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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">Th3</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: CQC_LANG:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> <br/>  for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="cqc_lang.html#NM1" title="CQC_LANG:NM.1">Substitution</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b4">x</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b5">a</font> being   <a href="qc_lang1.html#NM7" title="QC_LANG1:NM.7">free_QC-variable</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b6">l</font>, <font color="Olive" title="b7">ll</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">QC-variables</a> <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a</font> <a href="cqc_lang.html#K2" title="CQC_LANG:func.2">.--&gt;</a> <font color="Olive" title="b4">x</font> &amp; <font color="Olive" title="b7">ll</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K1" title="CQC_LANG:func.1">Subst</a> (<font color="Olive" title="b6">l</font>,<font color="Olive" title="b3">f</font>) &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">k</font> &amp; <font color="Olive" title="b2">k</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="b6">l</font> holds <br/>( ( <font color="Olive" title="b6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a</font> implies <font color="Olive" title="b7">ll</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x</font> ) &amp; ( <font color="Olive" title="b6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">a</font> implies <font color="Olive" title="b7">ll</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">k</font> ) )</div></div>
