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<b>let </b><font color="Maroon" title="c1">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/>



<b>assume </b><a NAME="E1:30"/><i><font color="Green" title="E33">A1</font></i>: 
( 0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> &amp;  <a href="calcul_1.html#R4" title="CALCUL_1:pred.4">|-</a> <font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )
 ;<br/>

<a NAME="E2:30"/>
<font color="Maroon" title="c2">f</font> <a href="calcul_1.html#R2" title="CALCUL_1:pred.2">is_Subsequence_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="goedelcp.html#E1:30"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="calcul_1.html#T13" title="CALCUL_1:th.13">CALCUL_1:13</a></i>;<br/>
<a NAME="E3:30"/><b>then </b>
 <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="calcul_1.html#R2" title="CALCUL_1:pred.2">is_Subsequence_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" title="CALCUL_1:th.5">CALCUL_1:5</a></i>;<br/>
<a NAME="E4:30"/><b>then </b><i><font color="Green" title="E34">A2</font></i>: 
 <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="calcul_1.html#R2" title="CALCUL_1:pred.2">is_Subsequence_of</a>  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" title="CALCUL_1:th.5">CALCUL_1:5</a></i>;<br/>
<a NAME="E5:30"/>
 <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" title="CALCUL_1:th.5">CALCUL_1:5</a></i>;<br/>
<a NAME="E6:30"/><b>then </b>
 <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" title="CALCUL_1:th.5">CALCUL_1:5</a></i>;<br/>
<b>hence </b><a NAME="E7:30"/>
 <a href="calcul_1.html#R4" title="CALCUL_1:pred.4">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="goedelcp.html#E1:30"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="goedelcp.html#E4:30"><i><font color="Green" title="E34">A2</font></i></a>, <a class="ref" href="calcul_1.html#T36" title="CALCUL_1:th.36">CALCUL_1:36</a></i>;<br/>


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