src/ZF/AC/AC1_WO2.ML
author clasohm
Tue, 30 Jan 1996 13:42:57 +0100
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(*  Title:      ZF/AC/AC1_WO2.ML
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    ID:         $Id$
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    Author:     Krzysztof Grabczewski
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The proof of AC1 ==> WO2
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*)
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open AC1_WO2;
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val [prem] = goal thy "f : (PROD X:Pow(x) - {0}. X) ==>  \
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\       ?g(f) : bij(x, LEAST i. HH(lam X:Pow(x)-{0}. {f`X}, x, i) = {x})";
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by (resolve_tac [bij_Least_HH_x RS bij_converse_bij] 1);
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by (rtac f_subsets_imp_UN_HH_eq_x 1);
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by (resolve_tac [lam_type RS apply_type] 1 THEN (assume_tac 2));
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by (fast_tac (AC_cs addSDs [equals0D, prem RS apply_type]) 1);
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by (fast_tac (AC_cs addSIs [prem RS Pi_weaken_type]) 1);
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val lemma1 = uresult();
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goalw thy [AC1_def, WO2_def, eqpoll_def] "!!Z. AC1 ==> WO2";
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by (rtac allI 1);
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by (eres_inst_tac [("x","Pow(A)-{0}")] allE 1);
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by (fast_tac (AC_cs addSDs [lemma1] addSIs [Ord_Least]) 1);
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qed "AC1_WO2";