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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/><b>let </b><font color="Maroon" title="c4">Sub</font> be   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a>;<br/>







<b>reconsider </b><font color="Maroon" title="c5">P'</font> = <font color="Maroon" title="c2">P</font> as   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-pred_symbol</a> ;<br/>
<a NAME="E2:14"/><i><font color="Green" title="E9">A1</font></i>: 
 <a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">ll</font>,<font color="Maroon" title="c4">Sub</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<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>,<font color="Maroon" title="c4">Sub</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
<b>by </b><i><a class="ref" href="substut1.html#T9" title="SUBSTUT1:th.9">SUBSTUT1:9</a></i>;<br/>
<a NAME="E3:14"/><b>then </b><i><font color="Green" title="E10">A2</font></i>: 
<span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">ll</font>,<font color="Maroon" title="c4">Sub</font></span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<a NAME="E4:14"/><i><font color="Green" title="E11">A3</font></i>: 
<span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">ll</font>,<font color="Maroon" title="c4">Sub</font></span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Sub</font>
 
<b>by </b><i><a class="txt" href="sublemma.html#E2:14"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<a NAME="E5:14"/>
<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/>
<a NAME="E6:14"/><b>then </b>
( <font color="Maroon" title="c5">P'</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <font color="Maroon" title="c3">ll</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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> &amp;  <a href="substut1.html#K26" title="SUBSTUT1:func.26">Sub_the_arguments_of</a> <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">ll</font>,<font color="Maroon" title="c4">Sub</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">ll</font> &amp;  <a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">ll</font>,<font color="Maroon" title="c4">Sub</font></span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </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="sublemma.html#E3:14"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="qc_lang1.html#D21" title="QC_LANG1:def.21">QC_LANG1:def 21</a>, <a class="ref" href="substut1.html#D29" title="SUBSTUT1:def.29">SUBSTUT1:def 29</a></i>;<br/>
<b>hence </b><a NAME="E7:14"/>
 <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p1">(<span class="default"><a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">ll</font>,<font color="Maroon" title="c4">Sub</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <span class="p1">(<span class="default"><a href="substut1.html#K3" title="SUBSTUT1:func.3">CQC_Subst</a> <font color="Maroon" title="c3">ll</font>,<font color="Maroon" title="c4">Sub</font></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E4:14"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="sublemma.html#T6" target="_self" title="SUBLEMMA:th.6">Th6</a></i>;<br/>


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