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<b>let </b><font color="Maroon" title="c1">Y</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">a</font> be    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ;<br/><b>let </b><font color="Maroon" title="c3">G</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1" title="BVFUNC_2:func.1">PARTITIONS</a> <font color="Maroon" title="c1">Y</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">B</font> be    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font>;<br/>









<b>assume </b><a NAME="E1:22"/>
<font color="Maroon" title="c3">G</font> is <a href="bvfunc_2.html#V2" title="BVFUNC_2:attr.2">independent</a>
 ;<br/>

<a NAME="E2:22"/><b>then </b><i><font color="Green" title="E5">A1</font></i>: 
 <a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c3">G</font></span>)</span>,<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">G</font></span>)</span>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c3">G</font>
 
<b>by </b><i><a class="ref" href="partit_2.html#T18" title="PARTIT_2:th.18">PARTIT_2:18</a></i>;<br/>
<a NAME="E3:22"/>
 <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">G</font> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a>  <a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">G</font>
 
<b>by </b><i><a class="ref" href="bvfunc11.html#T8" target="_self" title="BVFUNC11:th.8">Th8</a></i>;<br/>
<b>hence </b><a NAME="E4:22"/>
 <a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">G</font></span>)</span>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c3">G</font> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a>  <a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c3">G</font></span>)</span>,<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c3">G</font>
 <b>by </b><i><a class="txt" href="bvfunc11.html#E2:22"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="partit_2.html#T15" title="PARTIT_2:th.15">PARTIT_2:15</a></i>;<br/>


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