<?xml version="1.0"?>
<div class="add">

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>] <b>means </b>(  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> $1 &amp; $1 is <a href="ordinal1.html#V4" title="ORDINAL1:attr.4">limit_ordinal</a> );<br/>
<a NAME="E1:64_1_1"/><i><font color="Green" title="E33">A1</font></i>: 
 ex <font color="Olive" title="b1">A</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">A</font>]
 
<b>by </b><i><a class="ref" href="ordinal1.html#T51" target="_self" title="ORDINAL1:th.51">Th51</a></i>;<br/>
<a NAME="E2:64_1_1"/>
 ex <font color="Olive" title="b1">C</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> st <br/>( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">C</font>] &amp; ( for <font color="Olive" title="b2">A</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">A</font>] holds <br/><font color="Olive" title="b1">C</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b2">A</font> ) )
 
<b>from </b><i><a class="ref" href="ordinal1.html#S1" target="_self" title="ORDINAL1:sch.1">ORDINAL1:sch 1</a>(<a class="txt" href="#E1:64_1_1"><i><font color="Green" title="E33">A1</font></i></a>);<br/></i>
<b>hence </b><a NAME="E3:64_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>(  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="ordinal1.html#V4" title="ORDINAL1:attr.4">limit_ordinal</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a> &amp; ( for <font color="Olive" title="b2">A</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b2">A</font> is <a href="ordinal1.html#V4" title="ORDINAL1:attr.4">limit_ordinal</a> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
