<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:18"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K2">}</a></span> as   <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="zfmisc_1.html#T38">ZFMISC_1:38</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E4:18"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K6">meet</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="setfam_1.html#T12">SETFAM_1:12</a></i>;<br/>
<a NAME="E5:18"/><b>then </b><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="setfam_1.html#D10">SETFAM_1:def 10</a></i>;<br/>
<a NAME="E6:18"/>
( <font color="Maroon">c<sub>6</sub></font> is  non <a href="xboole_0.html#V1">empty</a> <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <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>2</sub></font> )
 
<b>by </b><i><a class="txt" href="cantor_1.html#E1:18"><i><font color="Green">E14</font></i></a>, <a class="ref" href="zfmisc_1.html#T38">ZFMISC_1:38</a></i>;<br/>
<a NAME="E7:18"/><b>then </b>
 <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="cantor_1.html#D4" target="_self">Def4</a></i>;<br/>
<b>hence </b><a NAME="E8:18"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="cantor_1.html#K2" target="_self">FinMeetCl</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="cantor_1.html#E5:18"><i><font color="Green">E15</font></i></a>, <a class="ref" href="cantor_1.html#T13" target="_self">Th13</a></i>;<br/>


</div>
