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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#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="yellow_9.html#M3" target="_self">Refinement</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> as    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="ref" href="yellow_9.html#D6" target="_self">Def6</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> as    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="yellow_9.html#T29" target="_self">Th29</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span> as    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="yellow_9.html#T29" target="_self">Th29</a></i>;<br/>
<a NAME="E4:91"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">c<sub>4</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> &amp; <font color="Maroon">c<sub>9</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> &amp; <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> &amp; <font color="Maroon">c<sub>10</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> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</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">CANTOR_1:def 5</a>, <a class="ref" href="pre_topc.html#D1">PRE_TOPC:def 1</a></i>;<br/>
<a NAME="E5:91"/><b>then </b><i><font color="Green">E42</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="cantor_1.html#D5">CANTOR_1:def 5</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a>, <a class="ref" href="xboole_1.html#T13">XBOOLE_1:13</a></i>;<br/>
<a NAME="E6:91"/><b>then </b><i><font color="Green">E43</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> <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>3</sub></font> &amp; <span class="p1"><a href="tarski.html#K2">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1"><a href="tarski.html#K2">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a>, <a class="ref" href="zfmisc_1.html#T38">ZFMISC_1:38</a></i>;<br/>
<a NAME="E7:91"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E8:91"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> is   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/>
<a NAME="E10:91"/>
( 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> <font color="Maroon">c<sub>6</sub></font> &amp; 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> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E11:91"/><b>then </b>
( <font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="yellow_9.html#E4:91"><i><font color="Green">E41</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>10</sub></font> as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>13</sub></font> as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>15</sub></font> as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/>
<i><font color="Green">E44</font></i>:  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> = 
 <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <span class="p2">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cantor_1.html#T13">CANTOR_1:13</a></i>
<br/>.= 
 <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <span class="p2">(<span class="default"><a href="cantor_1.html#K1">UniCl</a> <span class="p3">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow_9.html#T21" target="_self">Th21</a></i>
;<br/>
<a NAME="E16:91"/>
(  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>6</sub></font> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>9</sub></font> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>10</sub></font> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="yellow_9.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E17:91"/><b>then </b><i><font color="Green">E45</font></i>: 
(  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>6</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>3</sub></font> &amp;  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>9</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>1</sub></font> &amp;  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>10</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="ref" href="yellow_9.html#T22" target="_self">Th22</a></i>;<br/>
<a NAME="E18:91"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>5</sub></font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a>, <a class="ref" href="zfmisc_1.html#T12">ZFMISC_1:12</a></i>;<br/>
<a NAME="E19:91"/><b>then </b>
( <font color="Maroon">c<sub>16</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="yellow_9.html#E5:91"><i><font color="Green">E42</font></i></a>, <a class="txt" href="yellow_9.html#E6:91"><i><font color="Green">E43</font></i></a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a>, <a class="ref" href="xboole_1.html#T13">XBOOLE_1:13</a></i>;<br/>
<a NAME="E20:91"/><b>then </b><i><font color="Green">E46</font></i>: 
(  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>16</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>17</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="ref" href="cantor_1.html#T16">CANTOR_1:16</a></i>;<br/>
<a NAME="E21:91"/><b>then </b><i><font color="Green">E47</font></i>: 
(  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> &amp;  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="yellow_9.html#E17:91"><i><font color="Green">E45</font></i></a>, <a class="ref" href="cantor_1.html#T9">CANTOR_1:9</a></i>;<br/>
<a NAME="E22:91"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E23:91"/><b>then </b>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E24:91"/><b>then </b>
(  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> &amp;  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="yellow_9.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E25:91"/><b>then </b>
(  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>16</sub></font> &amp;  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>10</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>17</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E26:91"/><b>then </b>
(  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>10</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="txt" href="yellow_9.html#E20:91"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E27:91"/><b>then </b>
( 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">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> &amp; 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">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="yellow_9.html#E17:91"><i><font color="Green">E45</font></i></a>, <a class="ref" href="yellow_9.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E28:91"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E29:91"/><b>then </b>
 <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K2">FinMeetCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K1">UniCl</a> <span class="p2">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="cantor_1.html#T16">CANTOR_1:16</a></i>;<br/>
<a NAME="E30:91"/><b>then </b>
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="yellow_9.html#E15:91"><i><font color="Green">E44</font></i></a>, <a class="txt" href="yellow_9.html#E17:91"><i><font color="Green">E45</font></i></a>, <a class="ref" href="cantor_1.html#T9">CANTOR_1:9</a></i>;<br/>
<a NAME="E31:91"/><b>then </b>
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="yellow_9.html#E21:91"><i><font color="Green">E47</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E32:91"/><b>then </b>
 <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>11</sub></font> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#T22" target="_self">Th22</a></i>;<br/>
<b>hence </b><a NAME="E33:91"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> is    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="yellow_9.html#T23" target="_self">Th23</a></i>;<br/>


</div>
