<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E39">Th38</font></span>: <a NAME="T38"><span class="comment"><font color="firebrick">:: FLEXARY1:38</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b2">G</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b1">F</font> holds <br/> ex <font color="Olive" title="b3">o</font> being   <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive">b<sub>1</sub></font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>   <a href="flexary1.html#M1" title="FLEXARY1:mode.1">DoubleReorganization</a> of  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">G</font> st <br/> for <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">o</font> <a href="flexary1.html#K5" title="FLEXARY1:func.5">_</a> (<font color="Olive" title="b4">n</font>,1)</span>)</span> &amp;  ...  &amp; <font color="Olive" title="b1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">o</font> <a href="flexary1.html#K5" title="FLEXARY1:func.5">_</a> (<font color="Olive" title="b4">n</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">o</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">n</font></span>)</span></span>)</span>)</span>)</span></div></div>
