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

<b>let </b><font color="Maroon">H</font> be   <a href="modelc_1.html#NM1">CTL-formula</a>;<br/><b>let </b><font color="Maroon">F</font> be   <a href="modelc_1.html#NM1">CTL-formula</a>;<br/><b>let </b><font color="Maroon">sq</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>





<a NAME="E1:30"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st ( for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">n</font> holds <br/>for <font color="Olive">H</font>, <font color="Olive">F</font> being  <a href="modelc_1.html#NM1">CTL-formula</a><br/> for <font color="Olive">sq</font> being  <a href="finseq_1.html#NM1">FinSequence</a>  st  <a href="finseq_1.html#K3">len</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Olive">k</font> &amp; <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="finseq_1.html#K7">^</a> <font color="Olive">sq</font> holds <br/><font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> ) holds <br/>for <font color="Olive">H</font>, <font color="Olive">F</font> being  <a href="modelc_1.html#NM1">CTL-formula</a><br/> for <font color="Olive">sq</font> being  <a href="finseq_1.html#NM1">FinSequence</a>  st  <a href="finseq_1.html#K3">len</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Olive">n</font> &amp; <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="finseq_1.html#K7">^</a> <font color="Olive">sq</font> holds <br/><font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:30_1"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font> holds <br/>for <font color="Olive">H</font>, <font color="Olive">F</font> being  <a href="modelc_1.html#NM1">CTL-formula</a><br/> for <font color="Olive">sq</font> being  <a href="finseq_1.html#NM1">FinSequence</a>  st  <a href="finseq_1.html#K3">len</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Olive">k</font> &amp; <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="finseq_1.html#K7">^</a> <font color="Olive">sq</font> holds <br/><font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font>
 ;<br/>

<b>let </b><font color="Maroon">H</font> be   <a href="modelc_1.html#NM1">CTL-formula</a>;<br/><b>let </b><font color="Maroon">F</font> be   <a href="modelc_1.html#NM1">CTL-formula</a>;<br/><b>let </b><font color="Maroon">sq</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>





<b>assume </b><a NAME="E2:30_1"/><i><font color="Green">E50</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font> )
 ;<br/>

