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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="fin_topo.html#L1">FT_Space_Str</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:27"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="fin_topo.html#V2">filled</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<i><font color="Green">E20</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fintopo3.html#K4" target="_self">Fint</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="fin_topo.html#K7">^i</a>  = 
<span class="p1">(<span class="default"><a href="fintopo3.html#K5" target="_self">Fint</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="fin_topo.html#K7">^i</a> 

<br/>.= 
 <a href="fintopo3.html#K5" target="_self">Fint</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="fintopo3.html#T18" target="_self">Th18</a></i>
;<br/>
<b>thus </b><a NAME="E3:27"/>
 <a href="fintopo3.html#K5" target="_self">Fint</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="tarski.html#R1">c=</a>  <a href="fintopo3.html#K5" target="_self">Fint</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="fintopo3.html#E1:27"><i><font color="Green">E19</font></i></a>, <a class="txt" href="fintopo3.html#E2:27"><i><font color="Green">E20</font></i></a>, <a class="ref" href="fin_topo.html#T28">FIN_TOPO:28</a></i>;<br/>


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