--- a/src/ZF/QUniv.ML Wed Dec 07 12:34:47 1994 +0100
+++ b/src/ZF/QUniv.ML Wed Dec 07 13:12:04 1994 +0100
@@ -13,35 +13,35 @@
goalw QUniv.thy [quniv_def]
"!!X A. X <= univ(eclose(A)) ==> X : quniv(A)";
by (etac PowI 1);
-val qunivI = result();
+qed "qunivI";
goalw QUniv.thy [quniv_def]
"!!X A. X : quniv(A) ==> X <= univ(eclose(A))";
by (etac PowD 1);
-val qunivD = result();
+qed "qunivD";
goalw QUniv.thy [quniv_def] "!!A B. A<=B ==> quniv(A) <= quniv(B)";
by (etac (eclose_mono RS univ_mono RS Pow_mono) 1);
-val quniv_mono = result();
+qed "quniv_mono";
(*** Closure properties ***)
goalw QUniv.thy [quniv_def] "univ(eclose(A)) <= quniv(A)";
by (rtac (Transset_iff_Pow RS iffD1) 1);
by (rtac (Transset_eclose RS Transset_univ) 1);
-val univ_eclose_subset_quniv = result();
+qed "univ_eclose_subset_quniv";
(*Key property for proving A_subset_quniv; requires eclose in def of quniv*)
goal QUniv.thy "univ(A) <= quniv(A)";
by (rtac (arg_subset_eclose RS univ_mono RS subset_trans) 1);
by (rtac univ_eclose_subset_quniv 1);
-val univ_subset_quniv = result();
+qed "univ_subset_quniv";
val univ_into_quniv = standard (univ_subset_quniv RS subsetD);
goalw QUniv.thy [quniv_def] "Pow(univ(A)) <= quniv(A)";
by (rtac (arg_subset_eclose RS univ_mono RS Pow_mono) 1);
-val Pow_univ_subset_quniv = result();
+qed "Pow_univ_subset_quniv";
val univ_subset_into_quniv = standard
(PowI RS (Pow_univ_subset_quniv RS subsetD));
@@ -61,13 +61,13 @@
goalw QUniv.thy [QPair_def]
"!!A a. [| a <= univ(A); b <= univ(A) |] ==> <a;b> <= univ(A)";
by (REPEAT (ares_tac [sum_subset_univ] 1));
-val QPair_subset_univ = result();
+qed "QPair_subset_univ";
(** Quine disjoint sum **)
goalw QUniv.thy [QInl_def] "!!A a. a <= univ(A) ==> QInl(a) <= univ(A)";
by (etac (empty_subsetI RS QPair_subset_univ) 1);
-val QInl_subset_univ = result();
+qed "QInl_subset_univ";
val naturals_subset_nat =
rewrite_rule [Transset_def] (Ord_nat RS Ord_is_Transset)
@@ -78,7 +78,7 @@
goalw QUniv.thy [QInr_def] "!!A a. a <= univ(A) ==> QInr(a) <= univ(A)";
by (etac (nat_1I RS naturals_subset_univ RS QPair_subset_univ) 1);
-val QInr_subset_univ = result();
+qed "QInr_subset_univ";
(*** Closure for Quine-inspired products and sums ***)
@@ -87,12 +87,12 @@
"!!A a. [| a: quniv(A); b: quniv(A) |] ==> <a;b> : quniv(A)";
by (REPEAT (dtac PowD 1));
by (REPEAT (ares_tac [PowI, sum_subset_univ] 1));
-val QPair_in_quniv = result();
+qed "QPair_in_quniv";
goal QUniv.thy "quniv(A) <*> quniv(A) <= quniv(A)";
by (REPEAT (ares_tac [subsetI, QPair_in_quniv] 1
ORELSE eresolve_tac [QSigmaE, ssubst] 1));
-val QSigma_quniv = result();
+qed "QSigma_quniv";
val QSigma_subset_quniv = standard
(QSigma_mono RS (QSigma_quniv RSN (2,subset_trans)));
@@ -103,30 +103,30 @@
by (etac ([Transset_eclose RS Transset_univ, PowD] MRS
Transset_includes_summands RS conjE) 1);
