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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="metric_1.html#NM1">MetrSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pcomps_1.html#K4">TopSpaceMetr</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>



<b>assume </b><a NAME="E1:40"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="compts_1.html#V6">compact</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="compts_1.html#V6">compact</a> )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="40_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:40_1"/>
(  <a href="hausdorf.html#K1" target="_self">HausDist</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="weierstr.html#K10">max_dist_min</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> or  <a href="hausdorf.html#K1" target="_self">HausDist</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="weierstr.html#K10">max_dist_min</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 </span><b>by </b><i><a class="ref" href="xxreal_0.html#T16">XXREAL_0:16</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="40_1_1"><b>suppose </b></a><a NAME="E1:40_1_1"/>
 <a href="hausdorf.html#K1" target="_self">HausDist</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="weierstr.html#K10">max_dist_min</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:40_1_1"/>
 <a href="hausdorf.html#K1" target="_self">HausDist</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="hausdorf.html#E1:40"><i><font color="Green">E33</font></i></a>, <a class="ref" href="hausdorf.html#T30" target="_self">Th30</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="40_1_2"><b>suppose </b></a><a NAME="E1:40_1_2"/>
 <a href="hausdorf.html#K1" target="_self">HausDist</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="weierstr.html#K10">max_dist_min</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:40_1_2"/>
 <a href="hausdorf.html#K1" target="_self">HausDist</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="hausdorf.html#E1:40"><i><font color="Green">E33</font></i></a>, <a class="ref" href="hausdorf.html#T30" target="_self">Th30</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
