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<b>let </b><font color="Maroon">I</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">y</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green">E26</font></i>: 
not <font color="Maroon">I</font> is <a href="xboole_0.html#V1">empty</a>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green">E27</font></i>: 
<span class="p1"><a href="pzfmisc1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">x</font></span><a href="pzfmisc1.html#K1" target="_self">}</a></span> <a href="pboole.html#K3">/\</a> <span class="p1"><a href="pzfmisc1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">y</font></span><a href="pzfmisc1.html#K1" target="_self">}</a></span> <a href="pboole.html#R6">=</a>  <a href="pboole.html#K1">[0]</a> <font color="Maroon">I</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>now </b></a><div class="add"><b>consider </b><font color="Maroon">i</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:22_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/><b>take </b><font color="Maroon">i</font> = <font color="Maroon">i</font>;<br/><span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span><a href="tarski.html#K1">}</a></span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="pzfmisc1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">x</font></span><a href="pzfmisc1.html#K1" target="_self">}</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="pzfmisc1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">x</font></span><a href="pzfmisc1.html#K1" target="_self">}</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2"><a href="pzfmisc1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">y</font></span><a href="pzfmisc1.html#K1" target="_self">}</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="pzfmisc1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">x</font></span><a href="pzfmisc1.html#K1" target="_self">}</a></span> <a href="pboole.html#K3">/\</a> <span class="p2"><a href="pzfmisc1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">y</font></span><a href="pzfmisc1.html#K1" target="_self">}</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="pboole.html#D8">PBOOLE:def 8</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i>, <a class="ref" href="pboole.html#T5">PBOOLE:5</a></i>
;<br/><b>hence </b><a NAME="E4:22_1"/>
<font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:22"/>
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 ;<br/>


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