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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">M</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">SF</font> be   <a href="mssubfam.html#NM1">MSSubsetFamily</a> of <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">V</font> be    <a href="pboole.html#M4">ManySortedSubset</a> of <font color="Maroon">M</font>;<br/>







<b>assume </b><a NAME="E1:73"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">SF</font> <a href="pboole.html#R6">=</a> <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">V</font></span><a href="pzfmisc1.html#K1">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:73_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/><b>then consider </b><font color="Maroon">Q</font> being   <a href="setfam_1.html#NM1">Subset-Family</a> of <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span><b> such that </b><br/><a NAME="E3:73_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">SF</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>and </b><br/><a NAME="E4:73_1"/><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><a href="mssubfam.html#K6" target="_self">meet</a> <font color="Maroon">SF</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">Q</font>
 <b>by </b><i/>;<br/><a NAME="E5:73_1"/>
<font color="Maroon">Q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i>, , , <a class="ref" href="pboole.html#D16">PBOOLE:def 16</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="mssubfam.html#K6" target="_self">meet</a> <font color="Maroon">SF</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
 <a href="setfam_1.html#K6">meet</a> <font color="Maroon">Q</font>
<b>by </b><i>, <a class="ref" href="setfam_1.html#D10">SETFAM_1:def 10</a></i>
<br/>.= 
 <a href="setfam_1.html#K1">meet</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">V</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>, , , <a class="ref" href="pzfmisc1.html#D1">PZFMISC1:def 1</a></i>
<br/>.= 
<font color="Maroon">V</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="setfam_1.html#T11">SETFAM_1:11</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:73"/>
 <a href="mssubfam.html#K6" target="_self">meet</a> <font color="Maroon">SF</font> <a href="pboole.html#R6">=</a> <font color="Maroon">V</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


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