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

<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>set </b><font color="Maroon">M</font> =  <a href="modelc_1.html#K23" target="_self">EvalFamily</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>;<br/>
<a NAME="E1:63"/>
for <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">X</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K23" target="_self">EvalFamily</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font> holds <br/><font color="Olive">X</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:63_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K23" target="_self">EvalFamily</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>
 ;<br/>

<b>consider </b><font color="Maroon">n</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="E3:63_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K21" target="_self">EvalSet</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>,<font color="Maroon">n</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E6:63"><i><font color="Green">E56</font></i></a>, </i>;<br/>
<b>thus </b><a NAME="E4:63_1"/>
<font color="Maroon">X</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">Choice</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E3:63"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">Choice</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K23" target="_self">EvalFamily</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>
 <b>and </b><br/><a NAME="E4:63"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">X</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K23" target="_self">EvalFamily</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font> holds <br/><font color="Maroon">Choice</font> <a href="funct_1.html#K1">.</a> <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <font color="Olive">X</font>
 <b>by </b><i><a class="ref" href="wellord2.html#T28">WELLORD2:28</a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <font color="Maroon">Choice</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K21" target="_self">EvalSet</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>,<span class="p2">(<span class="default"><a href="modelc_1.html#K2" target="_self">k_nat</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E5:63"/><i><font color="Green">E52</font></i>: 
for <font color="Olive">n</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">n</font>) is   <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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:63_2"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 ;<br/>

<b>set </b><font color="Maroon">Y</font> = <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">n</font>);<br/>
<a NAME="E2:63_2"/><i><font color="Green">E54</font></i>: 
 <a href="modelc_1.html#K2" target="_self">k_nat</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E8:63"><i><font color="Green">E58</font></i></a>, </i>;<br/>
<b>reconsider </b><font color="Maroon">n</font> = <font color="Maroon">n</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="txt" href="modelc_1.html#E8:63"><i><font color="Green">E58</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">Z</font> =  <a href="modelc_1.html#K21" target="_self">EvalSet</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>,<font color="Maroon">n</font>;<br/>
<a NAME="E4:63_2"/>
 <a href="modelc_1.html#K21" target="_self">EvalSet</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>,<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K23" target="_self">EvalFamily</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E2:63_2"><i><font color="Green">E54</font></i></a></i>;<br/>
<a NAME="E5:63_2"/><b>then </b>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">n</font>) <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K21" target="_self">EvalSet</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>,<font color="Maroon">n</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E10:63"><i><font color="Green">E59</font></i></a>, <a class="txt" href="modelc_1.html#E6:63"><i><font color="Green">E56</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon">h</font> being   <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><b> such that </b><br/><a NAME="E7:63_2"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">n</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">h</font>
 <b>and </b><br/><a NAME="E8:63_2"/>
<font color="Maroon">h</font> <a href="modelc_1.html#R2" target="_self">is-PreEvaluation-for</a> <font color="Maroon">n</font>,<font color="Maroon">Kai</font>
 ;<br/>
<b>thus </b><a NAME="E9:63_2"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">n</font>) is   <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>
 <b>by </b><i><a class="txt" href="modelc_1.html#E12:63"><i><font color="Green">E60</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:63"/><i><font color="Green">E56</font></i>: 
for <font color="Olive">n</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">n</font>) <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:63_3"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 ;<br/>

