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<div><span class="kw">theorem </span><a NAME="T9"><span class="comment"><font color="firebrick">:: UPROOTS:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">S</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st ( <font color="Olive" title="b2">S</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  or <font color="Olive" title="b3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) holds <br/>(<font color="Olive" title="b2">S</font>,<font color="Olive" title="b3">n</font>) <a href="uproots.html#K1" title="UPROOTS:func.1">-bag</a>  <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Olive" title="b1">X</font></div></div>
