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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   <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>let </b><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#K14">Euclid</a> <font color="Maroon">n</font></span>)</span>;<br/>





<b>reconsider </b><font color="Maroon">M</font> =  <a href="pcomps_1.html#K4">TopSpaceMetr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">n</font></span>)</span> <a href="topmetr.html#K1" target="_self">|</a> <font color="Maroon">Q</font></span>)</span> as    <a href="pre_topc.html#M1">SubSpace</a> of  <a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font> <b>by </b><i/>;<br/>
<b>assume </b><a NAME="E2:26"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Q</font>
 ;<br/>

<a NAME="E3:26"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">n</font></span>)</span> <a href="topmetr.html#K1" target="_self">|</a> <font color="Maroon">Q</font></span>)</span> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">n</font></span>)</span> <a href="topmetr.html#K1" target="_self">|</a> <font color="Maroon">Q</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">Q</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:26"/><b>then </b>
(  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> &amp;  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">P</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> )
 
<b>by </b><i>, <a class="ref" href="pre_topc.html#D10">PRE_TOPC:def 10</a></i>;<br/>
<b>hence </b><a NAME="E5:26"/>
<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="pcomps_1.html#K4">TopSpaceMetr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">n</font></span>)</span> <a href="topmetr.html#K1" target="_self">|</a> <font color="Maroon">Q</font></span>)</span>
 <b>by </b><i><a class="ref" href="pre_topc.html#D10">PRE_TOPC:def 10</a></i>;<br/>


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