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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E37">Th35</font></span>: <a NAME="T35"><span class="comment"><font color="firebrick">:: ARMSTRNG:35</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">B</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">B</font> is  <a href="armstrng.html#V1" title="ARMSTRNG:attr.1">(B1)</a>  &amp; <font color="Olive" title="b2">B</font> is  <a href="armstrng.html#NV2" title="ARMSTRNG:NV.2">(B2)</a>  holds <br/>( <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</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="b2">B</font></span>)</span> &amp; (  for <font color="Olive" title="b3">G</font> being   <a href="armstrng.html#NM5" title="ARMSTRNG:NM.5">Full-family</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="armstrng.html#K9" title="ARMSTRNG:func.9">saturated-subsets</a> <font color="Olive" title="b3">G</font> holds <br/><font color="Olive" title="b3">G</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">X</font> <a href="armstrng.html#K10" title="ARMSTRNG:func.10">deps_encl_by</a> <font color="Olive" title="b2">B</font> ) )</div></div>
