# HG changeset patch
# User lcp
# Date 797163648 -7200
# Node ID 0697024c3cca0843aac7e076e5eac5c3bdab0110
# Parent  0df2af5cba40eb578cc90615a873c19ad938b8f2
Received some local definitions from AC_Equiv.thy.

diff -r 0df2af5cba40 -r 0697024c3cca src/ZF/AC/WO6_WO1.thy
--- a/src/ZF/AC/WO6_WO1.thy	Thu Apr 06 12:19:34 1995 +0200
+++ b/src/ZF/AC/WO6_WO1.thy	Thu Apr 06 12:20:48 1995 +0200
@@ -1,3 +1,45 @@
-(*Dummy theory to document dependencies *)
+(*  Title: 	ZF/AC/WO6_WO1.thy
+    ID:         $Id$
+    Author: 	Krzysztof Gr`abczewski
+
+The proof of "WO6 ==> WO1".
+
+From the book "Equivalents of the Axiom of Choice" by Rubin & Rubin,
+pages 2-5
+*)
+
+WO6_WO1 = "rel_is_fun" + AC_Equiv +
+
+consts
+(* Auxiliary definitions used in proof *)
+  NN       :: "i => i"
+  uu       :: "[i, i, i, i] => i"
+  vv1, ww1 :: "[i, i, i] => i"
+  vv2, ww2 :: "[i, i, i, i] => i"
+
+defs
 
-WO6_WO1 = "rel_is_fun" + AC_Equiv
+  NN_def  "NN(y) == {m:nat. EX a. EX f. Ord(a) & domain(f)=a  &  \
+\			    (UN b<a. f`b) = y & (ALL b<a. f`b lepoll m)}"
+
+  uu_def  "uu(f, beta, gamma, delta) == (f`beta * f`gamma) Int f`delta"
+  
+  vv1_def "vv1(f,b,m) == if(f`b ~= 0,   \
+\          domain(uu(f,b,   \
+\          LEAST g. (EX d. Ord(d) & (domain(uu(f,b,g,d)) ~= 0 &   \
+\	   domain(uu(f,b,g,d)) lesspoll m)),   \
+\          LEAST d. domain(uu(f,b,   \
+\          LEAST g. (EX d. Ord(d) & (domain(uu(f,b,g,d)) ~= 0 &   \
+\	   domain(uu(f,b,g,d)) lesspoll m)), d)) ~= 0 &   \
+\          domain(uu(f,b,   \
+\          LEAST g. (EX d. Ord(d) & (domain(uu(f,b,g,d)) ~= 0 &   \
+\	   domain(uu(f,b,g,d)) lesspoll m)), d)) lesspoll m)), 0)"
+
+  ww1_def "ww1(f,b,m) == f`b - vv1(f,b,m)"
+
+  vv2_def "vv2(f,b,g,s) ==   \
+\	   if(f`g ~= 0, {uu(f,b,g,LEAST d. uu(f,b,g,d) ~= 0)`s}, 0)"
+
+  ww2_def "ww2(f,b,g,s) == f`g - vv2(f,b,g,s)"
+
+end