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<b>let </b><font color="Maroon">V</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="metric_1.html#L1">MetrStruct</a> ;<br/>

<b>thus </b> <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">V</font></span>)</span> = 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font></span>)</span>
<b>by </b><i><a class="ref" href="grcat_1.html#D11">GRCAT_1:def 11</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>
<b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="vectmetr.html#D3" target="_self">VECTMETR:def 3</a><br/>

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/>

<b>thus </b> <a href="metric_1.html#K2">dist</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> = 
 <a href="metric_1.html#K2">dist</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">V</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>,<font color="Maroon">y</font>
<b>by </b><i><a class="ref" href="grcat_1.html#T11">GRCAT_1:11</a></i>
<br/>.= 
 <a href="metric_1.html#K2">dist</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">V</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">V</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i><a class="ref" href="grcat_1.html#T11">GRCAT_1:11</a></i>
;<br/>


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