<a NAME="E2:63_3"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">n</font>) is   <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>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E10:63"><i><font color="Green">E59</font></i></a>, <a class="txt" href="modelc_1.html#E1:63_3"><i><font color="Green">E57</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:63_3"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">n</font>) <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <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>
 <b>by </b><i><a class="ref" href="funct_2.html#T11">FUNCT_2:11</a></i>;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">f1</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> , <a href="funct_2.html#K1">Funcs</a> <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><b> such that </b><br/><a NAME="E8:63"/><i><font color="Green">E58</font></i>: 
for <font color="Olive">n</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">n</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S2">FUNCT_2:sch 2</a>(<a class="txt" href="modelc_1.html#E8:63"><i><font color="Green">E58</font></i></a>);<br/></i>
<b>consider </b><font color="Maroon">v0</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="modelc_1.html#U5" target="_self">Assignations</a> of <font color="Maroon">V</font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <span class="p1">(<span class="default"><a href="modelc_1.html#K22" target="_self">CastEval</a> <font color="Maroon">V</font>,<span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="modelc_1.html#K18" target="_self">CastCTLformula</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">v0</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<a NAME="E10:63"/><i><font color="Green">E59</font></i>: 
for <font color="Olive">H</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">H</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K13" target="_self">CTL_WFF</a>  holds <br/><font color="Maroon">H<sub>2</sub></font>(<font color="Olive">H</font>) <a href="hidden.html#R2">in</a> the <a href="modelc_1.html#U5" target="_self">Assignations</a> of <font color="Maroon">V</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/>
<b>consider </b><font color="Maroon">f</font> being   <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><b> such that </b><br/><a NAME="E12:63"/><i><font color="Green">E60</font></i>: 
for <font color="Olive">H</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">H</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K13" target="_self">CTL_WFF</a>  holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">H</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S2">FUNCT_2:sch 2</a>(<a class="txt" href="modelc_1.html#E12:63"><i><font color="Green">E60</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<a NAME="E13:63"/>
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">f</font> <a href="modelc_1.html#R2" target="_self">is-PreEvaluation-for</a> <font color="Olive">n</font>,<font color="Maroon">Kai</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4"><b>proof </b></a><div class="add">

<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">f</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>;<br/>
<a NAME="E1:63_4"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_1"><b>proof </b></a><div class="add">

<a NAME="E1:63_4_1"/>
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> 0 holds <br/>( ( <font color="Olive">H</font> is <a href="modelc_1.html#V2" target="_self">atomic</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Kai</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> ) &amp; ( <font color="Olive">H</font> is <a href="modelc_1.html#V3" target="_self">negative</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> 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">f</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="Olive">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">H</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> 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">f</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="Olive">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f</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="Olive">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">H</font> is <a href="modelc_1.html#V5" target="_self">ExistNext</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> 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">f</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="Olive">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">H</font> is <a href="modelc_1.html#V6" target="_self">ExistGlobal</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> 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">f</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="Olive">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">H</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> 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">f</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="Olive">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f</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="Olive">H</font></span>)</span></span>)</span> ) )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:63_4_1"/>
<font color="Maroon">S<sub>1</sub></font>[0]
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E2:63_4"/><i><font color="Green">E62</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="63_4_2"><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="E1:63_4_2"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font>]
 ;<br/>

