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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">p1</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" target="_self">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">p2</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" target="_self">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">x</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:54"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p2</font>
 <b>and </b><br/><a NAME="E2:54"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<a NAME="E3:54"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">x</font></span>)</span> <a href="euclid.html#K18" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="euclid.html#E1:54"><i><font color="Green">E35</font></i></a>, <a class="ref" href="euclid.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E4:54"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p2</font>
 
<b>by </b><i><a class="ref" href="euclid.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E5:54"/><b>then </b>
1 <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p2</font>
 
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T107">XCMPLX_1:107</a></i>;<br/>
<a NAME="E6:54"/><b>then </b>
1 <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> 1 <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p2</font>
 
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T107">XCMPLX_1:107</a></i>;<br/>
<b>hence </b><font color="Maroon">p1</font> = 
1 <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p2</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">p2</font>
<b>by </b><i/>
;<br/><br/>


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