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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">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon" title="c4">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="c5">l</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/>









<b>set </b><font color="Maroon" title="c6">S</font> = <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c5">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>;<br/>
<a NAME="E1:20"/>
<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c5">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">l</font>,<span class="p1">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="substut1.html#T9" title="SUBSTUT1:th.9">SUBSTUT1:9</a></i>;<br/>
<a NAME="E2:20"/><b>then </b><i><font color="Green" title="E13">A1</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c5">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <span class="p1">(<span class="default"><a href="sublemma.html#K5" title="SUBLEMMA:func.5">CQC_Subst</a> <font color="Maroon" title="c5">l</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="sublemma.html#T9" title="SUBLEMMA:th.9">SUBLEMMA:9</a></i>;<br/>
<a NAME="E3:20"/>
 <a href="cqc_sim1.html#K6" title="CQC_SIM1:func.6">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <span class="p2">(<span class="default"><a href="sublemma.html#K5" title="SUBLEMMA:func.5">CQC_Subst</a> <font color="Maroon" title="c5">l</font>,<span class="p3">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="cqc_sim1.html#T15" title="CQC_SIM1:th.15">CQC_SIM1:15</a></i>;<br/>
<b>hence </b><a NAME="E4:20"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c5">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <span class="p1">(<span class="default"><a href="sublemma.html#K5" title="SUBLEMMA:func.5">CQC_Subst</a> <font color="Maroon" title="c5">l</font>,<span class="p2">(<span class="default"><a href="substut2.html#K3" title="SUBSTUT2:func.3">Sbst</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span></span>)</span> &amp;  <a href="cqc_sim1.html#K6" title="CQC_SIM1:func.6">QuantNbr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c5">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K6" title="CQC_SIM1:func.6">QuantNbr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c5">l</font></span>)</span> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span> )
 <b>by </b><i><a class="txt" href="substut2.html#E2:20"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="cqc_sim1.html#T15" title="CQC_SIM1:th.15">CQC_SIM1:15</a></i>;<br/>


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