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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">I</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">M</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">SF</font> be   <a href="closure2.html#NM1">SubsetFamily</a> of <font color="Maroon">M</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:31"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E2:31"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">SF</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E3:31"/><i><font color="Green">E40</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="closure2.html#K4" target="_self">|:</a><span class="default"><font color="Maroon">SF</font></span><a href="closure2.html#K4" target="_self">:|</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E4:31"/><i><font color="Green">E45</font></i>: 
<span class="p1"><a href="closure2.html#K4" target="_self">|:</a><span class="default"><font color="Maroon">SF</font></span><a href="closure2.html#K4" target="_self">:|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="closure2.html#K3" target="_self">|.</a><span class="default"><font color="Maroon">SF</font></span><a href="closure2.html#K3" target="_self">.|</a></span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:31"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i>, , , </i>;<br/>
<b>hence </b><a NAME="E6:31"/>
<span class="p1"><a href="closure2.html#K4" target="_self">|:</a><span class="default"><font color="Maroon">SF</font></span><a href="closure2.html#K4" target="_self">:|</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</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/>


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