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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">Th1</font></span>: <a NAME="T1"><span class="comment"><font color="firebrick">:: ARMSTRNG:1</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">B</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">B</font> is  <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">cap-closed</a>  holds <br/> for <font color="Olive" title="b2">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">S</font> being   <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="b2">X</font>  st <font color="Olive" title="b2">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">B</font> &amp; <font color="Olive" title="b3">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">B</font> holds <br/> <a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Olive" title="b3">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">B</font></div></div>
