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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="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K1">REAL</a> ,<a href="numbers.html#K1">REAL</a> </span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="mcart_1.html#K1">`1</a> , <font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="mcart_1.html#K2">`2</a> , <font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="mcart_1.html#K1">`1</a> , <font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="mcart_1.html#K2">`2</a>  as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  <b>by </b><i><a class="ref" href="mcart_1.html#T10">MCART_1:10</a></i>;<br/>
<a NAME="E2:25"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="domain_1.html#K1">]</a></span> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T24">MCART_1:24</a></i>;<br/>
<b>then </b><a href="metric_4.html#K9" target="_self">Eukl_dist2</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="metric_1.html#K7">real_dist</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="metric_1.html#K7">real_dist</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="metric_4.html#D9" target="_self">Def9</a></i>
<br/>.= 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="metric_1.html#K7">real_dist</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="metric_1.html#K7">real_dist</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="metric_1.html#T10">METRIC_1:10</a></i>
<br/>.= 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="metric_1.html#K7">real_dist</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="metric_1.html#K7">real_dist</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="metric_1.html#T10">METRIC_1:10</a></i>
<br/>.= 
<a href="metric_4.html#K9" target="_self">Eukl_dist2</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="metric_4.html#E2:25"><i><font color="Green">E21</font></i></a>, <a class="ref" href="metric_4.html#D9" target="_self">Def9</a></i>
;<br/>
<b>hence </b><a NAME="E4:25"/>
<a href="metric_4.html#K9" target="_self">Eukl_dist2</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <a href="metric_4.html#K9" target="_self">Eukl_dist2</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 ;<br/>


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