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<b>let </b><font color="Maroon">r1</font> be   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">r2</font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:38_1_2_1"/>
<font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>assume </b><b>that </b><br/><a NAME="E2:38_1_2_1"/><i><font color="Green">E76</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">N</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> holds <br/> <a href="metric_1.html#K2">dist</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r1</font>
 <b>and </b><br/><a NAME="E3:38_1_2_1"/><i><font color="Green">E77</font></i>: 
for <font color="Olive">s</font> being  <a href="real_1.html#NM1">Real</a>  st ( for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">N</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> holds <br/> <a href="metric_1.html#K2">dist</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">s</font> ) holds <br/><font color="Maroon">r1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">s</font>
 <b>and </b><br/><a NAME="E4:38_1_2_1"/><i><font color="Green">E78</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">N</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> holds <br/> <a href="metric_1.html#K2">dist</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r2</font>
 <b>and </b><br/><a NAME="E5:38_1_2_1"/><i><font color="Green">E79</font></i>: 
for <font color="Olive">s</font> being  <a href="real_1.html#NM1">Real</a>  st ( for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">N</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> holds <br/> <a href="metric_1.html#K2">dist</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">s</font> ) holds <br/><font color="Maroon">r2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">s</font>
 ;<br/><a NAME="E6:38_1_2_1"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">r1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r2</font>
 <b>by </b><i>, </i>;<br/><a NAME="E7:38_1_2_1"/>
<font color="Maroon">r2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r1</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E8:38_1_2_1"/>
<font color="Maroon">r1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r2</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:38_1_2"/>
( not <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">r1</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">r2</font> <a href="hidden.html#R1">=</a> 0 implies <font color="Maroon">r1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r2</font> )
 ;<br/>


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