src/ZF/AC/AC1_WO2.ML

 (*  Title: 	ZF/AC/AC1_WO2.ML
     ID:         $Id$
-    Author: 	Krzysztof Gr`abczewski
+    Author: 	Krzysztof Grabczewski
 
 The proof of AC1 ==> WO2
 *)
 
 open AC1_WO2;
 
 val [prem] = goal thy "f : (PROD X:Pow(x) - {0}. X) ==>  \
 \	?g(f) : bij(x, LEAST i. HH(lam X:Pow(x)-{0}. {f`X}, x, i) = {x})";
 by (resolve_tac [bij_Least_HH_x RS bij_converse_bij] 1);
-by (resolve_tac [f_subsets_imp_UN_HH_eq_x] 1);
+by (rtac f_subsets_imp_UN_HH_eq_x 1);
 by (resolve_tac [lam_type RS apply_type] 1 THEN (assume_tac 2));
 by (fast_tac (AC_cs addSDs [equals0D, prem RS apply_type]) 1);
 by (fast_tac (AC_cs addSIs [prem RS Pi_weaken_type]) 1);
 val lemma1 = uresult();
 
 goalw thy [AC1_def, WO2_def, eqpoll_def] "!!Z. AC1 ==> WO2";
-by (resolve_tac [allI] 1);
+by (rtac allI 1);
 by (eres_inst_tac [("x","Pow(A)-{0}")] allE 1);
 by (fast_tac (AC_cs addSDs [lemma1] addSIs [Ord_Least]) 1);
 qed "AC1_WO2";