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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>







<a NAME="E1:2"/><i><font color="Green">E3</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K16">0.REAL</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="euclid.html#T46">EUCLID:46</a></i>;<br/>
<b>assume </b><a NAME="E2:2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K17">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K17">+</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E3:2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K17">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T9">JORDAN2C:9</a></i>;<br/>
<a NAME="E4:2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T9">JORDAN2C:9</a></i>;<br/>
<b>hence </b><font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="euclid.html#K16">0.REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="topreal9.html#E1:2"><i><font color="Green">E3</font></i></a>, <a class="ref" href="euclid.html#T31">EUCLID:31</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="euclid.html#T31">EUCLID:31</a></i>
;<br/><br/>


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