--- a/src/ZF/InfDatatype.ML Mon Jun 22 15:53:24 1998 +0200
+++ b/src/ZF/InfDatatype.ML Mon Jun 22 17:12:27 1998 +0200
@@ -11,7 +11,7 @@
transfer InfDatatype.thy Limit_VfromE
|> standard;
-goal InfDatatype.thy
+Goal
"!!K. [| f: W -> Vfrom(A,csucc(K)); |W| le K; InfCard(K) \
\ |] ==> EX j. f: W -> Vfrom(A,j) & j < csucc(K)";
by (res_inst_tac [("x", "UN w:W. LEAST i. f`w : Vfrom(A,i)")] exI 1);
@@ -29,14 +29,14 @@
by (assume_tac 1);
qed "fun_Vcsucc_lemma";
-goal InfDatatype.thy
+Goal
"!!K. [| W <= Vfrom(A,csucc(K)); |W| le K; InfCard(K) \
\ |] ==> EX j. W <= Vfrom(A,j) & j < csucc(K)";
by (asm_full_simp_tac (simpset() addsimps [subset_iff_id, fun_Vcsucc_lemma]) 1);
qed "subset_Vcsucc";
(*Version for arbitrary index sets*)
-goal InfDatatype.thy
+Goal
"!!K. [| |W| le K; InfCard(K); W <= Vfrom(A,csucc(K)) |] ==> \
\ W -> Vfrom(A,csucc(K)) <= Vfrom(A,csucc(K))";
by (safe_tac (claset() addSDs [fun_Vcsucc_lemma, subset_Vcsucc]));
@@ -50,7 +50,7 @@
Limit_has_succ, Un_least_lt] 1));
qed "fun_Vcsucc";
-goal InfDatatype.thy
+Goal
"!!K. [| f: W -> Vfrom(A, csucc(K)); |W| le K; InfCard(K); \
\ W <= Vfrom(A,csucc(K)) \
\ |] ==> f: Vfrom(A,csucc(K))";
@@ -62,7 +62,7 @@
(** Version where K itself is the index set **)
-goal InfDatatype.thy
+Goal
"!!K. InfCard(K) ==> K -> Vfrom(A,csucc(K)) <= Vfrom(A,csucc(K))";
by (forward_tac [InfCard_is_Card RS Card_is_Ord] 1);
by (REPEAT (ares_tac [fun_Vcsucc, Ord_cardinal_le,
@@ -70,7 +70,7 @@
lt_csucc RS leI RS le_imp_subset RS subset_trans] 1));
qed "Card_fun_Vcsucc";
-goal InfDatatype.thy
+Goal
"!!K. [| f: K -> Vfrom(A, csucc(K)); InfCard(K) \
\ |] ==> f: Vfrom(A,csucc(K))";
by (REPEAT (ares_tac [Card_fun_Vcsucc RS subsetD] 1));