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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E31">Th30</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: REARRAN1:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</font>, <font color="Olive" title="b2">D</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="b3">F</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Olive" title="b2">D</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b4">A</font> being   <a href="rearran1.html#NM1" title="REARRAN1:NM.1">RearrangmentGen</a> of <font color="Olive" title="b1">C</font>  st <font color="Olive" title="b3">F</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b2">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b1">C</font> holds <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">FinS</a> (<span class="p2">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> (<font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">A</font>)</span>)</span>,<font color="Olive" title="b1">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b1">C</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">FinS</a> (<span class="p2">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> (<font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">A</font>)</span>)</span>,<font color="Olive" title="b1">C</font>)</span>)</span> )</div></div>
