<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T55"><span class="comment"><font color="firebrick">:: RELSET_2:55</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">R</font> being   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font> holds <br/> (  <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <font color="Olive" title="b3">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">R</font> <a href="relset_1.html#K3" title="RELSET_1:func.3">~</a></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Olive" title="b2">B</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b3">R</font> <a href="relset_1.html#K3" title="RELSET_1:func.3">~</a></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">R</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">R</font> <a href="relset_1.html#K3" title="RELSET_1:func.3">~</a></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">proj2</a> <font color="Olive" title="b3">R</font></span>)</span> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="relset_2.html#T50" target="_self" onmouseover="rs('relset_2/T50')" onmouseout="rh()">Th50</a></span>;<br/></div></div>
