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<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" target="_self">TOP-REAL</a> 2</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" target="_self">REAL</a> 2 ;<br/>
<a NAME="E2:77"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K17" target="_self">+</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" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="euclid.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E3:77"/>
 <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" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="ref" href="euclid.html#T28" target="_self">Th28</a></i>;<br/>
<a NAME="E4:77"/><b>then </b><i><font color="Green">E52</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" target="_self">+</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> 2 &amp; 2 <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span> &amp; 1 <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E5:77"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 )
 
<b>by </b><i><a class="ref" href="euclid.html#D14" target="_self">Def14</a></i>;<br/>
<i><font color="Green">E54</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K17" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21" target="_self">`1</a>  = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K7" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="euclid.html#E2:77"><i><font color="Green">E51</font></i></a>, <a class="ref" href="euclid.html#D14" target="_self">Def14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21" target="_self">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21" target="_self">`1</a> </span>)</span>
<b>by </b><i><a class="txt" href="euclid.html#E4:77"><i><font color="Green">E52</font></i></a>, <a class="txt" href="euclid.html#E5:77"><i><font color="Green">E53</font></i></a>, <a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="rvsum_1.html#T26">RVSUM_1:26</a></i>
;<br/>
<a NAME="E7:77"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 2 )
 
<b>by </b><i><a class="ref" href="euclid.html#D15" target="_self">Def15</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K17" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22" target="_self">`2</a>  = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K7" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="euclid.html#E2:77"><i><font color="Green">E51</font></i></a>, <a class="ref" href="euclid.html#D15" target="_self">Def15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22" target="_self">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22" target="_self">`2</a> </span>)</span>
<b>by </b><i><a class="txt" href="euclid.html#E4:77"><i><font color="Green">E52</font></i></a>, <a class="txt" href="euclid.html#E7:77"><i><font color="Green">E55</font></i></a>, <a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="rvsum_1.html#T26">RVSUM_1:26</a></i>
;<br/>
<b>hence </b><a NAME="E9:77"/>
<font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K17" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23" 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.html#K21" target="_self">`1</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21" 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.html#K22" target="_self">`2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22" target="_self">`2</a> </span>)</span></span>)</span></span><a href="euclid.html#K23" target="_self">]|</a></span>
 <b>by </b><i><a class="txt" href="euclid.html#E6:77"><i><font color="Green">E54</font></i></a>, <a class="ref" href="euclid.html#T57" target="_self">Th57</a></i>;<br/>


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