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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E7">Th3</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: ARMSTRNG:3</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">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X</font>  ex <font color="Olive" title="b3">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font> st <br/>( <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Olive" title="b3">A</font> &amp; (  for <font color="Olive" title="b4">s</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b4">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">A</font> holds <br/><font color="Olive" title="b4">s</font> <a href="armstrng.html#R1" title="ARMSTRNG:pred.1">is_/\-irreducible_in</a> <font color="Olive" title="b1">X</font> ) )</div></div>
