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

<span class="kw">let </span><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>) implies (<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c4">x</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E1:3_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="metric_2.html#R1" title="METRIC_2:pred.1">tolerates</a> <font color="Maroon" title="c5">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c4">x</font>)</span><br/>

<a NAME="E2:3_1_1"/><span class="kw">then </span>
 <a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E3:3_1_1"/>
(<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c4">x</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