<a NAME="E2:63_4_2"/>
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">k</font> <a href="binop_2.html#K23">+</a> 1 holds <br/>( ( <font color="Olive">H</font> is <a href="modelc_1.html#V2" target="_self">atomic</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Kai</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> ) &amp; ( <font color="Olive">H</font> is <a href="modelc_1.html#V3" target="_self">negative</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> 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">f</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="Olive">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">H</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> 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">f</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="Olive">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f</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="Olive">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">H</font> is <a href="modelc_1.html#V5" target="_self">ExistNext</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> 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">f</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="Olive">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">H</font> is <a href="modelc_1.html#V6" target="_self">ExistGlobal</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> 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">f</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="Olive">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">H</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> 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">f</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="Olive">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f</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="Olive">H</font></span>)</span></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_2_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:63_4_2_1"/><i><font color="Green">E64</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="hs2(this)" href="javascript:()" title="63_4_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_4_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:63_4_2_1_1_1"/>
(  <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> or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 )
 </span><b>by </b><i>, <a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_4_2_1_1_1_1"><b>case </b></a><a NAME="E1:63_4_2_1_1_1_1"/>
 <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>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:63_4_2_1_1_1_1"/>
( ( <font color="Maroon">H</font> is <a href="modelc_1.html#V2" target="_self">atomic</a> implies <font color="Maroon">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V3" target="_self">negative</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V5" target="_self">ExistNext</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V6" target="_self">ExistGlobal</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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">f</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#E1:63_4_2_1"><i><font color="Green">E64</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_4_2_1_1_1_2"><b>case </b></a><a NAME="E1:63_4_2_1_1_1_2"/><i><font color="Green">E65</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1
 ;<br/><div class="add"><a NAME="E2:63_4_2_1_1_1_2"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K13" target="_self">CTL_WFF</a> 
 <b>by </b><i/>;<br/><i><font color="Green">E67</font></i>: <font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K18" target="_self">CastCTLformula</a> <font color="Maroon">H</font></span>)</span></span>)</span> = 
<font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font></span>)</span>
<b>by </b><i><a class="txt" href="modelc_1.html#E3:63_4_2_1_1_1_2"><i><font color="Green">E67</font></i></a>, </i>
<br/>.= 
<font color="Maroon">H<sub>1</sub></font>( <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>)
<b>by </b><i><a class="txt" href="modelc_1.html#E10:63"><i><font color="Green">E59</font></i></a></i>
;<br/><a NAME="E4:63_4_2_1_1_1_2"/><i><font color="Green">E68</font></i>: 
 <a href="modelc_1.html#K22" target="_self">CastEval</a> <font color="Maroon">V</font>,<span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="modelc_1.html#K18" target="_self">CastCTLformula</a> <font color="Maroon">H</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">v0</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>( <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>)
 <b>by </b><i><a class="txt" href="modelc_1.html#E5:63"><i><font color="Green">E52</font></i></a>, <a class="txt" href="modelc_1.html#E4:63_4_2_1_1_1_2"><i><font color="Green">E68</font></i></a></i>;<br/><b>set </b><font color="Maroon">f2</font> = <font color="Maroon">H<sub>1</sub></font>( <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>);<br/><b>reconsider </b><font color="Maroon">f2</font> = <font color="Maroon">H<sub>1</sub></font>( <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>) as   <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> <b>by </b><i><a class="txt" href="modelc_1.html#E6:63_4_2_1_1_1_2"><i><font color="Green">E69</font></i></a></i>;<br/><a NAME="E6:63_4_2_1_1_1_2"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">f</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#E1:63_4"><i><font color="Green">E61</font></i></a>, <a class="txt" href="modelc_1.html#E3:63_4_2_1_1_1_2"><i><font color="Green">E67</font></i></a>, <a class="txt" href="modelc_1.html#E6:63_4_2_1_1_1_2"><i><font color="Green">E69</font></i></a></i>;<br/><a NAME="E7:63_4_2_1_1_1_2"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Choice</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K21" target="_self">EvalSet</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E8:63_4_2_1_1_1_2"/>
 <a href="modelc_1.html#K21" target="_self">EvalSet</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K23" target="_self">EvalFamily</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>
 <b>by </b><i/>;<br/><a NAME="E9:63_4_2_1_1_1_2"/><b>then </b>
<font color="Maroon">Choice</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K21" target="_self">EvalSet</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K21" target="_self">EvalSet</a> <font color="Maroon">V</font>,<font color="Maroon">Kai</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E6:63"><i><font color="Green">E56</font></i></a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <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><b> such that </b><br/><a NAME="E11:63_4_2_1_1_1_2"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">f2</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">h</font>
 <b>and </b><br/><a NAME="E12:63_4_2_1_1_1_2"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">h</font> <a href="modelc_1.html#R2" target="_self">is-PreEvaluation-for</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>,<font color="Maroon">Kai</font>
 <b>by </b><i/>;<br/><a NAME="E13:63_4_2_1_1_1_2"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">f2</font> <a href="modelc_1.html#R2" target="_self">is-PreEvaluation-for</a> <font color="Maroon">k</font>,<font color="Maroon">Kai</font>
 <b>by </b><i><a class="ref" href="modelc_1.html#D13" target="_self">Def13</a>, <a class="ref" href="modelc_1.html#T1" target="_self">Th1</a>, <a class="txt" href="modelc_1.html#E2:63_4_2_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="ref" href="modelc_1.html#D12" target="_self">Def12</a></i>;<br/><a NAME="E14:63_4_2_1_1_1_2"/><i><font color="Green">E102</font></i>: 
( <font color="Maroon">H</font> is <a href="modelc_1.html#V3" target="_self">negative</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_2_1_1_1_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:63_4_2_1_1_1_2_2"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V3" target="_self">negative</a>
 ;<br/>

