src/ZF/AC/WO1_WO8.ML
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Tue, 01 Jun 1999 18:12:45 +0200
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(*  Title:      ZF/AC/WO1_WO8.ML
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    ID:         $Id$
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    Author:     Krzysztof Grabczewski
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The proof of WO8 <-> WO1 (Rubin & Rubin p. 6)
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*)
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(* ********************************************************************** *)
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(* Trivial implication "WO1 ==> WO8"                                      *)
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(* ********************************************************************** *)
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Goalw WO_defs "WO1 ==> WO8";
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by (Fast_tac 1);
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qed "WO1_WO8";
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(* ********************************************************************** *)
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(* The proof of "WO8 ==> WO1" - faithful image of Rubin & Rubin's proof   *)
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(* ********************************************************************** *)
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Goalw WO_defs "WO8 ==> WO1";
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by (rtac allI 1);
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by (eres_inst_tac [("x","{{x}. x:A}")] allE 1);
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by (etac impE 1);
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by (fast_tac (claset() addSEs [lam_sing_bij RS bij_is_inj RS
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                        well_ord_rvimage]) 2);
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by (res_inst_tac [("x","lam a:{{x}. x:A}. THE x. a={x}")] exI 1);
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by (fast_tac (claset() addSIs [lam_type]
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                addss (simpset() addsimps [singleton_eq_iff, the_equality])) 1);
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qed "WO8_WO1";