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<b>let </b><font color="Maroon">a</font> be   <a href="real_1.html#NM1">Real</a>;<br/><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">x1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">x2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:8"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">a</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font>
 <b>and </b><br/><a NAME="E2:8"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<a NAME="E3:8"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">a</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">a</font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:8"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">a</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">a</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:8"/><b>then </b>
1 <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">a</font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font>
 
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T107">XCMPLX_1:107</a></i>;<br/>
<a NAME="E6:8"/><b>then </b>
1 <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> 1 <a href="euclid.html#K9">*</a> <font color="Maroon">x2</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">x1</font> = 
1 <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">x2</font>
<b>by </b><i/>
;<br/><br/>


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