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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>assume </b><a NAME="E1:38"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="frechet.html#V3">Frechet</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>thus </b><a NAME="E2:38"/>
(  <a href="frechet2.html#K3" target="_self">Cl_Seq</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="frechet2.html#K3" target="_self">Cl_Seq</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="frechet2.html#K3" target="_self">Cl_Seq</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="frechet2.html#K3" target="_self">Cl_Seq</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="frechet2.html#K3" target="_self">Cl_Seq</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="frechet2.html#T20" target="_self">Th20</a>, <a class="ref" href="frechet2.html#T21" target="_self">Th21</a>, <a class="ref" href="frechet2.html#T22" target="_self">Th22</a></i>;<br/>

<b>thus </b> <a href="frechet2.html#K3" target="_self">Cl_Seq</a> <span class="p1">(<span class="default"><a href="frechet2.html#K3" target="_self">Cl_Seq</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="frechet2.html#K3" target="_self">Cl_Seq</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="frechet2.html#E1:38"><i><font color="Green">E32</font></i></a>, <a class="ref" href="frechet2.html#T23" target="_self">Th23</a></i>
<br/>.= 
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="frechet2.html#E1:38"><i><font color="Green">E32</font></i></a>, <a class="ref" href="frechet2.html#T23" target="_self">Th23</a></i>
<br/>.= 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="tops_1.html#T26">TOPS_1:26</a></i>
<br/>.= 
 <a href="frechet2.html#K3" target="_self">Cl_Seq</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="frechet2.html#E1:38"><i><font color="Green">E32</font></i></a>, <a class="ref" href="frechet2.html#T23" target="_self">Th23</a></i>
;<br/>


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