<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">P</font> be   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">k</font>;<br/><b>let </b><font color="Maroon">l</font> be   <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">k</font>;<br/>









<b>set </b><font color="Maroon">S</font> = <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="substut2.html#K3" target="_self">Sbst</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span>;<br/>
<a NAME="E1:20"/><i><font color="Green">E43</font></i>: 
<span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="substut2.html#K3" target="_self">Sbst</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span> <a href="hidden.html#R1">=</a>  <a href="sublemma.html#K4">Sub_P</a> <font color="Maroon">P</font>,<font color="Maroon">l</font>,<span class="p1">(<span class="default"><a href="substut2.html#K3" target="_self">Sbst</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="substut1.html#T9">SUBSTUT1:9</a></i>;<br/>
<a NAME="E2:20"/><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">l</font></span>)</span> <a href="substut2.html#K4" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> <a href="cqc_lang.html#K8">!</a> <span class="p1">(<span class="default"><a href="sublemma.html#K5">CQC_Subst</a> <font color="Maroon">l</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" target="_self">Sbst</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="sublemma.html#T9">SUBLEMMA:9</a></i>;<br/>
<a NAME="E3:20"/>
 <a href="cqc_sim1.html#K6">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="cqc_lang.html#K8">!</a> <span class="p2">(<span class="default"><a href="sublemma.html#K5">CQC_Subst</a> <font color="Maroon">l</font>,<span class="p3">(<span class="default"><a href="substut2.html#K3" target="_self">Sbst</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="cqc_sim1.html#T15">CQC_SIM1:15</a></i>;<br/>
<b>hence </b><a NAME="E4:20"/>
( <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">l</font></span>)</span> <a href="substut2.html#K4" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> <a href="cqc_lang.html#K8">!</a> <span class="p1">(<span class="default"><a href="sublemma.html#K5">CQC_Subst</a> <font color="Maroon">l</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" target="_self">Sbst</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span></span>)</span> &amp;  <a href="cqc_sim1.html#K6">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">l</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cqc_sim1.html#K6">QuantNbr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">l</font></span>)</span> <a href="substut2.html#K4" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="cqc_sim1.html#T15">CQC_SIM1:15</a></i>;<br/>


</div>
