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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E39">Th37</font></span>: <a NAME="T37"><span class="comment"><font color="firebrick">:: ARMSTRNG:37</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">F</font> being   <a href="armstrng.html#NM2" title="ARMSTRNG:NM.2">Dependency-set</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b2">F</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Olive" title="b1">X</font> <a href="armstrng.html#K10" title="ARMSTRNG:func.10">deps_encl_by</a> <span class="p1">(<span class="default"><a href="armstrng.html#K11" title="ARMSTRNG:func.11">enclosure_of</a> <font color="Olive" title="b2">F</font></span>)</span> &amp; (  for <font color="Olive" title="b3">G</font> being   <a href="armstrng.html#NM2" title="ARMSTRNG:NM.2">Dependency-set</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b2">F</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Olive" title="b3">G</font> &amp; <font color="Olive" title="b3">G</font> is  <a href="armstrng.html#V6" title="ARMSTRNG:attr.6">full_family</a>  holds <br/><font color="Olive" title="b1">X</font> <a href="armstrng.html#K10" title="ARMSTRNG:func.10">deps_encl_by</a> <span class="p1">(<span class="default"><a href="armstrng.html#K11" title="ARMSTRNG:func.11">enclosure_of</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Olive" title="b3">G</font> ) )</div></div>
