |] ==> A+B <= C+D";
 by (REPEAT (ares_tac [subset_refl,Un_mono,Sigma_mono] 1));
-val sum_mono = result();
+qed "sum_mono";
 
 (*Note that B->A and C->A are typically disjoint!*)
 goal ZF.thy "!!A B C. B<=C ==> A->B <= A->C";
 by (fast_tac (ZF_cs addIs [lam_type] addEs [Pi_lamE]) 1);
-val Pi_mono = result();
+qed "Pi_mono";
 
 goalw ZF.thy [lam_def] "!!A B. A<=B ==> Lambda(A,c) <= Lambda(B,c)";
 by (etac RepFun_mono 1);
-val lam_mono = result();
+qed "lam_mono";
 
 (** Quine-inspired ordered pairs, products, injections and sums **)
 
 goalw QPair.thy [QPair_def] "!!a b c d. [| a<=c;  b<=d |] ==> <a;b> <= <c;d>";
 by (REPEAT (ares_tac [sum_mono] 1));
-val QPair_mono = result();
+qed "QPair_mono";
 
 goal QPair.thy "!!A B C D. [| A<=C;  ALL x:A. B(x) <= D(x) |] ==>  \
 \                          QSigma(A,B) <= QSigma(C,D)";
 by (fast_tac qpair_cs 1);
-val QSigma_mono_lemma = result();
+qed "QSigma_mono_lemma";
 val QSigma_mono = ballI RSN (2,QSigma_mono_lemma);
 
 goalw QPair.thy [QInl_def] "!!a b. a<=b ==> QInl(a) <= QInl(b)";
 by (REPEAT (ares_tac [subset_refl RS QPair_mono] 1));
-val QInl_mono = result();
+qed "QInl_mono";
 
 goalw QPair.thy [QInr_def] "!!a b. a<=b ==> QInr(a) <= QInr(b)";
 by (REPEAT (ares_tac [subset_refl RS QPair_mono] 1));
-val QInr_mono = result();
+qed "QInr_mono";
 
 goal QPair.thy "!!A B C D. [| A<=C;  B<=D |] ==> A <+> B <= C <+> D";
 by (fast_tac qsum_cs 1);
-val qsum_mono = result();
+qed "qsum_mono";
 
 
 (** Converse, domain, range, field **)
 
 goal ZF.thy "!!r s. r<=s ==> converse(r) <= converse(s)";
 by (fast_tac ZF_cs 1);
-val converse_mono = result();
+qed "converse_mono";
 
 goal ZF.thy "!!r s. r<=s ==> domain(r)<=domain(s)";
 by (fast_tac ZF_cs 1);
-val domain_mono = result();
+qed "domain_mono";
 
 val domain_rel_subset = 
 	[domain_mono, domain_subset] MRS subset_trans |> standard;
 
 goal ZF.thy "!!r s. r<=s ==> range(r)<=range(s)";
 by (fast_tac ZF_cs 1);
-val range_mono = result();
+qed "range_mono";
 
 val range_rel_subset = 
 	[range_mono, range_subset] MRS subset_trans |> standard;
 
 goal ZF.thy "!!r s. r<=s ==> field(r)<=field(s)";
 by (fast_tac ZF_cs 1);
-val field_mono = result();
+qed "field_mono";
 
 goal ZF.thy "!!r A. r <= A*A ==> field(r) <= A";
 by (etac (field_mono RS subset_trans) 1);
 by (fast_tac ZF_cs 1);
-val field_rel_subset = result();
+qed "field_rel_subset";
 
 
 (** Images **)
@@ -134,58 +134,58 @@
 val [prem1,prem2] = goal ZF.thy
     "[| !! x y. <x,y>:r ==> <x,y>:s;  A<=B |] ==> r``A <= s``B";
 by (fast_tac (ZF_cs addIs [prem1, prem2 RS subsetD]) 1);
-val image_pair_mono = result();
+qed "image_pair_mono";
 
 val [prem1,prem2] = goal ZF.thy
     "[| !! x y. <x,y>:r ==> <x,y>:s;  A<=B |] ==> r-``A <= s-``B";
 by (fast_tac (ZF_cs addIs [prem1, prem2 RS subsetD]) 1);
-val vimage_pair_mono = result();
+qed "vimage_pair_mono";
 
 goal ZF.thy "!!r s. [| r<=s;  A<=B |] ==> r``A <= s``B";
 by (fast_tac ZF_cs 1);
-val image_mono = result();
+qed "image_mono";
 
 goal ZF.thy "!!r s. [| r<=s;  A<=B |] ==> r-``A <= s-``B";
 by (fast_tac ZF_cs 1);
-val vimage_mono = result();
+qed "vimage_mono";
 
 val [sub,PQimp] = goal ZF.thy
     "[| A<=B;  !!x. x:A ==> P(x) --> Q(x) |] ==> Collect(A,P) <= Collect(B,Q)";
 by (fast_tac (ZF_cs addIs [sub RS subsetD, PQimp RS mp]) 1);
-val Collect_mono = result();
+qed "Collect_mono";
 
 (** Monotonicity of implications -- some could go to FOL **)
 
 goal ZF.thy "!!A B x. A<=B ==> x:A --> x:B";
 by (fast_tac ZF_cs 1);
-val in_mono = result();
+qed "in_mono";
 
 goal IFOL.thy "!!P1 P2 Q1 Q2. [| P1-->Q1; P2-->Q2 |] ==> (P1&P2) --> (Q1&Q2)";
 by (Int.fast_tac 1);
-val conj_mono = result();
+qed "conj_mono";
 
 goal IFOL.thy "!!P1 P2 Q1 Q2. [| P1-->Q1; P2-->Q2 |] ==> (P1|P2) --> (Q1|Q2)";
 by (Int.fast_tac 1);
-val disj_mono = result();
+qed "disj_mono";
 
 goal IFOL.thy "!!P1 P2 Q1 Q2.[| Q1-->P1; P2-->Q2 |] ==> (P1-->P2)-->(Q1-->Q2)";
 by (Int.fast_tac 1);
-val imp_mono = result();
+qed "imp_mono";
 
 goal IFOL.thy "P-->P";
 by (rtac impI 1);
 by (assume_tac 1);
-val imp_refl = result();
+qed "imp_refl";
 
 val [PQimp] = goal IFOL.thy
     "[| !!x. P(x) --> Q(x) |] ==> (EX x.P(x)) --> (EX x.Q(x))";
 by (fast_tac (FOL_cs addIs [PQimp RS mp]) 1);
-val ex_mono = result();
+qed "ex_mono";
 
 val [PQimp] = goal IFOL.thy
     "[| !!x. P(x) --> Q(x) |] ==> (ALL x.P(x)) --> (ALL x.Q(x))";
 by (fast_tac (FOL_cs addIs [PQimp RS mp]) 1);
-val all_mono = result();
+qed "all_mono";
 
 (*Used in intr_elim.ML and in individual datatype definitions*)
 val basic_monos = [subset_refl, imp_refl, disj_mono, conj_mono,