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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="ordinal1.html#K5">omega</a> ;<br/><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="ordinal1.html#K5">omega</a> ;<br/>



<b>assume </b><a NAME="E1:66"/>
<font color="Maroon">i</font>,<font color="Maroon">j</font> <a href="arytm_3.html#R1" target="_self">are_relative_prime</a> 
 ;<br/>

<a NAME="E2:66"/><b>then </b>
(  <a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">i</font>,<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> &amp;  <a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">j</font>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:66"/>
(  not <font color="Maroon">j</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  or (  <a href="arytm_3.html#K8" target="_self">numerator</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="arytm_3.html#K10" target="_self">/</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> &amp;  <a href="arytm_3.html#K9" target="_self">denominator</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="arytm_3.html#K10" target="_self">/</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> ) )
 <b>by </b><i><a class="ref" href="arytm_3.html#T14" target="_self">Th14</a></i>;<br/>


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