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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">k</font>, <font color="Maroon" title="c4">l</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>assume </b><a NAME="E1:2"/><i><font color="Green" title="E3">A1</font></i>: 
( <font color="Maroon" title="c2">P</font> is   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c3">k</font> &amp; <font color="Maroon" title="c2">P</font> is   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c4">l</font> )
 ;<br/>

<a NAME="E2:2"/><b>then </b>
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">k</font> <a href="qc_lang1.html#K7" title="QC_LANG1:func.7">-ary_QC-pred_symbols</a> 
 
;<br/>
<a NAME="E3:2"/><b>then </b>
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">P1</font> where <font color="Olive" title="b1">P1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K5" title="QC_LANG1:func.5">QC-pred_symbols</a>  :  <a href="qc_lang1.html#K6" title="QC_LANG1:func.6">the_arity_of</a> <font color="Olive" title="b1">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D7" title="QC_LANG1:def.7">QC_LANG1:def 7</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">P1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K5" title="QC_LANG1:func.5">QC-pred_symbols</a> <b> such that </b><br/><a NAME="E5:2"/><i><font color="Green" title="E4">A2</font></i>: 
( <font color="Maroon" title="c5">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font> &amp;  <a href="qc_lang1.html#K6" title="QC_LANG1:func.6">the_arity_of</a> <font color="Maroon" title="c5">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> )
 ;<br/>
<a NAME="E6:2"/>
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">l</font> <a href="qc_lang1.html#K7" title="QC_LANG1:func.7">-ary_QC-pred_symbols</a> 
 
<b>by </b><i><a class="txt" href="substut2.html#E1:2"><i><font color="Green" title="E3">A1</font></i></a></i>;<br/>
<a NAME="E7:2"/><b>then </b>
<font color="Maroon" title="c2">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">P2</font> where <font color="Olive" title="b1">P2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K5" title="QC_LANG1:func.5">QC-pred_symbols</a>  :  <a href="qc_lang1.html#K6" title="QC_LANG1:func.6">the_arity_of</a> <font color="Olive" title="b1">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">l</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D7" title="QC_LANG1:def.7">QC_LANG1:def 7</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">P2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K5" title="QC_LANG1:func.5">QC-pred_symbols</a> <b> such that </b><br/><a NAME="E9:2"/><i><font color="Green" title="E5">A3</font></i>: 
( <font color="Maroon" title="c6">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font> &amp;  <a href="qc_lang1.html#K6" title="QC_LANG1:func.6">the_arity_of</a> <font color="Maroon" title="c6">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">l</font> )
 ;<br/>
<b>thus </b><a NAME="E10:2"/>
<font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">l</font>
 <b>by </b><i><a class="txt" href="substut2.html#E5:2"><i><font color="Green" title="E4">A2</font></i></a>, <a class="txt" href="substut2.html#E9:2"><i><font color="Green" title="E5">A3</font></i></a></i>;<br/>


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