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<b>let </b><font color="Maroon">a1</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">a2</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">a3</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="finseq_2.html#M2">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="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">x3</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="E1:29"/>
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">a2</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">a3</font> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<a NAME="E2:29"/><b>then </b>
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">a2</font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">a3</font>
 
;<br/>
<b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span> <a href="euclid.html#K8">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K8">-</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</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"><font color="Maroon">x1</font> <a href="euclid.html#K8">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K8">-</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</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"><span class="p3">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K8">-</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</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"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</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"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p4">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x3</font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">x3</font> <a href="euclid.html#K8">-</a> <font color="Maroon">x1</font></span>)</span></span>)</span>
<b>by </b><i/>
;<br/><br/>


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