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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">A</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">B</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/>









<b>assume </b><a NAME="E1:10"/>
<font color="Maroon">G</font> is <a href="bvfunc_2.html#V2">independent</a>
 ;<br/>

<a NAME="E2:10"/><b>then </b>
 <a href="bvfunc_2.html#K6">All</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#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">A</font>,<font color="Maroon">G</font></span>)</span></span>)</span>,<font color="Maroon">B</font>,<font color="Maroon">G</font> <a href="bvfunc_1.html#R1">'&lt;'</a>  <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> <font color="Maroon">a</font>,<font color="Maroon">B</font>,<font color="Maroon">G</font></span>)</span>,<font color="Maroon">A</font>,<font color="Maroon">G</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:10"/>
 <a href="valuat_1.html#K5">'not'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K7">Ex</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">A</font>,<font color="Maroon">G</font></span>)</span>,<font color="Maroon">B</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#R1">'&lt;'</a>  <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> <font color="Maroon">a</font>,<font color="Maroon">B</font>,<font color="Maroon">G</font></span>)</span>,<font color="Maroon">A</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/>


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