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<b>given </b><font color="Maroon">c<sub>1</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E1:43"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a> holds <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] means <font color="Maroon">a<sub>1</sub></font> is   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:43"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> iff ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:43_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is   <a href="ordinal1.html#NM2">Ordinal</a>
 ;<br/><a NAME="E2:43_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="ordinal1.html#E1:43"><i><font color="Green">E26</font></i></a></i>;<br/><b>hence </b><a NAME="E3:43_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="ordinal1.html#E3:43"><i><font color="Green">E27</font></i></a>, <a class="txt" href="ordinal1.html#E1:43_1"><i><font color="Green">E28</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:43"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> iff <font color="Olive">b<sub>1</sub></font> is   <a href="ordinal1.html#NM2">Ordinal</a> )
 
<b>by </b><i><a class="txt" href="ordinal1.html#E3:43"><i><font color="Green">E27</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:43"/>
contradiction
 <b>by </b><i><a class="ref" href="ordinal1.html#T37" target="_self">Th37</a></i>;<br/>


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