<?xml version="1.0"?>
<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>let </b><font color="Maroon">V</font> be    <a href="modelc_1.html#L2" target="_self">CTLModelStr</a> ;<br/><b>let </b><font color="Maroon">Kai</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="modelc_1.html#K19" target="_self">atomic_WFF</a> ,the <a href="modelc_1.html#U6" target="_self">BasicAssign</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">f1</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="modelc_1.html#K13" target="_self">CTL_WFF</a> ,the <a href="modelc_1.html#U5" target="_self">Assignations</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">f2</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="modelc_1.html#K13" target="_self">CTL_WFF</a> ,the <a href="modelc_1.html#U5" target="_self">Assignations</a> of <font color="Maroon">V</font>;<br/>









<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>( <font color="Maroon">f1</font> <a href="modelc_1.html#R2" target="_self">is-PreEvaluation-for</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">Kai</font> &amp; <font color="Maroon">f2</font> <a href="modelc_1.html#R2" target="_self">is-PreEvaluation-for</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">Kai</font> implies for <font color="Olive">H</font> being  <a href="modelc_1.html#NM1">CTL-formula</a>  st  <a href="finseq_1.html#K3">len</a> <font color="Olive">H</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a<sub>1</sub></font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> );<br/>
<a NAME="E1:56"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<b>by </b><i/>;<br/>
<a NAME="E2:56"/><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="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font> <a href="binop_2.html#K23">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:56_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font>]
 ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:56_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">f1</font> <a href="modelc_1.html#R2" target="_self">is-PreEvaluation-for</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1,<font color="Maroon">Kai</font>
 <b>and </b><br/><a NAME="E3:56_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">f2</font> <a href="modelc_1.html#R2" target="_self">is-PreEvaluation-for</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1,<font color="Maroon">Kai</font>
 ;<br/>

