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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#V2" target="_self">filled</a>  <a href="fin_topo.html#L1" target="_self">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>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>





<b>assume </b><a NAME="E1:40"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="fin_topo.html#K7" target="_self">^i</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E3:40"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="fin_topo.html#K1" target="_self">U_FT</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="fin_topo.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E4:40"/>
 <a href="fin_topo.html#K1" target="_self">U_FT</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="fin_topo.html#E1:40"><i><font color="Green">E20</font></i></a>, <a class="ref" href="fin_topo.html#T12" target="_self">Th12</a></i>;<br/>
<b>hence </b><a NAME="E5:40"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="fin_topo.html#E3:40"><i><font color="Green">E21</font></i></a></i>;<br/>


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