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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><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#NM6">QC-pred_symbol</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="substut1.html#NM1">CQC_Substitution</a>;<br/>













<b>assume </b><a NAME="E1:12"/><i><font color="Green">E8</font></i>: 
 <a href="substut1.html#K26">Sub_the_arguments_of</a> <span class="p1">(<span class="default"><a href="substut1.html#K17">Sub_P</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K26">Sub_the_arguments_of</a> <span class="p1">(<span class="default"><a href="substut1.html#K17">Sub_P</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>
 ;<br/>

<b>consider </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">vSUB</a> <b> such that </b><br/><a NAME="E3:12"/><i><font color="Green">E9</font></i>: 
(  <a href="substut1.html#K26">Sub_the_arguments_of</a> <span class="p1">(<span class="default"><a href="substut1.html#K17">Sub_P</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> &amp;  <a href="substut1.html#K17">Sub_P</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K17">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> )
 <b>by </b><i><a class="ref" href="substut1.html#D29">SUBSTUT1:def 29</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">c<sub>13</sub></font> being   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>14</sub></font> being    <a href="qc_lang1.html#M1">QC-variable_list</a> of <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>15</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K1">vSUB</a> <b> such that </b><br/><a NAME="E5:12"/><i><font color="Green">E10</font></i>: 
(  <a href="substut1.html#K26">Sub_the_arguments_of</a> <span class="p1">(<span class="default"><a href="substut1.html#K17">Sub_P</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> &amp;  <a href="substut1.html#K17">Sub_P</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K17">Sub_P</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 <b>by </b><i><a class="ref" href="substut1.html#D29">SUBSTUT1:def 29</a></i>;<br/>
<a NAME="E6:12"/>
 <a href="substut1.html#K17">Sub_P</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</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="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="ref" href="substut1.html#T9">SUBSTUT1:9</a></i>;<br/>
<a NAME="E7:12"/><b>then </b><i><font color="Green">E11</font></i>: 
<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="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="domain_1.html#K1">]</a></span> <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="sublemma.html#E3:12"><i><font color="Green">E9</font></i></a>, <a class="ref" href="substut1.html#T9">SUBSTUT1:9</a></i>;<br/>
<a NAME="E8:12"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>4</sub></font> <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>2</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>10</sub></font> <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> )
 
<b>by </b><i><a class="ref" href="qc_lang1.html#T23">QC_LANG1:23</a></i>;<br/>
<a NAME="E9:12"/><b>then </b><i><font color="Green">E12</font></i>: 
<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> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="sublemma.html#E7:12"><i><font color="Green">E11</font></i></a>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<a NAME="E10:12"/>
( <span class="p1">(<span class="default"><span class="p2"><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></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T58">FINSEQ_1:58</a></i>;<br/>
<a NAME="E11:12"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="sublemma.html#E9:12"><i><font color="Green">E12</font></i></a>, <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/>
<a NAME="E12:12"/>
 <a href="substut1.html#K17">Sub_P</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</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="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="ref" href="substut1.html#T9">SUBSTUT1:9</a></i>;<br/>
<a NAME="E13:12"/><b>then </b><i><font color="Green">E14</font></i>: 
<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="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span> <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>13</sub></font> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>15</sub></font></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E5:12"><i><font color="Green">E10</font></i></a>, <a class="ref" href="substut1.html#T9">SUBSTUT1:9</a></i>;<br/>
<a NAME="E14:12"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>5</sub></font> <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>3</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>14</sub></font> <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>13</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>14</sub></font> )
 
<b>by </b><i><a class="ref" href="qc_lang1.html#T23">QC_LANG1:23</a></i>;<br/>
<a NAME="E15:12"/><b>then </b><i><font color="Green">E15</font></i>: 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>13</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>14</sub></font> <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>3</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="sublemma.html#E13:12"><i><font color="Green">E14</font></i></a>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<a NAME="E16:12"/>
( <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>13</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T58">FINSEQ_1:58</a></i>;<br/>
<b>hence </b><a NAME="E17:12"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:12"><i><font color="Green">E8</font></i></a>, <a class="txt" href="sublemma.html#E3:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="sublemma.html#E5:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="sublemma.html#E11:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="sublemma.html#E15:12"><i><font color="Green">E15</font></i></a>, <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/>


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