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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: ARMSTRNG:51</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">C</font> being   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b2">C</font> is  <a href="armstrng.html#NV15" title="ARMSTRNG:NV.15">(C1)</a>  &amp; <font color="Olive" title="b2">C</font> is  <a href="armstrng.html#NV17" title="ARMSTRNG:NV.17">(C2)</a>  holds <br/> ex <font color="Olive" title="b3">R</font> being    <a href="armstrng.html#L1" title="ARMSTRNG:struct.1">DB-Rel</a>  st <br/>(  the <a href="armstrng.html#U1" title="ARMSTRNG:sel.1">Attributes</a> of <font color="Olive" title="b3">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="armstrng.html#K13" title="ARMSTRNG:func.13">candidate-keys</a> <span class="p1">(<span class="default"><a href="armstrng.html#K5" title="ARMSTRNG:func.5">Dependency-str</a> <font color="Olive" title="b3">R</font></span>)</span> )</div></div>
