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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="ordinal1.html#NM2">Ordinal</a>] <b>means </b> ex <font color="Olive">M</font> being  <a href="card_1.html#NM1">Cardinal</a> st <br/>( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">M</font> &amp;  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">X</font> <a href="card_1.html#NR2" target="_self">&lt;`</a> <font color="Olive">M</font> );<br/>
<a NAME="E1:21_1_1"/>
(  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">X</font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K1" target="_self">Card</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span> &amp;  <a href="card_1.html#K1" target="_self">Card</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1" target="_self">Card</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:21_1_1"/><b>then </b><i><font color="Green">E33</font></i>: 
 ex <font color="Olive">A</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">A</font>]
 
;<br/>
<b>consider </b><font color="Maroon">A</font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E4:21_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">A</font>]
 <b>and </b><br/><a NAME="E5:21_1_1"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">B</font>] holds <br/><font color="Maroon">A</font> <a href="ordinal1.html#R1">c=</a> <font color="Olive">B</font>
 <b>from </b><i><a class="ref" href="ordinal1.html#S1">ORDINAL1:sch 1</a>();<br/></i>
<b>consider </b><font color="Maroon">M</font> being   <a href="card_1.html#NM1">Cardinal</a><b> such that </b><br/><a NAME="E7:21_1_1"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> &amp;  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">X</font> <a href="card_1.html#NR2" target="_self">&lt;`</a> <font color="Maroon">M</font> )
 <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">M</font>
;<br/>

<b>thus </b><a NAME="E8:21_1_1"/>
 <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">X</font> <a href="card_1.html#NR2" target="_self">&lt;`</a> <font color="Maroon">M</font>
 <b>by </b><i/>;<br/>

<b>let </b><font color="Maroon">N</font> be   <a href="card_1.html#NM1">Cardinal</a>;<br/>

<b>assume </b><a NAME="E9:21_1_1"/>
 <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">X</font> <a href="card_1.html#NR2" target="_self">&lt;`</a> <font color="Maroon">N</font>
 ;<br/>

<b>hence </b><a NAME="E10:21_1_1"/>
<font color="Maroon">M</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">N</font>
 <b>by </b><i>, </i>;<br/>


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