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<div><span class="kw">theorem </span><a NAME="T45"><span class="comment"><font color="firebrick">:: ARMSTRNG:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">G</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">B</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="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="b3">B</font> is  <a href="armstrng.html#V1" title="ARMSTRNG:attr.1">(B1)</a>  &amp; <font color="Olive" title="b3">B</font> is  <a href="armstrng.html#NV2" title="ARMSTRNG:NV.2">(B2)</a>  &amp; <font color="Olive" title="b2">G</font> <a href="armstrng.html#R5" title="ARMSTRNG:pred.5">is_generator-set_of</a> <font color="Olive" title="b3">B</font> holds <br/> <a href="armstrng.html#K2" title="ARMSTRNG:func.2">/\-IRR</a> <font color="Olive" title="b3">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">G</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></div></div>
