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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="qc_lang1.html#K16">the_arguments_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/>
<a NAME="E1:57"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font> is <a href="qc_lang1.html#V2">atomic</a>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D17">QC_LANG1:def 17</a></i>;<br/>
<a NAME="E2:57"/><b>then </b>
 <a href="substut1.html#K9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K8">Bound_Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K16">the_arguments_of</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="substut1.html#T3">SUBSTUT1:3</a></i>;<br/>
<a NAME="E3:57"/><b>then </b><i><font color="Green">E45</font></i>: 
 <a href="substut1.html#K9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</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">the_arguments_of</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K16">the_arguments_of</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="qc_lang1.html#K16">the_arguments_of</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K2">bound_QC-variables</a>  ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="substut1.html#D7">SUBSTUT1:def 7</a></i>;<br/>
<a NAME="E4:57"/>
 <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K22">still_not-bound_in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="qc_lang3.html#T9">QC_LANG3:9</a></i>;<br/>
<a NAME="E5:57"/><b>then </b><i><font color="Green">E46</font></i>: 
 <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="qc_lang3.html#K1">variables_in</a> <font color="Maroon">c<sub>3</sub></font>,<a href="qc_lang1.html#K2">bound_QC-variables</a> 
 
<b>by </b><i><a class="ref" href="qc_lang3.html#T6">QC_LANG3:6</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">c<sub>6</sub></font> being   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>7</sub></font> being    <a href="qc_lang1.html#M1">QC-variable_list</a> of <font color="Maroon">c<sub>5</sub></font><b> such that </b><br/><a NAME="E7:57"/><i><font color="Green">E47</font></i>: 
(  <a href="qc_lang1.html#K16">the_arguments_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="txt" href="sublemma.html#E1:57"><i><font color="Green">E44</font></i></a>, <a class="ref" href="qc_lang1.html#D22">QC_LANG1:def 22</a></i>;<br/>
<a NAME="E8:57"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="qc_lang1.html#T23">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">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T58">FINSEQ_1:58</a></i>;<br/>
<a NAME="E10:57"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="sublemma.html#E7:57"><i><font color="Green">E47</font></i></a>, <a class="txt" href="sublemma.html#E8:57"><i><font color="Green">E48</font></i></a>, <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/>
<b>hence </b><a NAME="E11:57"/>
 <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="substut1.html#K9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E3:57"><i><font color="Green">E45</font></i></a>, <a class="txt" href="sublemma.html#E5:57"><i><font color="Green">E46</font></i></a>, <a class="txt" href="sublemma.html#E7:57"><i><font color="Green">E47</font></i></a>, <a class="ref" href="qc_lang3.html#D2">QC_LANG3:def 2</a></i>;<br/>


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