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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">x1</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>, <font color="Maroon">x2</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/>



<b>assume </b><a NAME="E1:35"/>
<font color="Maroon">x1</font> <a href="euclidlp.html#R1" target="_self">//</a> <font color="Maroon">x2</font>
 ;<br/>

<a NAME="E2:35"/><b>then </b><i><font color="Green">E59</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font> &amp;  ex <font color="Olive">r</font> being  <a href="real_1.html#NM1">Real</a> st <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Olive">r</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font> )
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">a</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E4:35"/><i><font color="Green">E66</font></i>: 
<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>
 ;<br/>
<a NAME="E5:35"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i>, , <a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a></i>;<br/>
<b>hence </b><a NAME="E6:35"/>
 ex <font color="Olive">a</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font> )
 <b>by </b><i/>;<br/>


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