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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="sub_metr.html#NM1">PseudoMetricSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <a href="metric_2.html#K2" target="_self">-neighbour</a> ;<br/>



<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:52"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="metric_2.html#K1" target="_self">-neighbour</a> 
 <b>by </b><i><a class="ref" href="metric_2.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E3:52"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="metric_2.html#E2:52"><i><font color="Green">E27</font></i></a>, <a class="ref" href="metric_2.html#T9" target="_self">Th9</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:52"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="metric_2.html#K1" target="_self">-neighbour</a> 
 <b>by </b><i><a class="ref" href="metric_2.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E6:52"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="metric_2.html#E5:52"><i><font color="Green">E29</font></i></a>, <a class="ref" href="metric_2.html#T9" target="_self">Th9</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><a href="metric_2.html#K10" target="_self">nbourdist</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> = 
 <a href="metric_1.html#K4">dist</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="metric_2.html#E3:52"><i><font color="Green">E28</font></i></a>, <a class="ref" href="metric_2.html#D13" target="_self">Def13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="metric_2.html#K10" target="_self">nbourdist</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="metric_2.html#E3:52"><i><font color="Green">E28</font></i></a>, <a class="txt" href="metric_2.html#E6:52"><i><font color="Green">E30</font></i></a>, <a class="ref" href="metric_2.html#D13" target="_self">Def13</a></i>
;<br/>
<b>hence </b><a NAME="E8:52"/>
<span class="p1">(<span class="default"><a href="metric_2.html#K10" target="_self">nbourdist</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="metric_2.html#K10" target="_self">nbourdist</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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