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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>

<b>assume </b><a NAME="E1:16"/><i><font color="Green">E10</font></i>: 
(  <a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c<sub>1</sub></font> <a href="arytm_3.html#R1" target="_self">are_relative_prime</a>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 ;<br/>

<a NAME="E2:16"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> 1 or 1 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#T24">ORDINAL1:24</a></i>;<br/>
<a NAME="E3:16"/><b>then </b>
( 1 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11">*^</a> <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11">*^</a> 1 )
 
<b>by </b><i><a class="txt" href="arytm_3.html#E1:16"><i><font color="Green">E10</font></i></a>, <a class="ref" href="arytm_3.html#T5" target="_self">Th5</a>, <a class="ref" href="ordinal2.html#T55">ORDINAL2:55</a>, <a class="ref" href="ordinal2.html#T56">ORDINAL2:56</a>, <a class="ref" href="ordinal3.html#T17">ORDINAL3:17</a></i>;<br/>
<b>hence </b><a NAME="E4:16"/>
contradiction
 <b>by </b><i><a class="txt" href="arytm_3.html#E1:16"><i><font color="Green">E10</font></i></a>, <a class="ref" href="arytm_3.html#D2" target="_self">Def2</a></i>;<br/>


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