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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/>





<a NAME="E1:90"/>
<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/>
<b>then consider </b><font color="Maroon" title="c4">k</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="c5">ll'</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-variable_list</a> of <font color="Maroon" title="c4">k</font>, <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="c4">k</font><b> such that </b><br/><a NAME="E3:90"/><i><font color="Green" title="E54">A1</font></i>: 
(  <a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_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="c6">P'</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="c5">ll'</font> )
 <b>by </b><i><a class="ref" href="qc_lang1.html#D21" title="QC_LANG1:def.21">QC_LANG1:def 21</a></i>;<br/>
<a NAME="E4:90"/>
( <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="c5">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="c5">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="E5:90"/><b>then </b>
( <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> &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="c6">P'</font> )
 
<b>by </b><i><a class="txt" href="substut1.html#E3:90"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="finseq_1.html#T58" title="FINSEQ_1:th.58">FINSEQ_1:58</a></i>;<br/>
<b>hence </b><a NAME="E6:90"/>
 <a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_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="c2">P</font>
 <b>by </b><i><a class="txt" href="substut1.html#E3:90"><i><font color="Green" title="E54">A1</font></i></a></i>;<br/>


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