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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> ;<br/>

<b>assume </b><a NAME="E1:68"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="substut1.html#V5" target="_self">Sub_negative</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> <b> such that </b><br/><a NAME="E3:68"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K20" target="_self">Sub_not</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="substut1.html#D26" target="_self">Def26</a></i>;<br/>
<a NAME="E4:68"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="txt" href="substut1.html#E3:68"><i><font color="Green">E40</font></i></a></i>;<br/>
<a NAME="E5:68"/><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default"><a href="substut1.html#K27" target="_self">Sub_the_argument_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="substut1.html#K18" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> 
 
<b>by </b><i><a class="txt" href="substut1.html#E3:68"><i><font color="Green">E40</font></i></a>, <a class="ref" href="substut1.html#D30" target="_self">Def30</a></i>;<br/>
<a NAME="E6:68"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="substut1.html#K18" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="substut1.html#E4:68"><i><font color="Green">E41</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E7:68"/>
 <a href="qc_lang1.html#K12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> is <a href="qc_lang1.html#V3">negative</a>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D18">QC_LANG1:def 18</a></i>;<br/>
<a NAME="E8:68"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="substut1.html#E6:68"><i><font color="Green">E43</font></i></a>, <a class="ref" href="qc_lang1.html#T45">QC_LANG1:45</a></i>;<br/>
<b>hence </b><a NAME="E9:68"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K27" target="_self">Sub_the_argument_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="substut1.html#E5:68"><i><font color="Green">E42</font></i></a>, <a class="ref" href="qc_lang2.html#T2">QC_LANG2:2</a></i>;<br/>


</div>
