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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">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>





<a NAME="E1:15"/><i><font color="Green">E11</font></i>: 
 <a href="jordan6.html#K6">Vertical_Line</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <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> : <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="jordan6.html#D6">JORDAN6:def 6</a></i>;<br/>
<b>assume </b><a NAME="E2:15"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K6">Vertical_Line</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K6">Vertical_Line</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E3:15"/><b>then </b><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="jordan6.html#T34">JORDAN6:34</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E4:15"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <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/>
<a NAME="E6:15"/>
<font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="jordan1a.html#E3:15"><i><font color="Green">E12</font></i></a>, <a class="txt" href="jordan1a.html#E4:15"><i><font color="Green">E13</font></i></a>, <a class="ref" href="goboard7.html#T5">GOBOARD7:5</a></i>;<br/>
<b>hence </b><a NAME="E7:15"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K6">Vertical_Line</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="jordan1a.html#E1:15"><i><font color="Green">E11</font></i></a></i>;<br/>


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