<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>



<b>assume </b><a NAME="E1:62"/><i><font color="Green">E60</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="calcul_1.html#R4" target="_self">|-</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="calcul_1.html#R4" target="_self">|-</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>;<br/>
<a NAME="E2:62"/>
 <a href="calcul_1.html#K1" target="_self">Ant</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" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E3:62"/><b>then </b>
(  <a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font> <a href="calcul_1.html#R2" target="_self">is_Subsequence_of</a>  <a href="calcul_1.html#K1" target="_self">Ant</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" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> &amp;  <a href="calcul_1.html#K2" target="_self">Suc</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" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a>, <a class="ref" href="calcul_1.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E4:62"/><b>then </b><i><font color="Green">E61</font></i>: 
 <a href="calcul_1.html#R4" target="_self">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="calcul_1.html#E1:62"><i><font color="Green">E60</font></i></a>, <a class="ref" href="calcul_1.html#T36" target="_self">Th36</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>;<br/>
<a NAME="E5:62"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>;<br/>
<a NAME="E6:62"/><b>then </b>
<span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E7:62"/><b>then </b><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="calcul_1.html#K2" target="_self">Suc</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" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E8:62"/><i><font color="Green">E63</font></i>: 
 <a href="calcul_1.html#K1" target="_self">Ant</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" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E9:62"/><b>then </b><i><font color="Green">E64</font></i>: 
<span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="calcul_1.html#K2" target="_self">Suc</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" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="calcul_1.html#E7:62"><i><font color="Green">E62</font></i></a>, <a class="ref" href="finseq_2.html#T19">FINSEQ_2:19</a></i>;<br/>
<a NAME="E10:62"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="calcul_1.html#E8:62"><i><font color="Green">E63</font></i></a>, <a class="ref" href="calcul_1.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E11:62"/><b>then </b>
 <a href="calcul_1.html#K2" target="_self">Suc</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" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="calcul_1.html#R1" target="_self">is_tail_of</a>  <a href="calcul_1.html#K1" target="_self">Ant</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" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="calcul_1.html#E9:62"><i><font color="Green">E64</font></i></a>, <a class="ref" href="calcul_1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E12:62"/><b>then </b><i><font color="Green">E65</font></i>: 
 <a href="calcul_1.html#R4" target="_self">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T33" target="_self">Th33</a></i>;<br/>
<a NAME="E13:62"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E14:62"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E15:62"/><b>then </b><i><font color="Green">E66</font></i>: 
 <a href="calcul_1.html#R4" target="_self">|-</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="calcul_1.html#E4:62"><i><font color="Green">E61</font></i></a>, <a class="txt" href="calcul_1.html#E12:62"><i><font color="Green">E65</font></i></a>, <a class="ref" href="calcul_1.html#T44" target="_self">Th44</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span>;<br/>
<a NAME="E16:62"/>
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="calcul_1.html#E1:62"><i><font color="Green">E60</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E17:62"/><b>then </b>
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E18:62"/><b>then </b>
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E19:62"/><b>then </b><i><font color="Green">E67</font></i>: 
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E20:62"/><i><font color="Green">E68</font></i>: 
 <a href="calcul_1.html#K1" target="_self">Ant</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" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E21:62"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E22:62"/><b>then </b>
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E23:62"/><b>then </b>
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E24:62"/><b>then </b>
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E25:62"/><b>then </b><i><font color="Green">E69</font></i>: 
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E26:62"/>
 <a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="calcul_1.html#K1" target="_self">Ant</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" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E27:62"/><b>then </b>
 <a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="calcul_1.html#E20:62"><i><font color="Green">E68</font></i></a>, <a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E28:62"/><b>then </b><i><font color="Green">E70</font></i>: 
 <a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E29:62"/>
 <a href="calcul_1.html#K2" target="_self">Suc</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="calcul_1.html#E20:62"><i><font color="Green">E68</font></i></a>, <a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E30:62"/><b>then </b>
 <a href="calcul_1.html#K2" target="_self">Suc</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E31:62"/><b>then </b><i><font color="Green">E71</font></i>: 
 <a href="calcul_1.html#K2" target="_self">Suc</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E32:62"/>
(  <a href="calcul_1.html#K2" target="_self">Suc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="calcul_1.html#K2" target="_self">Suc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E33:62"/><b>then </b>
 <a href="calcul_1.html#R4" target="_self">|-</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="calcul_1.html#E1:62"><i><font color="Green">E60</font></i></a>, <a class="txt" href="calcul_1.html#E15:62"><i><font color="Green">E66</font></i></a>, <a class="txt" href="calcul_1.html#E19:62"><i><font color="Green">E67</font></i></a>, <a class="txt" href="calcul_1.html#E25:62"><i><font color="Green">E69</font></i></a>, <a class="txt" href="calcul_1.html#E28:62"><i><font color="Green">E70</font></i></a>, <a class="txt" href="calcul_1.html#E31:62"><i><font color="Green">E71</font></i></a>, <a class="ref" href="calcul_1.html#T37" target="_self">Th37</a></i>;<br/>
<a NAME="E34:62"/><b>then </b>
 <a href="calcul_1.html#R4" target="_self">|-</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="calcul_1.html#K2" target="_self">Suc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>
<b>hence </b><a NAME="E35:62"/>
 <a href="calcul_1.html#R4" target="_self">|-</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self">Th5</a></i>;<br/>


</div>
