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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM8">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>





<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span>;<br/>
<b>assume </b><a NAME="E1:39"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> )
 ;<br/>

<a NAME="E2:39"/><b>then </b><i><font color="Green">E21</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> 2 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a>, <a class="ref" href="finseq_4.html#T27">FINSEQ_4:27</a></i>;<br/>
<b>hence </b><a NAME="E3:39"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E4:39"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2 &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2 )
 
<b>by </b><i><a class="txt" href="topreal3.html#E1:39"><i><font color="Green">E20</font></i></a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<b>hence </b><a NAME="E5:39"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 )
 <b>by </b><i><a class="txt" href="topreal3.html#E1:39"><i><font color="Green">E20</font></i></a>, <a class="txt" href="topreal3.html#E2:39"><i><font color="Green">E21</font></i></a>, <a class="ref" href="finseq_3.html#T104">FINSEQ_3:104</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="topreal1.html#D10">TOPREAL1:def 10</a><br/>

<b>thus </b><a NAME="E6:39"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="topreal1.html#V2">unfolded</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="topreal1.html#D8">TOPREAL1:def 8</a><br/>

<b>assume </b><a NAME="E1:39_1"/><i><font color="Green">E22</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:39_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 
<b>by </b><i><a class="txt" href="topreal3.html#E2:39"><i><font color="Green">E21</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E3:39_1"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="topreal3.html#E1:39_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,2</span>)</span>
<b>by </b><i><a class="txt" href="topreal3.html#E2:39"><i><font color="Green">E21</font></i></a>, <a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="topreal3.html#E2:39"><i><font color="Green">E21</font></i></a>, <a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="txt" href="topreal3.html#E1:39"><i><font color="Green">E20</font></i></a>, <a class="txt" href="topreal3.html#E2:39"><i><font color="Green">E21</font></i></a>, <a class="txt" href="topreal3.html#E3:39_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="topreal3.html#T39" target="_self">Th39</a></i>
;<br/><br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E7:39"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="topreal1.html#V3">s.n.c.</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="topreal1.html#D9">TOPREAL1:def 9</a><br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:39_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:39_2_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_2_1_1_1"><b>suppose </b></a><a NAME="E1:39_2_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:39_2_1_1_1"/><b>then </b>
 <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>;<br/><a NAME="E3:39_2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>hence </b><a NAME="E4:39_2_1_1_1"/>
 <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_2_1_1_2"><b>suppose </b></a><a NAME="E1:39_2_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:39_2_1_1_2"/><b>then </b>
 <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="topreal3.html#E1:39"><i><font color="Green">E20</font></i></a>, <a class="txt" href="topreal3.html#E1:39_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="topreal3.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E3:39_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>hence </b><a NAME="E4:39_2_1_1_2"/>
 <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:39_2"/>
 <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 ;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="topreal1.html#D7">TOPREAL1:def 7</a><br/>

<b>assume </b><a NAME="E8:39"/><i><font color="Green">E22</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<a NAME="E9:39"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 2 &amp; <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 
<b>by </b><i><a class="txt" href="topreal3.html#E2:39"><i><font color="Green">E21</font></i></a>, <a class="txt" href="topreal3.html#E8:39"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:39_3"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="topreal3.html#E9:39"><i><font color="Green">E23</font></i></a>, <a class="ref" href="cqc_the1.html#T3">CQC_THE1:3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_3_1"><b>suppose </b></a><a NAME="E1:39_3_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:39_3_1"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K21">`1</a>  or <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K22">`2</a>  )
 <b>by </b><i><a class="txt" href="topreal3.html#E2:39"><i><font color="Green">E21</font></i></a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_3_2"><b>suppose </b></a><a NAME="E1:39_3_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>hence </b><a NAME="E2:39_3_2"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K21">`1</a>  or <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K22">`2</a>  )
 <b>by </b><i><a class="txt" href="topreal3.html#E1:39"><i><font color="Green">E20</font></i></a>, <a class="txt" href="topreal3.html#E2:39"><i><font color="Green">E21</font></i></a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
