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

<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#K4" title="CQC_LANG:func.4">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ;<br/>



<b>assume </b><a NAME="E1:61"/><i><font color="Green" title="E58">A1</font></i>: 
(  <a href="calcul_1.html#R4" title="CALCUL_1:pred.4">|-</a> <font color="Maroon" title="c2">f</font> &amp;  <a href="calcul_1.html#R4" title="CALCUL_1:pred.4">|-</a> <span class="p1">(<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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )
 ;<br/>

<b>set </b><font color="Maroon" title="c3">f1</font> = <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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><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>;<br/>
<a NAME="E2:61"/>
 <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"><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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><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="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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" target="_self" title="CALCUL_1:th.5">Th5</a></i>;<br/>
<a NAME="E3:61"/><b>then </b>
(  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">f</font> <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"><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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><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> &amp;  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c2">f</font> <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"><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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><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> )
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self" title="CALCUL_1:th.5">Th5</a>, <a class="ref" href="calcul_1.html#T8" target="_self" title="CALCUL_1:th.8">Th8</a></i>;<br/>
<a NAME="E4:61"/><b>then </b><i><font color="Green" title="E59">A2</font></i>: 
 <a href="calcul_1.html#R4" title="CALCUL_1:pred.4">|-</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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><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="calcul_1.html#E1:61"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="calcul_1.html#T36" target="_self" title="CALCUL_1:th.36">Th36</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">f2</font> = <span class="p1">(<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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c5">f3</font> = <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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>;<br/>
<a NAME="E5:61"/><i><font color="Green" title="E60">A3</font></i>: 
(  <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"><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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> &amp;  <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"><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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">f</font> )
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self" title="CALCUL_1:th.5">Th5</a></i>;<br/>
<a NAME="E6:61"/>
 <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"><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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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>)</span></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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p1">(<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>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self" title="CALCUL_1:th.5">Th5</a></i>;<br/>
<a NAME="E7:61"/><b>then </b>
 <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"><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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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>)</span></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"><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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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>)</span></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" target="_self" title="CALCUL_1:th.5">Th5</a></i>;<br/>
<a NAME="E8:61"/><b>then </b><i><font color="Green" title="E61">A4</font></i>: 
 <a href="calcul_1.html#R4" title="CALCUL_1:pred.4">|-</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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="calcul_1.html#E1:61"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="calcul_1.html#E5:61"><i><font color="Green" title="E60">A3</font></i></a>, <a class="ref" href="calcul_1.html#T8" target="_self" title="CALCUL_1:th.8">Th8</a>, <a class="ref" href="calcul_1.html#T36" target="_self" title="CALCUL_1:th.36">Th36</a></i>;<br/>
<a NAME="E9:61"/><i><font color="Green" title="E62">A5</font></i>: 
 <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"><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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><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="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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" target="_self" title="CALCUL_1:th.5">Th5</a></i>;<br/>
<a NAME="E10:61"/><b>then </b><i><font color="Green" title="E63">A6</font></i>: 
 <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"><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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><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="relset_1.html#R2" title="RELSET_1:pred.2">=</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"><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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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>)</span></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" target="_self" title="CALCUL_1:th.5">Th5</a></i>;<br/>
<a NAME="E11:61"/><i><font color="Green" title="E64">A7</font></i>: 
 <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">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" 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> <span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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="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></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="txt" href="calcul_1.html#E9:61"><i><font color="Green" title="E62">A5</font></i></a>, <a class="ref" href="calcul_1.html#T5" target="_self" title="CALCUL_1:th.5">Th5</a></i>;<br/>
<a NAME="E12:61"/>
 <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"><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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c2">f</font>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T5" target="_self" title="CALCUL_1:th.5">Th5</a></i>;<br/>
<a NAME="E13:61"/><b>then </b><i><font color="Green" title="E65">A8</font></i>: 
 <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</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" 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> <span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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="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></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"><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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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>)</span></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" target="_self" title="CALCUL_1:th.5">Th5</a></i>;<br/>
<a NAME="E14:61"/>
1 <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> <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> <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="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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"><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>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T9" target="_self" title="CALCUL_1:th.9">Th9</a></i>;<br/>
<a NAME="E15:61"/><b>then </b>
 <a href="calcul_1.html#R4" title="CALCUL_1:pred.4">|-</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p2">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">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" 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> <span class="p5"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</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="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p5">(<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></span>)</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="calcul_1.html#E4:61"><i><font color="Green" title="E59">A2</font></i></a>, <a class="txt" href="calcul_1.html#E8:61"><i><font color="Green" title="E61">A4</font></i></a>, <a class="txt" href="calcul_1.html#E10:61"><i><font color="Green" title="E63">A6</font></i></a>, <a class="txt" href="calcul_1.html#E11:61"><i><font color="Green" title="E64">A7</font></i></a>, <a class="txt" href="calcul_1.html#E13:61"><i><font color="Green" title="E65">A8</font></i></a>, <a class="ref" href="calcul_1.html#T38" target="_self" title="CALCUL_1:th.38">Th38</a></i>;<br/>
<b>hence </b><a NAME="E16:61"/>
 <a href="calcul_1.html#R4" title="CALCUL_1:pred.4">|-</a> <span class="p1">(<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> <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="calcul_1.html#E9:61"><i><font color="Green" title="E62">A5</font></i></a>, <a class="ref" href="calcul_1.html#T5" target="_self" title="CALCUL_1:th.5">Th5</a></i>;<br/>


</div>