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

<b>assume </b><a NAME="E4:56_1"/><i><font color="Green">E54</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:56_1_1"/>
( <font color="Maroon">H</font> is <a href="modelc_1.html#V2" target="_self">atomic</a> or <font color="Maroon">H</font> is <a href="modelc_1.html#V3" target="_self">negative</a> or <font color="Maroon">H</font> is <a href="modelc_1.html#V5" target="_self">ExistNext</a> or <font color="Maroon">H</font> is <a href="modelc_1.html#V6" target="_self">ExistGlobal</a> or <font color="Maroon">H</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a> or <font color="Maroon">H</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a> )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1_1"><b>suppose </b></a><a NAME="E1:56_1_1_1"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V2" target="_self">atomic</a>
 ;<br/><div class="add"><a NAME="E2:56_1_1_1"/><b>then </b>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Kai</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:56_1_1_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="modelc_1.html#E3:56_1"><i><font color="Green">E53</font></i></a>, </i>;<br/><b>hence </b><a NAME="E3:56_1_1_1"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:56_1_1_1"><i><font color="Green">E55</font></i></a>, , <a class="txt" href="modelc_1.html#E4:56_1"><i><font color="Green">E54</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1_2"><b>suppose </b></a><a NAME="E1:56_1_1_2"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V3" target="_self">negative</a>
 ;<br/><div class="add"><a NAME="E2:56_1_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" target="_self">the_argument_of</a> <font color="Maroon">H</font></span>)</span> <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/>;<br/><a NAME="E3:56_1_1_2"/><b>then </b><i><font color="Green">E57</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" target="_self">the_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>by </b><i>, </i>;<br/><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> = 
the <a href="modelc_1.html#U8" target="_self">Not</a> of <font color="Maroon">V</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" target="_self">the_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="modelc_1.html#E1:56_1_1_2"><i><font color="Green">E56</font></i></a>, , <a class="txt" href="modelc_1.html#E4:56_1"><i><font color="Green">E54</font></i></a>, </i>
<br/>.= 
the <a href="modelc_1.html#U8" target="_self">Not</a> of <font color="Maroon">V</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" target="_self">the_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="modelc_1.html#E2:56_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="modelc_1.html#E3:56_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="modelc_1.html#E4:56_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="modelc_1.html#D12" target="_self">Def12</a>, <a class="txt" href="modelc_1.html#E3:56_1_1_2"><i><font color="Green">E57</font></i></a></i>
;<br/><b>hence </b><a NAME="E5:56_1_1_2"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:56_1_1_2"><i><font color="Green">E56</font></i></a>, , <a class="txt" href="modelc_1.html#E3:56_1"><i><font color="Green">E53</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1_3"><b>suppose </b></a><a NAME="E1:56_1_1_3"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V5" target="_self">ExistNext</a>
 ;<br/><div class="add"><a NAME="E2:56_1_1_3"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" target="_self">the_argument_of</a> <font color="Maroon">H</font></span>)</span> <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/>;<br/><a NAME="E3:56_1_1_3"/><b>then </b><i><font color="Green">E59</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" target="_self">the_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>by </b><i>, </i>;<br/><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> = 
the <a href="modelc_1.html#U9" target="_self">EneXt</a> of <font color="Maroon">V</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" target="_self">the_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="modelc_1.html#E4:56_1"><i><font color="Green">E54</font></i></a>, </i>
<br/>.= 
the <a href="modelc_1.html#U9" target="_self">EneXt</a> of <font color="Maroon">V</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" target="_self">the_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="modelc_1.html#E2:56_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="modelc_1.html#E3:56_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="modelc_1.html#D12" target="_self">Def12</a>, <a class="txt" href="modelc_1.html#E4:56_1"><i><font color="Green">E54</font></i></a></i>
;<br/><b>hence </b><a NAME="E5:56_1_1_3"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font>
 <b>by </b><i>, , <a class="txt" href="modelc_1.html#E3:56_1"><i><font color="Green">E53</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1_4"><b>suppose </b></a><a NAME="E1:56_1_1_4"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V6" target="_self">ExistGlobal</a>
 ;<br/><div class="add"><a NAME="E2:56_1_1_4"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" target="_self">the_argument_of</a> <font color="Maroon">H</font></span>)</span> <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/>;<br/><a NAME="E3:56_1_1_4"/><b>then </b><i><font color="Green">E61</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" target="_self">the_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>by </b><i>, </i>;<br/><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> = 
the <a href="modelc_1.html#U10" target="_self">EGlobal</a> of <font color="Maroon">V</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" target="_self">the_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="modelc_1.html#E4:56_1"><i><font color="Green">E54</font></i></a>, </i>
<br/>.= 
the <a href="modelc_1.html#U10" target="_self">EGlobal</a> of <font color="Maroon">V</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" target="_self">the_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="modelc_1.html#E2:56_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="modelc_1.html#E3:56_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="modelc_1.html#D12" target="_self">Def12</a>, <a class="txt" href="modelc_1.html#E4:56_1"><i><font color="Green">E54</font></i></a></i>
;<br/><b>hence </b><a NAME="E5:56_1_1_4"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font>
 <b>by </b><i>, , <a class="txt" href="modelc_1.html#E3:56_1"><i><font color="Green">E53</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1_5"><b>suppose </b></a><a NAME="E1:56_1_1_5"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a>
 ;<br/><div class="add"><a NAME="E2:56_1_1_5"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span> <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/>;<br/><a NAME="E3:56_1_1_5"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>by </b><i>, </i>;<br/><a NAME="E4:56_1_1_5"/><b>then </b><i><font color="Green">E63</font></i>: 
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E2:56_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="modelc_1.html#E3:56_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="modelc_1.html#D12" target="_self">Def12</a>, <a class="txt" href="modelc_1.html#E4:56_1"><i><font color="Green">E54</font></i></a></i>;<br/><a NAME="E5:56_1_1_5"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span> <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>, </i>;<br/><a NAME="E6:56_1_1_5"/><b>then </b><i><font color="Green">E64</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>by </b><i>, </i>;<br/><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> = 
the <a href="modelc_1.html#U7" target="_self">And</a> of <font color="Maroon">V</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="modelc_1.html#E4:56_1"><i><font color="Green">E54</font></i></a>, </i>
<br/>.= 
the <a href="modelc_1.html#U7" target="_self">And</a> of <font color="Maroon">V</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="modelc_1.html#E2:56_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="modelc_1.html#E3:56_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="modelc_1.html#D12" target="_self">Def12</a>, <a class="txt" href="modelc_1.html#E4:56_1"><i><font color="Green">E54</font></i></a></i>
;<br/><b>hence </b><a NAME="E8:56_1_1_5"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font>
 <b>by </b><i>, , <a class="txt" href="modelc_1.html#E3:56_1"><i><font color="Green">E53</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1_6"><b>suppose </b></a><a NAME="E1:56_1_1_6"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a>
 ;<br/><div class="add"><a NAME="E2:56_1_1_6"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span> <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/>;<br/><a NAME="E3:56_1_1_6"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>by </b><i>, </i>;<br/><a NAME="E4:56_1_1_6"/><b>then </b><i><font color="Green">E66</font></i>: 
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E2:56_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="modelc_1.html#E3:56_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="modelc_1.html#D12" target="_self">Def12</a>, <a class="txt" href="modelc_1.html#E4:56_1"><i><font color="Green">E54</font></i></a></i>;<br/><a NAME="E5:56_1_1_6"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span> <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>, </i>;<br/><a NAME="E6:56_1_1_6"/><b>then </b><i><font color="Green">E67</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>by </b><i>, </i>;<br/><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> = 
the <a href="modelc_1.html#U11" target="_self">EUntill</a> of <font color="Maroon">V</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="modelc_1.html#E4:56_1"><i><font color="Green">E54</font></i></a>, </i>
<br/>.= 
the <a href="modelc_1.html#U11" target="_self">EUntill</a> of <font color="Maroon">V</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" target="_self">the_left_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" target="_self">the_right_argument_of</a> <font color="Maroon">H</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="modelc_1.html#E2:56_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="modelc_1.html#E3:56_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="modelc_1.html#D12" target="_self">Def12</a>, <a class="txt" href="modelc_1.html#E4:56_1"><i><font color="Green">E54</font></i></a></i>
;<br/><b>hence </b><a NAME="E8:56_1_1_6"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font>
 <b>by </b><i>, , <a class="txt" href="modelc_1.html#E3:56_1"><i><font color="Green">E53</font></i></a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E3:56"/>
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#S1">NAT_1:sch 1</a>(, );<br/></i>
<b>hence </b><a NAME="E4:56"/>
( <font color="Maroon">f1</font> <a href="modelc_1.html#R2" target="_self">is-PreEvaluation-for</a> <font color="Maroon">n</font>,<font color="Maroon">Kai</font> &amp; <font color="Maroon">f2</font> <a href="modelc_1.html#R2" target="_self">is-PreEvaluation-for</a> <font color="Maroon">n</font>,<font color="Maroon">Kai</font> implies for <font color="Olive">H</font> being  <a href="modelc_1.html#NM1">CTL-formula</a>  st  <a href="finseq_1.html#K3">len</a> <font color="Olive">H</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> )
 ;<br/>


</div>
