<?xml version="1.0"?>
<div class="add">

<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">x</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>thus </b> <a href="euclid.html#K6">-</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="euclid.html#K5">0*</a> <font color="Maroon">n</font></span>)</span> <a href="euclid.html#K8">-</a> <font color="Maroon">x</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default">0 <a href="euclid.html#K9">*</a> <font color="Maroon">x</font></span>)</span> <a href="euclid.html#K8">-</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="real_1.html#K3">+</a> 1</span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K6">-</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default">1 <a href="euclid.html#K9">*</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K6">-</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T7">EUCLID_4:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x</font></span>)</span> <a href="euclid.html#K7">+</a> <font color="Maroon">x</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K6">-</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K5">0*</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T1">EUCLID_4:1</a></i>
;<br/>


</div>