by (REPEAT (ares_tac [conjI,PowI] 1));
-val quniv_QPair_D = result();
+qed "quniv_QPair_D";
val quniv_QPair_E = standard (quniv_QPair_D RS conjE);
goal QUniv.thy "<a;b> : quniv(A) <-> a: quniv(A) & b: quniv(A)";
by (REPEAT (ares_tac [iffI, QPair_in_quniv, quniv_QPair_D] 1
ORELSE etac conjE 1));
-val quniv_QPair_iff = result();
+qed "quniv_QPair_iff";
(** Quine disjoint sum **)
goalw QUniv.thy [QInl_def] "!!A a. a: quniv(A) ==> QInl(a) : quniv(A)";
by (REPEAT (ares_tac [zero_in_quniv,QPair_in_quniv] 1));
-val QInl_in_quniv = result();
+qed "QInl_in_quniv";
goalw QUniv.thy [QInr_def] "!!A b. b: quniv(A) ==> QInr(b) : quniv(A)";
by (REPEAT (ares_tac [one_in_quniv, QPair_in_quniv] 1));
-val QInr_in_quniv = result();
+qed "QInr_in_quniv";
goal QUniv.thy "quniv(C) <+> quniv(C) <= quniv(C)";
by (REPEAT (ares_tac [subsetI, QInl_in_quniv, QInr_in_quniv] 1
ORELSE eresolve_tac [qsumE, ssubst] 1));
-val qsum_quniv = result();
+qed "qsum_quniv";
val qsum_subset_quniv = standard
(qsum_mono RS (qsum_quniv RSN (2,subset_trans)));
@@ -156,7 +156,7 @@
by (dtac (Transset_Vfrom_succ RS equalityD1 RS subsetD RS PowD) 1);
by (assume_tac 1);
by (fast_tac ZF_cs 1);
-val doubleton_in_Vfrom_D = result();
+qed "doubleton_in_Vfrom_D";
(*This weaker version says a, b exist at the same level*)
val Vfrom_doubleton_D = standard (Transset_Vfrom RS Transset_doubleton_D);
@@ -173,13 +173,13 @@
"!!X. [| <a,b> : Vfrom(X,succ(i)); Transset(X) |] ==> \
\ a: Vfrom(X,i) & b: Vfrom(X,i)";
by (fast_tac (ZF_cs addSDs [doubleton_in_Vfrom_D, Vfrom_doubleton_D]) 1);
-val Pair_in_Vfrom_D = result();
+qed "Pair_in_Vfrom_D";
goal Univ.thy
"!!X. Transset(X) ==> \
\ (a*b) Int Vfrom(X, succ(i)) <= (a Int Vfrom(X,i)) * (b Int Vfrom(X,i))";
by (fast_tac (ZF_cs addSDs [Pair_in_Vfrom_D]) 1);
-val product_Int_Vfrom_subset = result();
+qed "product_Int_Vfrom_subset";
(*** Intersecting <a;b> with Vfrom... ***)
@@ -190,7 +190,7 @@
by (rtac Un_mono 1);
by (REPEAT (ares_tac [product_Int_Vfrom_subset RS subset_trans,
[Int_lower1, subset_refl] MRS Sigma_mono] 1));
-val QPair_Int_Vfrom_succ_subset = result();
+qed "QPair_Int_Vfrom_succ_subset";
(**** "Take-lemma" rules for proving a=b by coinduction and c: quniv(A) ****)
@@ -200,7 +200,7 @@
"!!X. Transset(X) ==> \
\ <a;b> Int Vfrom(X,i) <= <a Int Vfrom(X,i); b Int Vfrom(X,i)>";
by (etac (Transset_Vfrom RS Transset_sum_Int_subset) 1);
-val QPair_Int_Vfrom_subset = result();
+qed "QPair_Int_Vfrom_subset";
(*[| a Int Vset(i) <= c; b Int Vset(i) <= d |] ==> <a;b> Int Vset(i) <= <c;d>*)
val QPair_Int_Vset_subset_trans = standard
@@ -219,4 +219,4 @@
(*Limit(i) case*)
by (asm_simp_tac (ZF_ss addsimps [Limit_Vfrom_eq, Int_UN_distrib, subset_refl,
UN_mono, QPair_Int_Vset_subset_trans]) 1);
-val QPair_Int_Vset_subset_UN = result();
+qed "QPair_Int_Vset_subset_UN";