<?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> 3</span>)</span>;<br/>



<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> 3 <b>by </b><i><a class="ref" href="euclid.html#T25">EUCLID:25</a></i>;<br/>
<a NAME="E2:7"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K17">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="euclid.html#D10">EUCLID:def 10</a></i>;<br/>
<a NAME="E3:7"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="ref" href="euclid.html#T28">EUCLID:28</a></i>;<br/>
<a NAME="E4:7"/><b>then </b><i><font color="Green">E10</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 3
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E5:7"/><b>then </b><i><font color="Green">E11</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E6:7"/><i><font color="Green">E12</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="euclid_5.html#E4:7"><i><font color="Green">E10</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E7:7"/><i><font color="Green">E13</font></i>: 
3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="euclid_5.html#E4:7"><i><font color="Green">E10</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E8:7"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="euclid_5.html#K1" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="euclid_5.html#K1" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> 1 )
 
<b>by </b><i><a class="ref" href="euclid_5.html#D1" target="_self">Def1</a></i>;<br/>
<i><font color="Green">E15</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K17">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid_5.html#K1" target="_self">`1</a>  = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> 1
<b>by </b><i><a class="txt" href="euclid_5.html#E2:7"><i><font color="Green">E9</font></i></a>, <a class="ref" href="euclid_5.html#D1" target="_self">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span>
<b>by </b><i><a class="txt" href="euclid_5.html#E5:7"><i><font color="Green">E11</font></i></a>, <a class="txt" href="euclid_5.html#E8:7"><i><font color="Green">E14</font></i></a>, <a class="ref" href="rvsum_1.html#T26">RVSUM_1:26</a></i>
;<br/>
<a NAME="E10:7"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="euclid_5.html#K2" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> 2 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="euclid_5.html#K2" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> 2 )
 
<b>by </b><i><a class="ref" href="euclid_5.html#D2" target="_self">Def2</a></i>;<br/>
<i><font color="Green">E17</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K17">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid_5.html#K2" target="_self">`2</a>  = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> 2
<b>by </b><i><a class="txt" href="euclid_5.html#E2:7"><i><font color="Green">E9</font></i></a>, <a class="ref" href="euclid_5.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span>
<b>by </b><i><a class="txt" href="euclid_5.html#E6:7"><i><font color="Green">E12</font></i></a>, <a class="txt" href="euclid_5.html#E10:7"><i><font color="Green">E16</font></i></a>, <a class="ref" href="rvsum_1.html#T26">RVSUM_1:26</a></i>
;<br/>
<a NAME="E12:7"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="euclid_5.html#K3" target="_self">`3</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> 3 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="euclid_5.html#K3" target="_self">`3</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> 3 )
 
<b>by </b><i><a class="ref" href="euclid_5.html#D3" target="_self">Def3</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K17">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid_5.html#K3" target="_self">`3</a>  = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> 3
<b>by </b><i><a class="txt" href="euclid_5.html#E2:7"><i><font color="Green">E9</font></i></a>, <a class="ref" href="euclid_5.html#D3" target="_self">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span>
<b>by </b><i><a class="txt" href="euclid_5.html#E7:7"><i><font color="Green">E13</font></i></a>, <a class="txt" href="euclid_5.html#E12:7"><i><font color="Green">E18</font></i></a>, <a class="ref" href="rvsum_1.html#T26">RVSUM_1:26</a></i>
;<br/>
<b>hence </b><a NAME="E14:7"/>
<font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K17">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid_5.html#K4" target="_self">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span></span>)</span></span><a href="euclid_5.html#K4" target="_self">]|</a></span>
 <b>by </b><i><a class="txt" href="euclid_5.html#E9:7"><i><font color="Green">E15</font></i></a>, <a class="txt" href="euclid_5.html#E11:7"><i><font color="Green">E17</font></i></a>, <a class="ref" href="euclid_5.html#T3" target="_self">Th3</a></i>;<br/>


</div>
