<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c4">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font>;<br/><b>let </b><font color="Maroon" title="c5">R</font> be    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>;<br/><b>let </b><font color="Maroon" title="c6">S</font> be    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>;<br/>











<span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="relset_2.html#K5" title="RELSET_2:func.5">.:^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">R</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">X</font></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">R</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">X</font></span>)</span>
<b>by </b><i><a class="ref" href="relset_2.html#T49" target="_self" title="RELSET_2:th.49">Th49</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">X</font>
<b>by </b><i><a class="ref" href="relat_1.html#T159" title="RELAT_1:th.159">RELAT_1:159</a></i>
;<br/>
<b>then </b><font color="Maroon" title="c6">S</font> <a href="relset_2.html#K5" title="RELSET_2:func.5">.:^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">R</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">X</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="relset_2.html#K5" title="RELSET_2:func.5">.:^</a> <font color="Maroon" title="c4">X</font>
<b>by </b><i><a class="ref" href="relset_2.html#T50" target="_self" title="RELSET_2:th.50">Th50</a></i>
;<br/>
<b>hence </b><a NAME="E3:67"/>
<font color="Maroon" title="c6">S</font> <a href="relset_2.html#K5" title="RELSET_2:func.5">.:^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">R</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="relset_2.html#K5" title="RELSET_2:func.5">.:^</a> <font color="Maroon" title="c4">X</font>
 ;<br/>


</div>
