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

<span class="kw">let </span><font color="Maroon" title="c1">V</font> be    <a href="modelc_1.html#L2" title="MODELC_1:struct.2">CTLModelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">Kai</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a> ,the <a href="modelc_1.html#U6" title="MODELC_1:sel.6">BasicAssign</a> of <font color="Maroon" title="c1">V</font>  ex <font color="Olive" title="b2">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font> st <font color="Olive" title="b2">f</font> <a href="modelc_1.html#R1" title="MODELC_1:pred.1">is-Evaluation-for</a> <font color="Olive" title="b1">Kai</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">Kai</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a> ,the <a href="modelc_1.html#U6" title="MODELC_1:sel.6">BasicAssign</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font> st <font color="Olive" title="b1">f</font> <a href="modelc_1.html#R1" title="MODELC_1:pred.1">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">M</font> =  <a href="modelc_1.html#K23" title="MODELC_1:func.23">EvalFamily</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">v0</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>;<br/>
<a NAME="E2:63"/>
for <font color="Olive" title="b1">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K23" title="MODELC_1:func.23">EvalFamily</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font> holds <br/><font color="Olive" title="b1">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K23" title="MODELC_1:func.23">EvalFamily</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font> implies <font color="Maroon" title="c5">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:63_1"/>
<font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K23" title="MODELC_1:func.23">EvalFamily</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<a NAME="E2:63_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c5">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K21" title="MODELC_1:func.21">EvalSet</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Olive" title="b1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D31" target="_self" title="MODELC_1:def.31">Def31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:63_1"/>
<font color="Maroon" title="c5">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">Choice</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E4:63"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">Choice</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K23" title="MODELC_1:func.23">EvalFamily</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>
 <span class="kw">and </span><br/><a NAME="E5:63"/><span class="lab"><font color="Green" title="E56">A1</font></span>: 
for <font color="Olive" title="b1">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K23" title="MODELC_1:func.23">EvalFamily</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font> holds <br/><font color="Maroon" title="c5">Choice</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="wellord2.html#T28" title="WELLORD2:th.28">WELLORD2:28</a></span>;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <span class="kw">-&gt; </span>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  = <font color="Maroon" title="c5">Choice</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K21" title="MODELC_1:func.21">EvalSet</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<span class="p2">(<span class="default"><a href="modelc_1.html#K2" title="MODELC_1:func.2">k_nat</a> $1</span>)</span></span>)</span>;<br/>
<a NAME="E6:63"/><span class="lab"><font color="Green" title="E57">A2</font></span>: 
for <font color="Olive" title="b1">n</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">n</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  implies <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:63_2"/><span class="lab"><font color="Green" title="E58">A3</font></span>: 
<font color="Maroon" title="c6">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font></span><br/>

<a NAME="E2:63_2"/><span class="lab"><font color="Green" title="E59">A4</font></span>: 
 <a href="modelc_1.html#K2" title="MODELC_1:func.2">k_nat</a> <font color="Maroon" title="c6">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_2"><span class="lab"><font color="Green" title="E58">A3</font></span></a>, <a class="ref" href="modelc_1.html#D2" target="_self" title="MODELC_1:def.2">Def2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">Y</font> = <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">n</font> = <font color="Maroon" title="c6">n</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_2"><span class="lab"><font color="Green" title="E58">A3</font></span></a></span>;<br/>
<a NAME="E4:63_2"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K21" title="MODELC_1:func.21">EvalSet</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c8">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:63"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E2:63_2"><span class="lab"><font color="Green" title="E59">A4</font></span></a>, <a class="txt" href="modelc_1.html#E63"><span class="lab"><font color="Green" title="E54">Lm30</font></span></a></span>;<br/>
<a NAME="E5:63_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">h</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> &amp; <font color="Olive" title="b1">h</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a> <font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c2">Kai</font> )
 
;<br/>
<span class="kw">hence </span><a NAME="E6:63_2"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E7:63"/><span class="lab"><font color="Green" title="E58">A5</font></span>: 
for <font color="Olive" title="b1">n</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">n</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">n</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  implies <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:63_3"/>
<font color="Maroon" title="c6">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font></span><br/>

<a NAME="E2:63_3"/><span class="kw">then </span>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:63"><span class="lab"><font color="Green" title="E57">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:63_3"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">consider </span><font color="Maroon" title="c6">f1</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E9:63"/><span class="lab"><font color="Green" title="E59">A6</font></span>: 
for <font color="Olive" title="b1">n</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds <br/><font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">n</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S2" title="FUNCT_2:sch.2">FUNCT_2:sch 2</a>(<a class="txt" href="#E7:63"><span class="lab"><font color="Green" title="E58">A5</font></span></a>);<br/></span>
<span class="kw">deffunc </span><font color="Maroon">H<sub>2</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <span class="kw">-&gt; </span>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  = <span class="p1">(<span class="default"><a href="modelc_1.html#K22" title="MODELC_1:func.22">CastEval</a> <font color="Maroon" title="c1">V</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="modelc_1.html#K18" title="MODELC_1:func.18">CastCTLformula</a> $1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c4">v0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1;<br/>
<a NAME="E10:63"/><span class="lab"><font color="Green" title="E60">A7</font></span>: 
for <font color="Olive" title="b1">H</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>  holds <br/><font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b1">H</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E12:63"/><span class="lab"><font color="Green" title="E61">A8</font></span>: 
for <font color="Olive" title="b1">H</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>  holds <br/><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b1">H</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S2" title="FUNCT_2:sch.2">FUNCT_2:sch 2</a>(<a class="txt" href="#E10:63"><span class="lab"><font color="Green" title="E60">A7</font></span></a>);<br/></span>
<span class="kw">take </span>
<font color="Maroon" title="c7">f</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="modelc_1.html#R1" title="MODELC_1:pred.1">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font></span><br/>

