<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">M</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="metric_1.html#NM1" title="METRIC_1:NM.1">MetrSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:19_1"/>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">x</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</a> 
 ;<br/><a NAME="E2:19_1"/><b>then </b>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">q</font> where <font color="Olive" title="b1">q</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font> : <font color="Maroon" title="c2">x</font> <a href="metric_2.html#R3" title="METRIC_2:pred.3">tolerates</a> <font color="Olive" title="b1">q</font> </span>}</span> 
 ;<br/><a NAME="E3:19_1"/><b>then </b>
 ex <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font> st <br/>( <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">q</font> &amp; <font color="Maroon" title="c2">x</font> <a href="metric_2.html#R3" title="METRIC_2:pred.3">tolerates</a> <font color="Olive" title="b1">q</font> )
 ;<br/><b>hence </b><a NAME="E4:19_1"/>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="ref" href="metric_2.html#T18" target="_self" title="METRIC_2:th.18">Th18</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:19"/>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 ;<br/>

<a NAME="E3:19"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="metric_2.html#R3" title="METRIC_2:pred.3">tolerates</a> <font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="ref" href="metric_2.html#T18" target="_self" title="METRIC_2:th.18">Th18</a></i>;<br/>
<a NAME="E4:19"/><b>then </b>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">q</font> where <font color="Olive" title="b1">q</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font> : <font color="Maroon" title="c2">x</font> <a href="metric_2.html#R3" title="METRIC_2:pred.3">tolerates</a> <font color="Olive" title="b1">q</font> </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E5:19"/>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">x</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</a> 
 ;<br/>


</div>
