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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>, <font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:2"/><i><font color="Green">E3</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> is   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E2:2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="qc_lang1.html#K7">-ary_QC-pred_symbols</a> 
 
;<br/>
<a NAME="E3:2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K5">QC-pred_symbols</a>  :  <a href="qc_lang1.html#K6">the_arity_of</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D7">QC_LANG1:def 7</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K5">QC-pred_symbols</a> <b> such that </b><br/><a NAME="E5:2"/><i><font color="Green">E4</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="qc_lang1.html#K6">the_arity_of</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>
<a NAME="E6:2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="qc_lang1.html#K7">-ary_QC-pred_symbols</a> 
 
<b>by </b><i><a class="txt" href="substut2.html#E1:2"><i><font color="Green">E3</font></i></a></i>;<br/>
<a NAME="E7:2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K5">QC-pred_symbols</a>  :  <a href="qc_lang1.html#K6">the_arity_of</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D7">QC_LANG1:def 7</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K5">QC-pred_symbols</a> <b> such that </b><br/><a NAME="E9:2"/><i><font color="Green">E5</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="qc_lang1.html#K6">the_arity_of</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>
<b>thus </b><a NAME="E10:2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="substut2.html#E5:2"><i><font color="Green">E4</font></i></a>, <a class="txt" href="substut2.html#E9:2"><i><font color="Green">E5</font></i></a></i>;<br/>


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