<a NAME="E3:30_1"/><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">sq</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E4:30_1"/><i><font color="Green">E53</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E5:30_1"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E6:30_1"/><b>then </b><i><font color="Green">E54</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">F</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<div><i><font color="Green">E55</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:30_1_1"/>
<font color="Maroon">H</font> is <a href="modelc_1.html#V2" target="_self">atomic</a>
 ;<br/><b>then consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:30_1_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K7" target="_self">atom.</a> <font color="Maroon">k</font>
 <b>by </b><i/>;<br/><a NAME="E4:30_1_1"/><i><font color="Green">E57</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><a NAME="E5:30_1_1"/><b>then </b>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> )
 <b>by </b><i>, , , <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E6:30_1_1"/><b>then </b>
1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">sq</font></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="binop_2.html#K23">+</a> 0
 <b>by </b><i>, , <a class="ref" href="modelc_1.html#D3" target="_self">Def3</a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:30_1_1"/><b>then </b>
<font color="Maroon">sq</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/><b>hence </b><a NAME="E8:30_1_1"/>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E58</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:30_1_2"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V3" target="_self">negative</a>
 ;<br/><b>then consider </b><font color="Maroon">H1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E3:30_1_2"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K8" target="_self">'not'</a> <font color="Maroon">H1</font>
 <b>by </b><i/>;<br/><a NAME="E4:30_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, <a class="ref" href="modelc_1.html#D3" target="_self">Def3</a>, </i>;<br/><a NAME="E5:30_1_2"/><b>then </b>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="modelc_1.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><a NAME="E6:30_1_2"/><b>then </b>
<font color="Maroon">F</font> is <a href="modelc_1.html#V3" target="_self">negative</a>
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">F1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E8:30_1_2"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K8" target="_self">'not'</a> <font color="Maroon">F1</font>
 <b>by </b><i/>;<br/><a NAME="E9:30_1_2"/>
(  <a href="modelc_1.html#K8" target="_self">'not'</a> <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font> &amp;  <a href="modelc_1.html#K8" target="_self">'not'</a> <font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/><a NAME="E10:30_1_2"/><b>then </b><i><font color="Green">E62</font></i>: 
<font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font>
 <b>by </b><i>, <a class="ref" href="modelc_1.html#D4" target="_self">Def4</a>, , <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/><a NAME="E11:30_1_2"/>
( <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">0</span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1 <a href="hidden.html#R1">=</a> 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="ref" href="modelc_1.html#D4" target="_self">Def4</a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><a NAME="E12:30_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E13:30_1_2"/>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:30_1"><i><font color="Green">E28</font></i></a>, , <a class="ref" href="modelc_1.html#D4" target="_self">Def4</a>, , <a class="ref" href="modelc_1.html#D5" target="_self">Def5</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E63</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:30_1_3"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a>
 ;<br/><b>then consider </b><font color="Maroon">G1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a>, <font color="Maroon">G</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E3:30_1_3"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G1</font> <a href="modelc_1.html#K9" target="_self">'&amp;'</a> <font color="Maroon">G</font>
 <b>by </b><i/>;<br/><a NAME="E4:30_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, <a class="ref" href="modelc_1.html#D4" target="_self">Def4</a>, </i>;<br/><a NAME="E5:30_1_3"/><b>then </b>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="modelc_1.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><a NAME="E6:30_1_3"/><b>then </b>
<font color="Maroon">F</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a>
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">F1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a>, <font color="Maroon">H1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E8:30_1_3"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="modelc_1.html#K9" target="_self">'&amp;'</a> <font color="Maroon">H1</font>
 <b>by </b><i/>;<br/><a NAME="E9:30_1_3"/>
( <font color="Maroon">G1</font> <a href="modelc_1.html#K9" target="_self">'&amp;'</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G</font> &amp; <font color="Maroon">F1</font> <a href="modelc_1.html#K9" target="_self">'&amp;'</a> <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><font color="Maroon">F1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font></span>)</span></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/><a NAME="E10:30_1_3"/><b>then </b><i><font color="Green">E67</font></i>: 
<font color="Maroon">G1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="modelc_1.html#D5" target="_self">Def5</a>, <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/><a NAME="E11:30_1_3"/><b>then </b><i><font color="Green">E68</font></i>: 
( (  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font> or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font> ) &amp; (  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font> implies  ex <font color="Olive">sq'</font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">G1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <font color="Olive">sq'</font> ) &amp; (  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font> implies  ex <font color="Olive">sq'</font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G1</font> <a href="finseq_1.html#K7">^</a> <font color="Olive">sq'</font> ) )
 <b>by </b><i><a class="ref" href="finseq_1.html#T64">FINSEQ_1:64</a></i>;<br/><div><i><font color="Green">E69</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_3_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">sq'</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><a NAME="E1:30_1_3_1"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">G1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq'</font>
 ;<br/><a NAME="E2:30_1_3_1"/>
( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G1</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G1</font></span>)</span> <a href="hidden.html#R1">=</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">1</span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 &amp; 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1 )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><a NAME="E3:30_1_3_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E4:30_1_3_1"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E5:30_1_3_1"/>
