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<div><span class="kw">theorem </span><a NAME="T63"><span class="comment"><font color="firebrick">:: RELSET_2:63</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">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b4">Y</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b2">B</font><br/>  for <font color="Olive" title="b5">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/> ( <font color="Olive" title="b5">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">.:^</a> <font color="Olive" title="b3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">.:^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">R</font> <a href="relset_1.html#K3" title="RELSET_1:func.3">~</a></span>)</span> <a href="relset_2.html#K6" title="RELSET_2:func.6">.:^</a> <span class="p2">(<span class="default"><font color="Olive" title="b5">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">.:^</a> <font color="Olive" title="b3">X</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b5">R</font> <a href="relset_1.html#K3" title="RELSET_1:func.3">~</a></span>)</span> <a href="relset_2.html#K6" title="RELSET_2:func.6">.:^</a> <font color="Olive" title="b4">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">R</font> <a href="relset_1.html#K3" title="RELSET_1:func.3">~</a></span>)</span> <a href="relset_2.html#K6" title="RELSET_2:func.6">.:^</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">.:^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b5">R</font> <a href="relset_1.html#K3" title="RELSET_1:func.3">~</a></span>)</span> <a href="relset_2.html#K6" title="RELSET_2:func.6">.:^</a> <font color="Olive" title="b4">Y</font></span>)</span></span>)</span> )</div></div>
