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<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">h</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>



<b>thus </b><a NAME="E1:91"/>
( <font color="Maroon">h</font> is   <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">k</font> implies ( <font color="Maroon">h</font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="qc_lang1.html#K2">bound_QC-variables</a>  &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:91_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">h</font> is   <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">k</font>
 ;<br/>

<a NAME="E2:91_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> <a href="tarski.html#R1">c=</a>  <a href="qc_lang1.html#K2">bound_QC-variables</a> 
 
<b>by </b><i><a class="ref" href="cqc_lang.html#D5">CQC_LANG:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:91_1"/>
<font color="Maroon">h</font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="qc_lang1.html#K2">bound_QC-variables</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>

<b>thus </b><a NAME="E4:91_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 <b>by </b><i>, <a class="ref" href="qc_lang1.html#D8">QC_LANG1:def 8</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:91"/>
( <font color="Maroon">h</font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="qc_lang1.html#K2">bound_QC-variables</a>  &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> implies <font color="Maroon">h</font> is   <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">k</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:91_2"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">h</font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="qc_lang1.html#K2">bound_QC-variables</a>  &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> )
 ;<br/>

<a NAME="E2:91_2"/><b>then </b><i><font color="Green">E45</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> <a href="tarski.html#R1">c=</a>  <a href="qc_lang1.html#K2">bound_QC-variables</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E3:91_2"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> <a href="tarski.html#R1">c=</a>  <a href="qc_lang1.html#K1">QC-variables</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:91_2"/><b>then </b>
<font color="Maroon">h</font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="qc_lang1.html#K1">QC-variables</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E5:91_2"/>
<font color="Maroon">h</font> is   <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">k</font>
 <b>by </b><i>, , <a class="ref" href="cqc_lang.html#D5">CQC_LANG:def 5</a>, <a class="ref" href="qc_lang1.html#D8">QC_LANG1:def 8</a></i>;<br/>


</div><b>end;</b></div>


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