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<div><span class="kw">theorem </span><a NAME="T48"><span class="comment"><font color="firebrick">:: MATRIX11:48</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>  st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 holds <br/> ex <font color="Olive" title="b2">ODD</font>, <font color="Olive" title="b3">EVEN</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>( <font color="Olive" title="b3">EVEN</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b4">p</font> where <font color="Olive" title="b4">p</font> is    <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Element</a> of  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Permutations</a> <font color="Olive" title="b1">n</font> : <font color="Olive" title="b4">p</font> is  <a href="matrix_1.html#V6" title="MATRIX_1:attr.6">even</a>  </span> } </span>  &amp; <font color="Olive" title="b2">ODD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b4">q</font> where <font color="Olive" title="b4">q</font> is    <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Element</a> of  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Permutations</a> <font color="Olive" title="b1">n</font> : <font color="Olive" title="b4">q</font> is  <a href="matrix_1.html#NV7" title="MATRIX_1:NV.7">odd</a>  </span> } </span>  &amp; <font color="Olive" title="b3">EVEN</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Olive" title="b2">ODD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b3">EVEN</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">ODD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Permutations</a> <font color="Olive" title="b1">n</font> &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b3">EVEN</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="b2">ODD</font> )</div></div>
