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<b>let </b><font color="Maroon" title="c1">M</font> be   <a href="sub_metr.html#NM1" title="SUB_METR:NM.1">PseudoMetricSpace</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="E1:13_1"/>
<font color="Maroon" title="c2">x</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</a> 
 ;<br/><a NAME="E2:13_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">y</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</a> 
 <b>by </b><i><a class="ref" href="metric_2.html#T9" target="_self" title="METRIC_2:th.9">Th9</a></i>;<br/><b>hence </b><a NAME="E3:13_1"/>
<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#T7" target="_self" title="METRIC_2:th.7">Th7</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:13"/>
<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>
 ;<br/>

<a NAME="E3:13"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">y</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</a> 
 
;<br/>
<b>hence </b><a NAME="E4:13"/>
<font color="Maroon" title="c2">x</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</a> 
 <b>by </b><i><a class="ref" href="metric_2.html#T12" target="_self" title="METRIC_2:th.12">Th12</a></i>;<br/>


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