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<b>let </b><font color="Maroon">i</font> be  <a href="ordinal1.html#V3">ordinal</a>  <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7" target="_self">RAT+</a> , <font color="Maroon">j</font> be  <a href="ordinal1.html#V3">ordinal</a>  <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7" target="_self">RAT+</a> ;<br/>

<b>set </b><font color="Maroon">ni</font> =  <a href="arytm_3.html#K8" target="_self">numerator</a> <font color="Maroon">i</font>;<br/>
<b>set </b><font color="Maroon">nj</font> =  <a href="arytm_3.html#K8" target="_self">numerator</a> <font color="Maroon">j</font>;<br/>
<a NAME="E1:84"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a>  &amp; <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a>  )
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E2:84"/><b>then </b>
(  <a href="arytm_3.html#K9" target="_self">denominator</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="arytm_3.html#K9" target="_self">denominator</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> 1 )
 
<b>by </b><i/>;<br/>
<b>hence </b><font color="Maroon">i</font> <a href="arytm_3.html#K11" target="_self">+</a> <font color="Maroon">j</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K8" target="_self">numerator</a> <font color="Maroon">i</font></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> 1</span>)</span> <a href="arytm_3.html#K2" target="_self">+^</a> <span class="p2">(<span class="default">1 <a href="arytm_3.html#K3" target="_self">*^</a> <span class="p3">(<span class="default"><a href="arytm_3.html#K8" target="_self">numerator</a> <font color="Maroon">j</font></span>)</span></span>)</span></span>)</span> <a href="arytm_3.html#K10" target="_self">/</a> 1
<b>by </b><i><a class="ref" href="ordinal2.html#T56">ORDINAL2:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K8" target="_self">numerator</a> <font color="Maroon">i</font></span>)</span> <a href="arytm_3.html#K2" target="_self">+^</a> <span class="p2">(<span class="default">1 <a href="arytm_3.html#K3" target="_self">*^</a> <span class="p3">(<span class="default"><a href="arytm_3.html#K8" target="_self">numerator</a> <font color="Maroon">j</font></span>)</span></span>)</span></span>)</span> <a href="arytm_3.html#K10" target="_self">/</a> 1
<b>by </b><i><a class="ref" href="ordinal2.html#T56">ORDINAL2:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K8" target="_self">numerator</a> <font color="Maroon">i</font></span>)</span> <a href="arytm_3.html#K2" target="_self">+^</a> <span class="p2">(<span class="default"><a href="arytm_3.html#K8" target="_self">numerator</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="arytm_3.html#K10" target="_self">/</a> 1
<b>by </b><i><a class="ref" href="ordinal2.html#T56">ORDINAL2:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="arytm_3.html#K8" target="_self">numerator</a> <font color="Maroon">i</font></span>)</span> <a href="arytm_3.html#K2" target="_self">+^</a> <span class="p1">(<span class="default"><a href="arytm_3.html#K8" target="_self">numerator</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i><a class="ref" href="arytm_3.html#T11" target="_self">Th11</a></i>
<br/>.= 
<font color="Maroon">i</font> <a href="arytm_3.html#K2" target="_self">+^</a> <span class="p1">(<span class="default"><a href="arytm_3.html#K8" target="_self">numerator</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i><a class="ref" href="arytm_3.html#T22" target="_self">Th22</a>, </i>
<br/>.= 
<font color="Maroon">i</font> <a href="arytm_3.html#K2" target="_self">+^</a> <font color="Maroon">j</font>
<b>by </b><i><a class="ref" href="arytm_3.html#T22" target="_self">Th22</a>, </i>
;<br/><br/>


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