<?xml version="1.0"?>
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<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">B</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<a NAME="E1:21"/>
( <font color="Maroon">A</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E2:21"/><b>then </b>
(  <a href="finsub_1.html#K5" target="_self">Fin</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">B</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finsub_1.html#K5" target="_self">Fin</a> <font color="Maroon">A</font> &amp;  <a href="finsub_1.html#K5" target="_self">Fin</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">B</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finsub_1.html#K5" target="_self">Fin</a> <font color="Maroon">B</font> )
 
<b>by </b><i><a class="ref" href="finsub_1.html#D4" target="_self">Def4</a></i>;<br/>
<b>hence </b><a NAME="E3:21"/>
 <a href="finsub_1.html#K5" target="_self">Fin</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">B</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="finsub_1.html#K5" target="_self">Fin</a> <font color="Maroon">A</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="finsub_1.html#K5" target="_self">Fin</a> <font color="Maroon">B</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:21_1"/>
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="finsub_1.html#K5" target="_self">Fin</a> <font color="Maroon">A</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="finsub_1.html#K5" target="_self">Fin</a> <font color="Maroon">B</font></span>)</span>
 ;<br/><a NAME="E2:21_1"/><b>then </b>
( <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="finsub_1.html#K5" target="_self">Fin</a> <font color="Maroon">A</font> &amp; <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="finsub_1.html#K5" target="_self">Fin</a> <font color="Maroon">B</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E3:21_1"/><b>then </b>
( <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> &amp; <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> &amp; <font color="Maroon">X</font> is <a href="finset_1.html#V1">finite</a> )
 <b>by </b><i><a class="ref" href="finsub_1.html#D3" target="_self">Def3</a></i>;<br/><a NAME="E4:21_1"/><b>then </b>
( <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">B</font> &amp; <font color="Maroon">X</font> is <a href="finset_1.html#V1">finite</a> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E5:21_1"/>
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="finsub_1.html#K5" target="_self">Fin</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">B</font></span>)</span>
 <b>by </b><i><a class="ref" href="finsub_1.html#D3" target="_self">Def3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:21"/>
<span class="p1">(<span class="default"><a href="finsub_1.html#K5" target="_self">Fin</a> <font color="Maroon">A</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="finsub_1.html#K5" target="_self">Fin</a> <font color="Maroon">B</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finsub_1.html#K5" target="_self">Fin</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">B</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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