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<b>let </b><font color="Maroon">Y</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">a</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">Y</font>,<a href="margrel1.html#K6">BOOLEAN</a> ;<br/><b>let </b><font color="Maroon">G</font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1">PARTITIONS</a> <font color="Maroon">Y</font></span>)</span>;<br/><b>let </b><font color="Maroon">P</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">Q</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/>









<b>assume </b><a NAME="E1:19"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">G</font> is <a href="bvfunc_2.html#V2">independent</a>
 ;<br/>

<b>thus </b> <a href="bvfunc_2.html#K7">Ex</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K7">Ex</a> <font color="Maroon">a</font>,<font color="Maroon">P</font>,<font color="Maroon">G</font></span>)</span>,<font color="Maroon">Q</font>,<font color="Maroon">G</font> = 
 <a href="valuat_1.html#K5">'not'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K7">Ex</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K7">Ex</a> <font color="Maroon">a</font>,<font color="Maroon">P</font>,<font color="Maroon">G</font></span>)</span>,<font color="Maroon">Q</font>,<font color="Maroon">G</font></span>)</span></span>)</span>

<br/>.= 
 <a href="valuat_1.html#K5">'not'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K7">Ex</a> <font color="Maroon">a</font>,<font color="Maroon">P</font>,<font color="Maroon">G</font></span>)</span></span>)</span>,<font color="Maroon">Q</font>,<font color="Maroon">G</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_2.html#T21">BVFUNC_2:21</a></i>
<br/>.= 
 <a href="valuat_1.html#K5">'not'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">P</font>,<font color="Maroon">G</font></span>)</span>,<font color="Maroon">Q</font>,<font color="Maroon">G</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_2.html#T21">BVFUNC_2:21</a></i>
<br/>.= 
 <a href="valuat_1.html#K5">'not'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">Q</font>,<font color="Maroon">G</font></span>)</span>,<font color="Maroon">P</font>,<font color="Maroon">G</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
 <a href="valuat_1.html#K5">'not'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K7">Ex</a> <font color="Maroon">a</font>,<font color="Maroon">Q</font>,<font color="Maroon">G</font></span>)</span></span>)</span>,<font color="Maroon">P</font>,<font color="Maroon">G</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_2.html#T21">BVFUNC_2:21</a></i>
<br/>.= 
 <a href="valuat_1.html#K5">'not'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K7">Ex</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K7">Ex</a> <font color="Maroon">a</font>,<font color="Maroon">Q</font>,<font color="Maroon">G</font></span>)</span>,<font color="Maroon">P</font>,<font color="Maroon">G</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_2.html#T21">BVFUNC_2:21</a></i>
<br/>.= 
 <a href="bvfunc_2.html#K7">Ex</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K7">Ex</a> <font color="Maroon">a</font>,<font color="Maroon">Q</font>,<font color="Maroon">G</font></span>)</span>,<font color="Maroon">P</font>,<font color="Maroon">G</font>

;<br/>


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