<font color="Maroon">G1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:30_1"><i><font color="Green">E28</font></i></a>, , </i>;<br/></div><b>end;</b></div><div><i><font color="Green">E99</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_3_2"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">sq'</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><a NAME="E1:30_1_3_2"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq'</font>
 ;<br/><a NAME="E2:30_1_3_2"/>
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">sq</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font></span>)</span> <a href="hidden.html#R1">=</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">1</span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> &amp; 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">sq</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">sq</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="modelc_1.html#D5" target="_self">Def5</a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><a NAME="E3:30_1_3_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E4:30_1_3_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E5:30_1_3_2"/>
<font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G1</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:30_1"><i><font color="Green">E28</font></i></a>, , </i>;<br/></div><b>end;</b></div><a NAME="E14:30_1_3"/><b>then </b><i><font color="Green">E101</font></i>: 
<font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font>
 <b>by </b><i>, , , <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/><a NAME="E15:30_1_3"/>
( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G1</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G1</font></span>)</span> <a href="hidden.html#R1">=</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">1</span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1">(<span class="default">1 <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><a NAME="E16:30_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="binop_2.html#K23">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E17:30_1_3"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E18:30_1_3"/>
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:30_1"><i><font color="Green">E28</font></i></a>, , , <a class="ref" href="modelc_1.html#D5" target="_self">Def5</a>, , , , </i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E102</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:30_1_4"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V5" target="_self">ExistNext</a>
 ;<br/><b>then consider </b><font color="Maroon">H1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E3:30_1_4"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K10" target="_self">EX</a> <font color="Maroon">H1</font>
 <b>by </b><i/>;<br/><a NAME="E4:30_1_4"/>
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 2
 <b>by </b><i>, , </i>;<br/><a NAME="E5:30_1_4"/><b>then </b>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 2
 <b>by </b><i><a class="ref" href="modelc_1.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><a NAME="E6:30_1_4"/><b>then </b>
<font color="Maroon">F</font> is <a href="modelc_1.html#V5" target="_self">ExistNext</a>
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">F1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E8:30_1_4"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K10" target="_self">EX</a> <font color="Maroon">F1</font>
 <b>by </b><i/>;<br/><a NAME="E9:30_1_4"/>
(  <a href="modelc_1.html#K10" target="_self">EX</a> <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">2</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font> &amp;  <a href="modelc_1.html#K10" target="_self">EX</a> <font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">2</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">2</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">2</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/><a NAME="E10:30_1_4"/><b>then </b><i><font color="Green">E106</font></i>: 
<font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font>
 <b>by </b><i>, <a class="ref" href="modelc_1.html#D5" target="_self">Def5</a>, , <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/><a NAME="E11:30_1_4"/>
( <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">2</span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1 <a href="hidden.html#R1">=</a> 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">2</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="ref" href="modelc_1.html#D5" target="_self">Def5</a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><a NAME="E12:30_1_4"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E13:30_1_4"/>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:30_1"><i><font color="Green">E28</font></i></a>, , <a class="ref" href="modelc_1.html#D5" target="_self">Def5</a>, , </i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E107</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:30_1_5"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V6" target="_self">ExistGlobal</a>
 ;<br/><b>then consider </b><font color="Maroon">H1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E3:30_1_5"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K11" target="_self">EG</a> <font color="Maroon">H1</font>
 <b>by </b><i/>;<br/><a NAME="E4:30_1_5"/>
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 3
 <b>by </b><i>, <a class="ref" href="modelc_1.html#D5" target="_self">Def5</a>, </i>;<br/><a NAME="E5:30_1_5"/><b>then </b>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 3
 <b>by </b><i><a class="ref" href="modelc_1.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><a NAME="E6:30_1_5"/><b>then </b>
<font color="Maroon">F</font> is <a href="modelc_1.html#V6" target="_self">ExistGlobal</a>
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">F1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E8:30_1_5"/><i><font color="Green">E110</font></i>: 
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K11" target="_self">EG</a> <font color="Maroon">F1</font>
 <b>by </b><i/>;<br/><a NAME="E9:30_1_5"/>
(  <a href="modelc_1.html#K11" target="_self">EG</a> <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">3</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font> &amp;  <a href="modelc_1.html#K11" target="_self">EG</a> <font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">3</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">3</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">3</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/><a NAME="E10:30_1_5"/><b>then </b><i><font color="Green">E111</font></i>: 
<font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font>
 <b>by </b><i>, , , <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/><a NAME="E11:30_1_5"/>
( <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">3</span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1 <a href="hidden.html#R1">=</a> 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">3</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><a NAME="E12:30_1_5"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E13:30_1_5"/>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:30_1"><i><font color="Green">E28</font></i></a>, , , , </i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_6"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:30_1_6"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a>
 ;<br/><b>then consider </b><font color="Maroon">G1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a>, <font color="Maroon">G</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E3:30_1_6"/><i><font color="Green">E113</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G1</font> <a href="modelc_1.html#K12" target="_self">EU</a> <font color="Maroon">G</font>
