src/ZF/AC/WO1_WO8.ML

Krzysztof Grabczewski's (nearly) complete AC proofs

(*  Title: 	ZF/AC/WO1_WO8.ML
    ID:         $Id$
    Author: 	Krzysztof Gr`abczewski

The proof of WO8 <-> WO1 (Rubin & Rubin p. 6)
*)

(* ********************************************************************** *)
(* Trivial implication "WO1 ==> WO8"					  *)
(* ********************************************************************** *)

goalw thy WO_defs "!!Z. WO1 ==> WO8";
by (fast_tac ZF_cs 1);
result();

(* ********************************************************************** *)
(* The proof of "WO8 ==> WO1" - faithful image of Rubin & Rubin's proof	  *)
(* ********************************************************************** *)

goalw thy WO_defs "!!Z. WO8 ==> WO1";
by (resolve_tac [allI] 1);
by (eres_inst_tac [("x","{{x}. x:A}")] allE 1);
by (eresolve_tac [impE] 1);
by (fast_tac (AC_cs addSEs [lam_sing_bij RS bij_is_inj RS
			well_ord_rvimage]) 2);
by (res_inst_tac [("x","lam a:{{x}. x:A}. THE x. a={x}")] exI 1);
by (fast_tac (ZF_cs addSEs [RepFunE, singleton_eq_iff RS iffD1 RS sym]
		addSIs [lam_type, singletonI]
		addIs [the_equality RS ssubst]) 1);
result();