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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="qc_lang1.html#NM8">QC-formula</a>;<br/>

<b>given </b><font color="Maroon">c<sub>4</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a> <b> such that </b><a NAME="E1:35_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="qc_lang1.html#K13" target="_self">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>given </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a> <b> such that </b><a NAME="E2:35_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="qc_lang1.html#K13" target="_self">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default">2,0</span><a href="tarski.html#K4">]</a></span></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default">2,0</span><a href="tarski.html#K4">]</a></span></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="qc_lang1.html#K13" target="_self">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="qc_lang1.html#E1:35_1_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="qc_lang1.html#E2:35_1_1"><i><font color="Green">E28</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default">2,0</span><a href="tarski.html#K4">]</a></span></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>

<br/>.= 
<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default">2,0</span><a href="tarski.html#K4">]</a></span></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
;<br/>
<a NAME="E4:35_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/>
<a NAME="E5:35_1_1"/>
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> or  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
;<br/>
<b>then consider </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E7:35_1_1"/><i><font color="Green">E30</font></i>: 
( ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K10" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font> ) )
 <b>and </b><br/><a NAME="E8:35_1_1"/><i><font color="Green">E31</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E9:35_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="qc_lang1.html#E4:35_1_1"><i><font color="Green">E29</font></i></a></i>;<br/>
<a NAME="E10:35_1_1"/><i><font color="Green">E33</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">c<sub>6</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="qc_lang1.html#E8:35_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="qc_lang1.html#E9:35_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="finseq_1.html#T64">FINSEQ_1:64</a></i>;<br/>
<b>thus </b><a NAME="E11:35_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="qc_lang1.html#E7:35_1_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="qc_lang1.html#E10:35_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="qc_lang1.html#T37" target="_self">Th37</a></i>;<br/>


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