 <b>by </b><i/>;<br/><a NAME="E4:30_1_6"/>
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 4
 <b>by </b><i>, <a class="ref" href="modelc_1.html#D5" target="_self">Def5</a>, </i>;<br/><a NAME="E5:30_1_6"/><b>then </b>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 4
 <b>by </b><i><a class="ref" href="modelc_1.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><a NAME="E6:30_1_6"/><b>then </b>
<font color="Maroon">F</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a>
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">F1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a>, <font color="Maroon">H1</font> being   <a href="modelc_1.html#NM1">CTL-formula</a><b> such that </b><br/><a NAME="E8:30_1_6"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="modelc_1.html#K12" target="_self">EU</a> <font color="Maroon">H1</font>
 <b>by </b><i/>;<br/><a NAME="E9:30_1_6"/>
( <font color="Maroon">G1</font> <a href="modelc_1.html#K12" target="_self">EU</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G</font> &amp; <font color="Maroon">F1</font> <a href="modelc_1.html#K12" target="_self">EU</a> <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><font color="Maroon">F1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font></span>)</span></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">H1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/><a NAME="E10:30_1_6"/><b>then </b><i><font color="Green">E115</font></i>: 
<font color="Maroon">G1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/><a NAME="E11:30_1_6"/><b>then </b><i><font color="Green">E116</font></i>: 
( (  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font> or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font> ) &amp; (  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font> implies  ex <font color="Olive">sq'</font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">G1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <font color="Olive">sq'</font> ) &amp; (  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font> implies  ex <font color="Olive">sq'</font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G1</font> <a href="finseq_1.html#K7">^</a> <font color="Olive">sq'</font> ) )
 <b>by </b><i><a class="ref" href="finseq_1.html#T64">FINSEQ_1:64</a></i>;<br/><div><i><font color="Green">E117</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_6_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">sq'</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><a NAME="E1:30_1_6_1"/><i><font color="Green">E118</font></i>: 
<font color="Maroon">G1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq'</font>
 ;<br/><a NAME="E2:30_1_6_1"/>
( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G1</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G1</font></span>)</span> <a href="hidden.html#R1">=</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">4</span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 &amp; 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1 )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><a NAME="E3:30_1_6_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E4:30_1_6_1"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E5:30_1_6_1"/>
<font color="Maroon">G1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:30_1"><i><font color="Green">E28</font></i></a>, , </i>;<br/></div><b>end;</b></div><div><i><font color="Green">E119</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_6_2"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">sq'</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><a NAME="E1:30_1_6_2"/><i><font color="Green">E120</font></i>: 
<font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq'</font>
 ;<br/><a NAME="E2:30_1_6_2"/>
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">sq</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font></span>)</span> <a href="hidden.html#R1">=</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">4</span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> &amp; 1 <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">F1</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">sq</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">sq</font></span>)</span></span>)</span> )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><a NAME="E3:30_1_6_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> <a href="binop_2.html#K23">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E4:30_1_6_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E5:30_1_6_2"/>
<font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G1</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:30_1"><i><font color="Green">E28</font></i></a>, , </i>;<br/></div><b>end;</b></div><a NAME="E14:30_1_6"/><b>then </b><i><font color="Green">E121</font></i>: 
<font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font>
 <b>by </b><i>, , , <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/><a NAME="E15:30_1_6"/>
( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G1</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">G1</font></span>)</span> <a href="hidden.html#R1">=</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">4</span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">4</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1">(<span class="default">1 <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G1</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><a NAME="E16:30_1_6"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> <a href="binop_2.html#K23">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E17:30_1_6"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E18:30_1_6"/>
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:30_1"><i><font color="Green">E28</font></i></a>, , , , , , , </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E13:30_1"/>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="ref" href="modelc_1.html#D2" target="_self">Def2</a>, , <a class="ref" href="modelc_1.html#D3" target="_self">Def3</a>, <a class="ref" href="modelc_1.html#D4" target="_self">Def4</a>, , </i>;<br/>


</div><b>end;</b></div>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>for <font color="Olive">H</font>, <font color="Olive">F</font> being  <a href="modelc_1.html#NM1">CTL-formula</a><br/> for <font color="Olive">sq</font> being  <a href="finseq_1.html#NM1">FinSequence</a>  st  <a href="finseq_1.html#K3">len</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="finseq_1.html#K7">^</a> <font color="Olive">sq</font> holds <br/><font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font>;<br/>
<a NAME="E2:30"/><i><font color="Green">E122</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">k</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">n</font>] ) holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>]
 
<b>by </b><i><a class="txt" href="modelc_1.html#E1:30"><i><font color="Green">E27</font></i></a></i>;<br/>
<a NAME="E3:30"/><i><font color="Green">E123</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">n</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S4">NAT_1:sch 4</a>();<br/></i>
<a NAME="E4:30"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 
;<br/>
<b>hence </b><a NAME="E5:30"/>
( <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">sq</font> implies <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> )
 <b>by </b><i/>;<br/>


</div>
