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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V1">strict</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="cantor_1.html#M2" target="_self">prebasis</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:25"/><i><font color="Green">E20</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:25"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is    <a href="cantor_1.html#M2" target="_self">prebasis</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="cantor_1.html#M1" target="_self">Basis</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:25"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="cantor_1.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E5:25"/><i><font color="Green">E23</font></i>: 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K1" target="_self">UniCl</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="cantor_1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E6:25"/>
 <a href="cantor_1.html#K1" target="_self">UniCl</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K1" target="_self">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="cantor_1.html#E4:25"><i><font color="Green">E22</font></i></a>, <a class="ref" href="cantor_1.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E7:25"/><b>then </b><i><font color="Green">E24</font></i>: 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K1" target="_self">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="cantor_1.html#E5:25"><i><font color="Green">E23</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="cantor_1.html#M2" target="_self">prebasis</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="cantor_1.html#E2:25"><i><font color="Green">E21</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="cantor_1.html#M1" target="_self">Basis</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E10:25"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="cantor_1.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E11:25"/><i><font color="Green">E26</font></i>: 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K1" target="_self">UniCl</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="cantor_1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E12:25"/><i><font color="Green">E27</font></i>: 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="cantor_1.html#K1" target="_self">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" target="_self">FinMeetCl</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="cantor_1.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E13:25"/><i><font color="Green">E28</font></i>: 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="cantor_1.html#K1" target="_self">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" target="_self">FinMeetCl</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="cantor_1.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E14:25"/>
 <a href="cantor_1.html#K1" target="_self">UniCl</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K1" target="_self">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="cantor_1.html#E10:25"><i><font color="Green">E25</font></i></a>, <a class="ref" href="cantor_1.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E15:25"/><b>then </b><i><font color="Green">E29</font></i>: 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K1" target="_self">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="cantor_1.html#E11:25"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E16:25"/>
<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="cantor_1.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E17:25"/><b>then </b>
 <a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K2" target="_self">FinMeetCl</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="cantor_1.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E18:25"/><b>then </b>
 <a href="cantor_1.html#K1" target="_self">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K1" target="_self">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" target="_self">FinMeetCl</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="cantor_1.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E19:25"/><b>then </b><i><font color="Green">E30</font></i>: 
 <a href="cantor_1.html#K1" target="_self">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="cantor_1.html#E12:25"><i><font color="Green">E27</font></i></a>, <a class="txt" href="cantor_1.html#E15:25"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E20:25"/>
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="cantor_1.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E21:25"/><b>then </b>
 <a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K2" target="_self">FinMeetCl</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="cantor_1.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E22:25"/><b>then </b>
 <a href="cantor_1.html#K1" target="_self">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K1" target="_self">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" target="_self">FinMeetCl</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="cantor_1.html#T9" target="_self">Th9</a></i>;<br/>
<b>hence </b><a NAME="E23:25"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="cantor_1.html#E1:25"><i><font color="Green">E20</font></i></a>, <a class="txt" href="cantor_1.html#E7:25"><i><font color="Green">E24</font></i></a>, <a class="txt" href="cantor_1.html#E13:25"><i><font color="Green">E28</font></i></a>, <a class="txt" href="cantor_1.html#E19:25"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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