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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th15</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: HILB10_6:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   non  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">b</font> holds <br/>(  <a href="hilb10_1.html#K1" title="HILB10_1:func.1">Px</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">n</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="hilb10_1.html#K1" title="HILB10_1:func.1">Px</a> (<font color="Olive" title="b3">b</font>,<font color="Olive" title="b1">n</font>) &amp;  <a href="hilb10_1.html#K2" title="HILB10_1:func.2">Py</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">n</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="hilb10_1.html#K2" title="HILB10_1:func.2">Py</a> (<font color="Olive" title="b3">b</font>,<font color="Olive" title="b1">n</font>) )</div></div>
