--- a/src/ZF/InfDatatype.ML Wed Jun 28 10:56:34 2000 +0200
+++ b/src/ZF/InfDatatype.ML Wed Jun 28 10:57:35 2000 +0200
@@ -11,31 +11,31 @@
transfer InfDatatype.thy Limit_VfromE
|> standard;
-Goal "[| 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);
+Goal "[| f: D -> Vfrom(A,csucc(K)); |D| le K; InfCard(K) |] \
+\ ==> EX j. f: D -> Vfrom(A,j) & j < csucc(K)";
+by (res_inst_tac [("x", "UN d:D. LEAST i. f`d : Vfrom(A,i)")] exI 1);
by (rtac conjI 1);
by (rtac le_UN_Ord_lt_csucc 2);
by (rtac ballI 4 THEN
etac fun_Limit_VfromE 4 THEN REPEAT_SOME assume_tac);
by (fast_tac (claset() addEs [Least_le RS lt_trans1, ltE]) 2);
by (rtac Pi_type 1);
-by (rename_tac "w" 2);
+by (rename_tac "d" 2);
by (etac fun_Limit_VfromE 2 THEN REPEAT_SOME assume_tac);
-by (subgoal_tac "f`w : Vfrom(A, LEAST i. f`w : Vfrom(A,i))" 1);
+by (subgoal_tac "f`d : Vfrom(A, LEAST i. f`d : Vfrom(A,i))" 1);
by (fast_tac (claset() addEs [LeastI, ltE]) 2);
by (eresolve_tac [[subset_refl, UN_upper] MRS Vfrom_mono RS subsetD] 1);
by (assume_tac 1);
qed "fun_Vcsucc_lemma";
-Goal "[| 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);
+Goal "[| D <= Vfrom(A,csucc(K)); |D| le K; InfCard(K) |] \
+\ ==> EX j. D <= 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 "[| |W| le K; InfCard(K); W <= Vfrom(A,csucc(K)) |] ==> \
-\ W -> Vfrom(A,csucc(K)) <= Vfrom(A,csucc(K))";
+Goal "[| |D| le K; InfCard(K); D <= Vfrom(A,csucc(K)) |] ==> \
+\ D -> Vfrom(A,csucc(K)) <= Vfrom(A,csucc(K))";
by (safe_tac (claset() addSDs [fun_Vcsucc_lemma, subset_Vcsucc]));
by (resolve_tac [Vfrom RS ssubst] 1);
by (dtac fun_is_rel 1);
@@ -47,9 +47,9 @@
Limit_has_succ, Un_least_lt] 1));
qed "fun_Vcsucc";
-Goal "[| f: W -> Vfrom(A, csucc(K)); |W| le K; InfCard(K); \
-\ W <= Vfrom(A,csucc(K)) \
-\ |] ==> f: Vfrom(A,csucc(K))";
+Goal "[| f: D -> Vfrom(A, csucc(K)); |D| le K; InfCard(K); \
+\ D <= Vfrom(A,csucc(K)) |] \
+\ ==> f: Vfrom(A,csucc(K))";
by (REPEAT (ares_tac [fun_Vcsucc RS subsetD] 1));
qed "fun_in_Vcsucc";