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<b>let </b><font color="Maroon" title="c1">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">P</font> be   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c1">k</font>;<br/><b>let </b><font color="Maroon" title="c3">ll</font> be   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c1">k</font>;<br/>





<b>set </b><font color="Maroon" title="c4">l1</font> =  <a href="qc_lang1.html#K16" title="QC_LANG1:func.16">the_arguments_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font></span>)</span>;<br/>
<a NAME="E1:57"/><i><font color="Green" title="E44">A1</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D17" title="QC_LANG1:def.17">QC_LANG1:def 17</a></i>;<br/>
<a NAME="E2:57"/><b>then </b>
 <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K8" title="SUBSTUT1:func.8">Bound_Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K16" title="QC_LANG1:func.16">the_arguments_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="substut1.html#T3" title="SUBSTUT1:th.3">SUBSTUT1:3</a></i>;<br/>
<a NAME="E3:57"/><b>then </b><i><font color="Green" title="E45">A2</font></i>: 
 <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</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"><span class="p3">(<span class="default"><a href="qc_lang1.html#K16" title="QC_LANG1:func.16">the_arguments_of</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">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> <span class="p1">(<span class="default"><a href="qc_lang1.html#K16" title="QC_LANG1:func.16">the_arguments_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="qc_lang1.html#K16" title="QC_LANG1:func.16">the_arguments_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a>  ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="substut1.html#D7" title="SUBSTUT1:def.7">SUBSTUT1:def 7</a></i>;<br/>
<a NAME="E4:57"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K22" title="QC_LANG1:func.22">still_not-bound_in</a> <font color="Maroon" title="c3">ll</font>
 
<b>by </b><i><a class="ref" href="qc_lang3.html#T9" title="QC_LANG3:th.9">QC_LANG3:9</a></i>;<br/>
<a NAME="E5:57"/><b>then </b><i><font color="Green" title="E46">A3</font></i>: 
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang3.html#K1" title="QC_LANG3:func.1">variables_in</a> <font color="Maroon" title="c3">ll</font>,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> 
 
<b>by </b><i><a class="ref" href="qc_lang3.html#T6" title="QC_LANG3:th.6">QC_LANG3:6</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <font color="Maroon" title="c6">P'</font> being   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c5">n</font>, <font color="Maroon" title="c7">ll'</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-variable_list</a> of <font color="Maroon" title="c5">n</font><b> such that </b><br/><a NAME="E7:57"/><i><font color="Green" title="E47">A4</font></i>: 
(  <a href="qc_lang1.html#K16" title="QC_LANG1:func.16">the_arguments_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">ll'</font> &amp; <font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">P'</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <font color="Maroon" title="c7">ll'</font> )
 <b>by </b><i><a class="txt" href="sublemma.html#E1:57"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="qc_lang1.html#D22" title="QC_LANG1:def.22">QC_LANG1:def 22</a></i>;<br/>
<a NAME="E8:57"/><i><font color="Green" title="E48">A5</font></i>: 
( <font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">P</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">ll</font> &amp; <font color="Maroon" title="c6">P'</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <font color="Maroon" title="c7">ll'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c6">P'</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c7">ll'</font> )
 
<b>by </b><i><a class="ref" href="qc_lang1.html#T23" title="QC_LANG1:th.23">QC_LANG1:23</a></i>;<br/>
<a NAME="E9:57"/>
( <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c6">P'</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c7">ll'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">P'</font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">P</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">ll</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T58" title="FINSEQ_1:th.58">FINSEQ_1:58</a></i>;<br/>
<a NAME="E10:57"/><b>then </b>
<font color="Maroon" title="c7">ll'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">ll</font>
 
<b>by </b><i><a class="txt" href="sublemma.html#E7:57"><i><font color="Green" title="E47">A4</font></i></a>, <a class="txt" href="sublemma.html#E8:57"><i><font color="Green" title="E48">A5</font></i></a>, <a class="ref" href="finseq_1.html#T46" title="FINSEQ_1:th.46">FINSEQ_1:46</a></i>;<br/>
<b>hence </b><a NAME="E11:57"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="substut1.html#K9" title="SUBSTUT1:func.9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c3">ll</font></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E3:57"><i><font color="Green" title="E45">A2</font></i></a>, <a class="txt" href="sublemma.html#E5:57"><i><font color="Green" title="E46">A3</font></i></a>, <a class="txt" href="sublemma.html#E7:57"><i><font color="Green" title="E47">A4</font></i></a>, <a class="ref" href="qc_lang3.html#D2" title="QC_LANG3:def.2">QC_LANG3:def 2</a></i>;<br/>


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