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<a NAME="E1:9_1_1"/>
<font color="Maroon">P</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">k</font>,<font color="Olive">l</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">k</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Olive">l</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  : 7 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">l</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:9_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">k</font>,<font color="Maroon">l</font></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E4:9_1_1"/><i><font color="Green">E33</font></i>: 
7 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 ;<br/>
<a NAME="E5:9_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> <a href="mcart_1.html#K1">`1</a> 
 
<b>by </b><i>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<b>consider </b><font color="Maroon">w</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E7:9_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 7 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">w</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<a NAME="E8:9_1_1"/>
<font color="Maroon">w</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E9:9_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <font color="Maroon">P</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> 7 <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i>, </i>;<br/>


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