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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="finseq_1.html#M2">FinSequence</a> of  <a href="qc_lang1.html#K1">QC-variables</a> ;<br/>

<b>given </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">c<sub>5</sub></font> being   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>6</sub></font> being    <a href="qc_lang1.html#M1">QC-variable_list</a> of <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>7</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K1" target="_self">vSUB</a> <b> such that </b><a NAME="E1:52_1_2"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K17" target="_self">Sub_P</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 ;<br/>

<b>given </b><font color="Maroon">c<sub>8</sub></font> being   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">c<sub>9</sub></font> being   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>10</sub></font> being    <a href="qc_lang1.html#M1">QC-variable_list</a> of <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>11</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K1" target="_self">vSUB</a> <b> such that </b><a NAME="E2:52_1_2"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K17" target="_self">Sub_P</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 ;<br/>

<a NAME="E3:52_1_2"/><i><font color="Green">E30</font></i>: 
( <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>6</sub></font> &amp; <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>10</sub></font> )
 
<b>by </b><i><a class="ref" href="qc_lang1.html#T23">QC_LANG1:23</a></i>;<br/>
<a NAME="E4:52_1_2"/>
( <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"><font color="Maroon">c<sub>5</sub></font> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></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"><font color="Maroon">c<sub>9</sub></font> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span><a href="domain_1.html#K1">]</a></span> )
 
<b>by </b><i><a class="txt" href="substut1.html#E1:52_1_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="substut1.html#E2:52_1_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="substut1.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E5:52_1_2"/><b>then </b><i><font color="Green">E31</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> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="substut1.html#K18" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="substut1.html#K18" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="substut1.html#K18" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>10</sub></font> )
 
<b>by </b><i><a class="txt" href="substut1.html#E3:52_1_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E6:52_1_2"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="substut1.html#K18" target="_self">`1</a>  is <a href="qc_lang1.html#V2">atomic</a>
 
<b>by </b><i><a class="txt" href="substut1.html#E1:52"><i><font color="Green">E27</font></i></a>, <a class="ref" href="substut1.html#T11" target="_self">Th11</a></i>;<br/>
<b>then </b><font color="Maroon">c<sub>5</sub></font> = 
 <a href="qc_lang1.html#K15">the_pred_symbol_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>
<b>by </b><i><a class="txt" href="substut1.html#E5:52_1_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="qc_lang1.html#D21">QC_LANG1:def 21</a></i>
<br/>.= 
<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="substut1.html#E5:52_1_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="substut1.html#E6:52_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="qc_lang1.html#D21">QC_LANG1:def 21</a></i>
;<br/>
<b>hence </b><a NAME="E8:52_1_2"/>
<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#E1:52_1_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="substut1.html#E2:52_1_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="substut1.html#E5:52_1_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/>


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