<a NAME="E2:63_4_2_1_1_1_2_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="E3:63_4_2_1_1_1_2_2"/><b>then </b><i><font color="Green">E104</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><a class="txt" href="modelc_1.html#E2:63_4_2_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<font color="Maroon">f</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#E7:63_4_2_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="modelc_1.html#D13" target="_self">Def13</a>, <a class="ref" href="modelc_1.html#T1" target="_self">Th1</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">f</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#E1:63_4_2_1"><i><font color="Green">E64</font></i></a>, , </i>
;<br/>
<b>hence </b><a NAME="E5:63_4_2_1_1_1_2_2"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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>
 ;<br/>


</div><b>end;</b></div><a NAME="E15:63_4_2_1_1_1_2"/><i><font color="Green">E105</font></i>: 
( <font color="Maroon">H</font> is <a href="modelc_1.html#V5" target="_self">ExistNext</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_2_1_1_1_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:63_4_2_1_1_1_2_3"/><i><font color="Green">E106</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V5" target="_self">ExistNext</a>
 ;<br/>

<a NAME="E2:63_4_2_1_1_1_2_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="E3:63_4_2_1_1_1_2_3"/><b>then </b><i><font color="Green">E107</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><a class="txt" href="modelc_1.html#E2:63_4_2_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<font color="Maroon">f</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#E7:63_4_2_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="modelc_1.html#D13" target="_self">Def13</a>, <a class="ref" href="modelc_1.html#T1" target="_self">Th1</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">f</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#E1:63_4_2_1"><i><font color="Green">E64</font></i></a>, , </i>
;<br/>
<b>hence </b><a NAME="E5:63_4_2_1_1_1_2_3"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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>
 ;<br/>


</div><b>end;</b></div><a NAME="E16:63_4_2_1_1_1_2"/><i><font color="Green">E108</font></i>: 
( <font color="Maroon">H</font> is <a href="modelc_1.html#V6" target="_self">ExistGlobal</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_2_1_1_1_2_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:63_4_2_1_1_1_2_4"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V6" target="_self">ExistGlobal</a>
 ;<br/>

<a NAME="E2:63_4_2_1_1_1_2_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="E3:63_4_2_1_1_1_2_4"/><b>then </b><i><font color="Green">E110</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><a class="ref" href="nat_1.html#T38">NAT_1:38</a>, <a class="txt" href="modelc_1.html#E2:63_4_2_1_1_1_2"><i><font color="Green">E66</font></i></a></i>;<br/>
<font color="Maroon">f</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#E7:63_4_2_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="modelc_1.html#D13" target="_self">Def13</a>, <a class="ref" href="modelc_1.html#T1" target="_self">Th1</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">f</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#E1:63_4_2_1"><i><font color="Green">E64</font></i></a>, , </i>
;<br/>
<b>hence </b><a NAME="E5:63_4_2_1_1_1_2_4"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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>
 ;<br/>


</div><b>end;</b></div><a NAME="E17:63_4_2_1_1_1_2"/><i><font color="Green">E111</font></i>: 
( <font color="Maroon">H</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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">f</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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_2_1_1_1_2_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:63_4_2_1_1_1_2_5"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a>
 ;<br/>

