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<div><span class="kw">theorem </span><a NAME="T64"><span class="comment"><font color="firebrick">:: QC_LANG3:64</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">A</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> <br/>  for <font color="Olive" title="b3">P</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font>,<font color="Olive" title="b2">A</font><br/>  for <font color="Olive" title="b4">l</font> being   <a href="qc_lang1.html#NM9" title="QC_LANG1:NM.9">QC-variable_list</a> of <font color="Olive" title="b1">k</font>,<font color="Olive" title="b2">A</font> holds   <a href="qc_lang3.html#K6" title="QC_LANG3:func.6">Fixed</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="qc_lang1.html#K10" title="QC_LANG1:func.10">!</a> <font color="Olive" title="b4">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b4">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font></span>)</span> where <font color="Olive" title="b5">i</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b5">i</font> &amp; <font color="Olive" title="b5">i</font> <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> <font color="Olive" title="b4">l</font> &amp; <font color="Olive" title="b4">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K4" title="QC_LANG1:func.4">fixed_QC-variables</a> <font color="Olive" title="b2">A</font> ) </span> } </span>  <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T37" target="_self" onmouseover="rs('qc_lang3/T37')" onmouseout="rh()">Th37</a></span>;<br/></div></div>
