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<b>let </b><font color="Maroon" title="c3">i</font>, <font color="Maroon" title="c4">j</font> be  <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_3.html#K5" title="ARYTM_3:func.5">RAT+</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">i</font> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c4">j</font></span><br/>

<b>set </b><font color="Maroon" title="c5">ni</font> =  <a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <font color="Maroon" title="c3">i</font>;<br/>
<b>set </b><font color="Maroon" title="c6">nj</font> =  <a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <font color="Maroon" title="c4">j</font>;<br/>
<a NAME="E1:74"/><i><font color="Green" title="E67">A1</font></i>: 
( <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  &amp; <font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  )
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E2:74"/><b>then </b>
(  <a href="arytm_3.html#K7" title="ARYTM_3:func.7">denominator</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="arytm_3.html#K7" title="ARYTM_3:func.7">denominator</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<b>by </b><i><a class="ref" href="arytm_3.html#D9" target="_self" title="ARYTM_3:def.9">Def9</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c3">i</font> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <font color="Maroon" title="c4">j</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <font color="Maroon" title="c4">j</font></span>)</span></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> 1
<b>by </b><i><a class="ref" href="ordinal2.html#T56" title="ORDINAL2:th.56">ORDINAL2:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p1">(<span class="default"><a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <font color="Maroon" title="c4">j</font></span>)</span>
<b>by </b><i><a class="ref" href="arytm_3.html#T46" target="_self" title="ARYTM_3:th.46">Th46</a></i>
<br/>.= 
<font color="Maroon" title="c3">i</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p1">(<span class="default"><a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <font color="Maroon" title="c4">j</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:74"><i><font color="Green" title="E67">A1</font></i></a>, <a class="ref" href="arytm_3.html#D8" target="_self" title="ARYTM_3:def.8">Def8</a></i>
<br/>.= 
<font color="Maroon" title="c3">i</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c4">j</font>
<b>by </b><i><a class="txt" href="#E1:74"><i><font color="Green" title="E67">A1</font></i></a>, <a class="ref" href="arytm_3.html#D8" target="_self" title="ARYTM_3:def.8">Def8</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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