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<b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X2</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y2</font> be    <a href="hidden.html#M1">set</a> ;<br/>









<b>assume </b><a NAME="E1:92"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" target="_self">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">Y1</font></span><a href="zfmisc_1.html#K2" target="_self">:]</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2" target="_self">[:</a><span class="default"><font color="Maroon">X2</font>,<font color="Maroon">Y2</font></span><a href="zfmisc_1.html#K2" target="_self">:]</a></span>
 ;<br/>

<a NAME="E2:92"/><b>then </b><i><font color="Green">E26</font></i>: 
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" target="_self">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">Y1</font></span><a href="zfmisc_1.html#K2" target="_self">:]</a></span> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" target="_self">[:</a><span class="default"><font color="Maroon">X2</font>,<font color="Maroon">Y2</font></span><a href="zfmisc_1.html#K2" target="_self">:]</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:92"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X1</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y1</font> )
 <b>and </b><br/><a NAME="E5:92"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">x2</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:92"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X2</font> &amp; <font color="Maroon">y2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y2</font> )
 <b>and </b><br/><a NAME="E8:92"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x2</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="txt" href="zfmisc_1.html#E21"><i><font color="Green">Lemma42</font></i></a>, </i>;<br/>
<a NAME="E9:92"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> )
 
<b>by </b><i><a class="txt" href="zfmisc_1.html#E25"><i><font color="Green">Lemma44</font></i></a>, <a class="ref" href="zfmisc_1.html#T17" target="_self">Th17</a>, <a class="txt" href="zfmisc_1.html#E3"><i><font color="Green">Lemma27</font></i></a></i>;<br/>
<a NAME="E10:92"/><b>then </b>
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y2</font> )
 
<b>by </b><i><a class="txt" href="zfmisc_1.html#E23"><i><font color="Green">Lemma43</font></i></a>, <a class="txt" href="zfmisc_1.html#E28"><i><font color="Green">Lemma45</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E11:92"/>
 ex <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X2</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y2</font> )
 <b>by </b><i><a class="txt" href="zfmisc_1.html#E25"><i><font color="Green">Lemma44</font></i></a></i>;<br/>


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