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<div><span class="kw">theorem </span><a NAME="T56"><span class="comment"><font color="firebrick">:: ARMSTRNG:56</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">F</font> being   <a href="armstrng.html#NM2" title="ARMSTRNG:NM.2">Dependency-set</a> of <font color="Olive" title="b1">X</font>  st  ex <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font> st <br/>( <span class="p1"><a href="armstrng.html#K6" title="ARMSTRNG:func.6">[</a><span class="default"><font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font></span><a href="armstrng.html#K6" title="ARMSTRNG:func.6">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">F</font> &amp; <font color="Olive" title="b4">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A</font> &amp;  not <font color="Olive" title="b5">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A</font> ) holds <br/><font color="Olive" title="b2">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="armstrng.html#K14" title="ARMSTRNG:func.14">charact_set</a> <font color="Olive" title="b3">F</font> ;<br/></div></div>
