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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="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</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="substut1.html#K16" target="_self">QC-Sub-WFF</a> <b> such that </b><a NAME="E1:54_1_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K21" target="_self">Sub_&amp;</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K19" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K19" target="_self">`2</a>  )
 ;<br/>

<b>given </b><font color="Maroon">c<sub>5</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><a NAME="E2:54_1_1"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K21" target="_self">Sub_&amp;</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K19" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="substut1.html#K19" target="_self">`2</a>  )
 ;<br/>

<a NAME="E3:54_1_1"/><i><font color="Green">E32</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"><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> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</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> &amp; <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</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>3</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#E1:54_1_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="substut1.html#E2:54_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="substut1.html#D21" target="_self">Def21</a></i>;<br/>
<a NAME="E4:54_1_1"/><b>then </b><i><font color="Green">E33</font></i>: 
<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> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">2,0</span><a href="domain_1.html#K1">]</a></span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10">@</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> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3"><a href="domain_1.html#K1">[</a><span class="default">2,0</span><a href="domain_1.html#K1">]</a></span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K10">@</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>)</span> <a href="finseq_1.html#K8">^</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>4</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>
<b>by </b><i><a class="txt" href="substut1.html#E4:54_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="qc_lang1.html#D15">QC_LANG1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3"><a href="domain_1.html#K1">[</a><span class="default">2,0</span><a href="domain_1.html#K1">]</a></span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</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>5</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="qc_lang1.html#D15">QC_LANG1:def 15</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">2,0</span><a href="domain_1.html#K1">]</a></span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
;<br/>
<a NAME="E6:54_1_1"/><b>then </b><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="finseq_1.html#K8">^</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>4</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</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>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="finseq_1.html#K8">^</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>5</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/>
<a NAME="E7:54_1_1"/>
(  <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>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></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">@</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> or  <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>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></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">@</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></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="E9:54_1_1"/><i><font color="Green">E35</font></i>: 
( ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K10">@</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> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K10">@</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K10">@</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K10">@</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>and </b><br/><a NAME="E10:54_1_1"/><i><font color="Green">E36</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="E11:54_1_1"/><i><font color="Green">E37</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="substut1.html#E6:54_1_1"><i><font color="Green">E34</font></i></a></i>;<br/>
<a NAME="E12:54_1_1"/><i><font color="Green">E38</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="substut1.html#E10:54_1_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="substut1.html#E11:54_1_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="finseq_1.html#T64">FINSEQ_1:64</a></i>;<br/>
<a NAME="E13:54_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K10">@</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> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K10">@</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D12">QC_LANG1:def 12</a></i>;<br/>
<a NAME="E14:54_1_1"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> 
 
<b>by </b><i><a class="txt" href="substut1.html#E9:54_1_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="substut1.html#E12:54_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="qc_lang1.html#T37">QC_LANG1:37</a></i>;<br/>
<a NAME="E15:54_1_1"/>
( <font color="Maroon">c<sub>2</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"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </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> &amp; <font color="Maroon">c<sub>3</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"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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="ref" href="substut1.html#T10" target="_self">Th10</a></i>;<br/>
<b>hence </b><a NAME="E16:54_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="substut1.html#E3:54_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="substut1.html#E14:54_1_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>


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