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<b>thus </b><a NAME="E1:55_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a>  implies  ex <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="ordinal1.html#K5">omega</a>  st <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 ;<br/>

<b>assume </b><a NAME="E2:55_1_1"/>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a> 
 ;<br/>

<a NAME="E3:55_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">RATplus</font> <a href="subset_1.html#K6">\</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">k</font>,1</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="ordinal1.html#K5">omega</a>  : verum </span>}</span> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E4:55_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">RATplus</font>
 
;<br/>
<b>then consider </b><font color="Maroon">a</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="ordinal1.html#K5">omega</a> , <font color="Maroon">b</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="ordinal1.html#K5">omega</a> <b> such that </b><br/><a NAME="E6:55_1_1"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="arytm_3.html#R1" target="_self">are_relative_prime</a>  &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>
<b>take </b>
<font color="Maroon">a</font>
;<br/>

<b>take </b>
<font color="Maroon">b</font>
;<br/>

<b>thus </b><a NAME="E7:55_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i/>;<br/>


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