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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>









<a NAME="E1:34"/><i><font color="Green">E17</font></i>: 
<span class="p1"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="relset_2.html#NK1" target="_self">}_}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="relset_2.html#NK1" target="_self">}_}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="relset_2.html#NK1" target="_self">}_}</a></span>
 
<b>by </b><i><a class="ref" href="relset_2.html#T3" target="_self">Th3</a></i>;<br/>
<b>assume </b><a NAME="E2:34"/><i><font color="Green">E18</font></i>: 
<span class="p1">(<span class="default"><a href="relset_2.html#K3" target="_self">.:</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="relset_2.html#NK1" target="_self">}_}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<font color="Maroon">c<sub>5</sub></font> <a href="relset_2.html#K5" target="_self">.:^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
 <a href="setfam_1.html#K8">Intersect</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_2.html#K3" target="_self">.:</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p2"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="relset_2.html#NK1" target="_self">}_}</a></span></span>)</span>

<br/>.= 
 <a href="setfam_1.html#K8">Intersect</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_2.html#K3" target="_self">.:</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p3"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="relset_2.html#NK1" target="_self">}_}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_2.html#K3" target="_self">.:</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p3"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="relset_2.html#NK1" target="_self">}_}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T153">RELAT_1:153</a>, <a class="txt" href="relset_2.html#E1:34"><i><font color="Green">E17</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="relset_2.html#K5" target="_self">.:^</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="relset_2.html#E2:34"><i><font color="Green">E18</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E4:34"/>
<font color="Maroon">c<sub>5</sub></font> <a href="relset_2.html#K5" target="_self">.:^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="relset_2.html#K5" target="_self">.:^</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>


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