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<b>let </b><font color="Maroon" title="c1">a</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">x2</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c2">n</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:8"/><i><font color="Green" title="E7">A1</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">x2</font>
 <b>and </b><br/><a NAME="E2:8"/><i><font color="Green" title="E8">A2</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<a NAME="E3:8"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">x2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="euclid_4.html#E1:8"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="euclid_4.html#T4" target="_self" title="EUCLID_4:th.4">Th4</a></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#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">x2</font>
 
<b>by </b><i><a class="ref" href="euclid_4.html#T4" target="_self" title="EUCLID_4:th.4">Th4</a></i>;<br/>
<a NAME="E5:8"/><b>then </b>
1 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">x2</font>
 
<b>by </b><i><a class="txt" href="euclid_4.html#E2:8"><i><font color="Green" title="E8">A2</font></i></a>, <a class="ref" href="xcmplx_1.html#T107" title="XCMPLX_1:th.107">XCMPLX_1:107</a></i>;<br/>
<a NAME="E6:8"/><b>then </b>
1 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">x2</font>
 
<b>by </b><i><a class="txt" href="euclid_4.html#E2:8"><i><font color="Green" title="E8">A2</font></i></a>, <a class="ref" href="xcmplx_1.html#T107" title="XCMPLX_1:th.107">XCMPLX_1:107</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c3">x1</font> = 
1 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c4">x2</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T3" target="_self" title="EUCLID_4:th.3">Th3</a></i>
<br/>.= 
<font color="Maroon" title="c4">x2</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T3" target="_self" title="EUCLID_4:th.3">Th3</a></i>
;<br/><br/>


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