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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></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">c<sub>1</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>













<b>assume </b><a NAME="E1:22"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="bvfunc_2.html#V2">independent</a> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K3">}</a></span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/>

<a NAME="E2:22"/>
<span class="p1"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K3">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="enumset1.html#T48">ENUMSET1:48</a></i>;<br/>
<a NAME="E3:22"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="enumset1.html#K3">}</a></span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:22"><i><font color="Green">E15</font></i></a>, <a class="ref" href="enumset1.html#T48">ENUMSET1:48</a></i>;<br/>
<b>hence </b><a NAME="E4:22"/>
 <a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E1:22"><i><font color="Green">E15</font></i></a>, <a class="ref" href="bvfunc14.html#T24" target="_self">Th24</a></i>;<br/>


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