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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E16">Th16</font></span>: <a NAME="T16"><span class="comment"><font color="firebrick">:: HILB10_2:16</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">O</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a><br/>  for <font color="Olive" title="b4">A</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 <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Olive" title="b3">O</font></span>)</span>  st <font color="Olive" title="b1">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Olive" title="b3">O</font></span>)</span>,<font color="Olive" title="b4">A</font>)</span>)</span> &amp; <font color="Olive" title="b2">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Olive" title="b3">O</font></span>)</span>,<font color="Olive" title="b4">A</font>)</span>)</span> &amp; <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">m</font> holds <br/><span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Olive" title="b3">O</font></span>)</span>,<font color="Olive" title="b4">A</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">n</font> <a href="pre_poly.html#R1" title="PRE_POLY:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Olive" title="b3">O</font></span>)</span>,<font color="Olive" title="b4">A</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b2">m</font></div></div>
