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<div><span class="kw">theorem </span><a NAME="T50"><span class="comment"><font color="firebrick">:: ARMSTRNG:50</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <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><br/>  for <font color="Olive" title="b3">B</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   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>  &amp; <font color="Olive" title="b3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b4">b</font> where <font color="Olive" title="b4">b</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font> :  for <font color="Olive" title="b5">K</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b5">K</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">C</font> holds <br/> not <font color="Olive" title="b5">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">b</font> </span> } </span>  holds <br/><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"><font color="Olive" title="b1">X</font> <a href="armstrng.html#K10" title="ARMSTRNG:func.10">deps_encl_by</a> <font color="Olive" title="b3">B</font></span>)</span></div></div>
