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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>

<b>assume </b><a NAME="E1:36"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="qc_lang1.html#V2">atomic</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">c<sub>3</sub></font> being   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>4</sub></font> being    <a href="qc_lang1.html#M1">QC-variable_list</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E3:36"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="qc_lang1.html#D17">QC_LANG1:def 17</a></i>;<br/>
<a NAME="E4:36"/>
( <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <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#K4">free_QC-variables</a>  ) </span>}</span>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <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#K3">fixed_QC-variables</a>  ) </span>}</span>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="txt" href="substut2.html#E3:36"><i><font color="Green">E21</font></i></a>, <a class="ref" href="cqc_lang.html#T17">CQC_LANG:17</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="cqc_lang.html#T15">CQC_LANG:15</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E6:36"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="substut2.html#E3:36"><i><font color="Green">E21</font></i></a></i>;<br/>


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