<a NAME="E2:63_4_2_1_1_1_2_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="E3:63_4_2_1_1_1_2_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><a class="txt" href="modelc_1.html#E2:63_4_2_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E4:63_4_2_1_1_1_2_5"/><b>then </b><i><font color="Green">E113</font></i>: 
<font color="Maroon">f</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#E1:63_4_2_1"><i><font color="Green">E64</font></i></a>, </i>;<br/>
<a NAME="E5:63_4_2_1_1_1_2_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="E6:63_4_2_1_1_1_2_5"/><b>then </b><i><font color="Green">E114</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><a class="ref" href="nat_1.html#T38">NAT_1:38</a>, <a class="txt" href="modelc_1.html#E2:63_4_2_1_1_1_2"><i><font color="Green">E66</font></i></a></i>;<br/>
<font color="Maroon">f</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#E7:63_4_2_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="modelc_1.html#D13" target="_self">Def13</a>, <a class="ref" href="modelc_1.html#T1" target="_self">Th1</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">f</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">f</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="ref" href="modelc_1.html#D14" target="_self">Def14</a>, , <a class="txt" href="modelc_1.html#E1:63_4_2_1"><i><font color="Green">E64</font></i></a>, </i>
;<br/>
<b>hence </b><a NAME="E8:63_4_2_1_1_1_2_5"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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">f</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>
 ;<br/>


</div><b>end;</b></div><a NAME="E18:63_4_2_1_1_1_2"/>
( <font color="Maroon">H</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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">f</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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_2_1_1_1_2_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:63_4_2_1_1_1_2_6"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">H</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a>
 ;<br/>

<a NAME="E2:63_4_2_1_1_1_2_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="E3:63_4_2_1_1_1_2_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><a class="ref" href="nat_1.html#T38">NAT_1:38</a>, <a class="txt" href="modelc_1.html#E2:63_4_2_1_1_1_2"><i><font color="Green">E66</font></i></a></i>;<br/>
<a NAME="E4:63_4_2_1_1_1_2_6"/><b>then </b><i><font color="Green">E116</font></i>: 
<font color="Maroon">f</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#E1:63_4_2_1"><i><font color="Green">E64</font></i></a>, </i>;<br/>
<a NAME="E5:63_4_2_1_1_1_2_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="E6:63_4_2_1_1_1_2_6"/><b>then </b><i><font color="Green">E117</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><a class="txt" href="modelc_1.html#E2:63_4_2_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<font color="Maroon">f</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#E7:63_4_2_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="modelc_1.html#D13" target="_self">Def13</a>, <a class="ref" href="modelc_1.html#T1" target="_self">Th1</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">f</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">f</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="ref" href="modelc_1.html#D14" target="_self">Def14</a>, , <a class="txt" href="modelc_1.html#E1:63_4_2_1"><i><font color="Green">E64</font></i></a>, </i>
;<br/>
<b>hence </b><a NAME="E8:63_4_2_1_1_1_2_6"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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">f</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>
 ;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E19:63_4_2_1_1_1_2"/>
( ( <font color="Maroon">H</font> is <a href="modelc_1.html#V2" target="_self">atomic</a> implies <font color="Maroon">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V3" target="_self">negative</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V5" target="_self">ExistNext</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V6" target="_self">ExistGlobal</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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">f</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#E7:63_4_2_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="modelc_1.html#D13" target="_self">Def13</a>, <a class="ref" href="modelc_1.html#T1" target="_self">Th1</a>, , , , , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:63_4_2_1"/>
( ( <font color="Maroon">H</font> is <a href="modelc_1.html#V2" target="_self">atomic</a> implies <font color="Maroon">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V3" target="_self">negative</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V4" target="_self">conjunctive</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V5" target="_self">ExistNext</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V6" target="_self">ExistGlobal</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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> ) &amp; ( <font color="Maroon">H</font> is <a href="modelc_1.html#V7" target="_self">ExistUntill</a> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 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">f</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">f</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> ) )
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:63_4_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1]
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E3:63_4"/>
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>(<a class="txt" href="modelc_1.html#E2:63_4"><i><font color="Green">E62</font></i></a>, );<br/></i>
<b>hence </b><a NAME="E4:63_4"/>
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">f</font> <a href="modelc_1.html#R2" target="_self">is-PreEvaluation-for</a> <font color="Olive">n</font>,<font color="Maroon">Kai</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E14:63"/>
<font color="Maroon">f</font> <a href="modelc_1.html#R1" target="_self">is-Evaluation-for</a> <font color="Maroon">Kai</font>
 <b>by </b><i/>;<br/>


</div>
