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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">P</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="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">Q</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="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">R</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="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/>



<b>assume </b><a NAME="E1:48"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">P</font> is <a href="compts_1.html#V6">compact</a> &amp; <font color="Maroon">Q</font> is <a href="compts_1.html#V6">compact</a> &amp; <font color="Maroon">R</font> is <a href="compts_1.html#V6">compact</a> )
 ;<br/>

<b>reconsider </b><font color="Maroon">P1</font> = <font color="Maroon">P</font>, <font color="Maroon">Q1</font> = <font color="Maroon">Q</font>, <font color="Maroon">R1</font> = <font color="Maroon">R</font> as  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> <span class="p2">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">n</font></span>)</span></span>)</span> ;<br/>
<a NAME="E3:48"/>
(  <a href="hausdorf.html#K1" target="_self">HausDist</a> <font color="Maroon">P1</font>,<font color="Maroon">R1</font> <a href="hidden.html#R1">=</a>  <a href="hausdorf.html#K3" target="_self">HausDist</a> <font color="Maroon">P</font>,<font color="Maroon">R</font> &amp;  <a href="hausdorf.html#K1" target="_self">HausDist</a> <font color="Maroon">P1</font>,<font color="Maroon">Q1</font> <a href="hidden.html#R1">=</a>  <a href="hausdorf.html#K3" target="_self">HausDist</a> <font color="Maroon">P</font>,<font color="Maroon">Q</font> &amp;  <a href="hausdorf.html#K1" target="_self">HausDist</a> <font color="Maroon">Q1</font>,<font color="Maroon">R1</font> <a href="hidden.html#R1">=</a>  <a href="hausdorf.html#K3" target="_self">HausDist</a> <font color="Maroon">Q</font>,<font color="Maroon">R</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:48"/>
 <a href="hausdorf.html#K3" target="_self">HausDist</a> <font color="Maroon">P</font>,<font color="Maroon">R</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="hausdorf.html#K3" target="_self">HausDist</a> <font color="Maroon">P</font>,<font color="Maroon">Q</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="hausdorf.html#K3" target="_self">HausDist</a> <font color="Maroon">Q</font>,<font color="Maroon">R</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


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