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<b>let </b><font color="Maroon" title="c1">S</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> ;<br/>

<b>assume </b><a NAME="E1:68"/>
<font color="Maroon" title="c1">S</font> is <a href="substut1.html#V5" title="SUBSTUT1:attr.5">Sub_negative</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">S'</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> <b> such that </b><br/><a NAME="E3:68"/><i><font color="Green" title="E40">A1</font></i>: 
<font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K20" title="SUBSTUT1:func.20">Sub_not</a> <font color="Maroon" title="c2">S'</font>
 <b>by </b><i><a class="ref" href="substut1.html#D26" target="_self" title="SUBSTUT1:def.26">Def26</a></i>;<br/>
<a NAME="E4:68"/><i><font color="Green" title="E41">A2</font></i>: 
<span class="p1">(<span class="default"><a href="substut1.html#K27" title="SUBSTUT1:func.27">Sub_the_argument_of</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">S'</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> 
 
<b>by </b><i><a class="txt" href="substut1.html#E3:68"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="substut1.html#D30" target="_self" title="SUBSTUT1:def.30">Def30</a></i>;<br/>
<a NAME="E5:68"/><i><font color="Green" title="E42">A3</font></i>: 
<font color="Maroon" title="c1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S'</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="substut1.html#E3:68"><i><font color="Green" title="E40">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="E6:68"/>
 <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S'</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D18" title="QC_LANG1:def.18">QC_LANG1:def 18</a></i>;<br/>
<a NAME="E7:68"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">S'</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="substut1.html#E5:68"><i><font color="Green" title="E42">A3</font></i></a>, <a class="ref" href="qc_lang1.html#T45" title="QC_LANG1:th.45">QC_LANG1:45</a></i>;<br/>
<b>hence </b><a NAME="E8:68"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K27" title="SUBSTUT1:func.27">Sub_the_argument_of</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="substut1.html#E4:68"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="qc_lang2.html#T2" title="QC_LANG2:th.2">QC_LANG2:2</a></i>;<br/>


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