<a NAME="E13:63"/>
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c7">f</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a> <font color="Olive" title="b1">n</font>,<font color="Maroon" title="c2">Kai</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ] <span class="kw">means </span><font color="Maroon" title="c7">f</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a> $1,<font color="Maroon" title="c2">Kai</font>;<br/>
<a NAME="E1:63_4"/><span class="lab"><font color="Green" title="E62">A9</font></span>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E1:63_4_1"/><span class="lab"><font color="Green" title="E63">A10</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/>

<a NAME="E2:63_4_1"/>
for <font color="Olive" title="b1">H</font> being  <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 holds <br/>( ( <font color="Olive" title="b1">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">H</font> be   <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 implies ( ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:63_4_1_1"/><span class="lab"><font color="Green" title="E64">A11</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_4_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:63_4_1_1_1_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1_1"><span class="lab"><font color="Green" title="E64">A11</font></span></a>, <a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_4_1_1_1_1_1"><span class="kw">case </span></a><a NAME="E1:63_4_1_1_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:63_4_1_1_1_1_1"/>
( ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1"><span class="lab"><font color="Green" title="E63">A10</font></span></a>, <a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_4_1_1_1_1_2"><span class="kw">case </span></a><a NAME="E1:63_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E65">A12</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) )</span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c10">f2</font> = <font color="Maroon">H<sub>1</sub></font>( <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>);<br/><a NAME="E2:63_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E66">A13</font></span>: 
<font color="Maroon" title="c9">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#T1" target="_self" title="MODELC_1:th.1">Th1</a></span>;<br/><span class="kw">then </span><font color="Maroon" title="c6">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K18" title="MODELC_1:func.18">CastCTLformula</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c6">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D24" target="_self" title="MODELC_1:def.24">Def24</a></span>
<br/>.= 
<font color="Maroon">H<sub>1</sub></font>( <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:63"><span class="lab"><font color="Green" title="E59">A6</font></span></a></span>
;<br/><a NAME="E4:63_4_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A14</font></span>: 
 <a href="modelc_1.html#K22" title="MODELC_1:func.22">CastEval</a> <font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="modelc_1.html#K18" title="MODELC_1:func.18">CastCTLformula</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c4">v0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>( <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D30" target="_self" title="MODELC_1:def.30">Def30</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">f2</font> = <font color="Maroon">H<sub>1</sub></font>( <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>) as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font> ;<br/><a NAME="E6:63_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E68">A15</font></span>: 
<font color="Maroon" title="c11">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Choice</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K21" title="MODELC_1:func.21">EvalSet</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D2" target="_self" title="MODELC_1:def.2">Def2</a></span>;<br/><a NAME="E7:63_4_1_1_1_1_2"/>
<font color="Maroon" title="c5">Choice</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K21" title="MODELC_1:func.21">EvalSet</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K21" title="MODELC_1:func.21">EvalSet</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:63"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="modelc_1.html#E63"><span class="lab"><font color="Green" title="E54">Lm30</font></span></a></span>;<br/><a NAME="E8:63_4_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A16</font></span>: 
 ex <font color="Olive" title="b1">h</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Maroon" title="c11">f2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">h</font> &amp; <font color="Olive" title="b1">h</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>,<font color="Maroon" title="c2">Kai</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E68">A15</font></span></a></span>;<br/><a NAME="E9:63_4_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A17</font></span>: 
<font color="Maroon" title="c11">f2</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a> <font color="Maroon" title="c8">k</font>,<font color="Maroon" title="c2">Kai</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E65">A12</font></span></a>, <a class="txt" href="modelc_1.html#E55"><span class="lab"><font color="Green" title="E47">Lm25</font></span></a></span>;<br/><a NAME="E10:63_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E71">A18</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:63"><span class="lab"><font color="Green" title="E61">A8</font></span></a>, <a class="txt" href="#E2:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E66">A13</font></span></a>, <a class="txt" href="#E4:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E67">A14</font></span></a></span>;<br/><a NAME="E11:63_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E72">A19</font></span>: 
( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_1_1_1_1_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:63_4_1_1_1_1_2_2"/><span class="lab"><font color="Green" title="E73">A20</font></span>: 
<font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:63_4_1_1_1_1_2_2"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_1.html#E47"><span class="lab"><font color="Green" title="E40">Lm22</font></span></a></span>;<br/>
<a NAME="E3:63_4_1_1_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A21</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E65">A12</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> = 
the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="txt" href="#E8:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="txt" href="#E1:63_4_1_1_1_1_2_2"><span class="lab"><font color="Green" title="E73">A20</font></span></a>, <a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></span>
<br/>.= 
the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1"><span class="lab"><font color="Green" title="E63">A10</font></span></a>, <a class="txt" href="#E9:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="txt" href="#E3:63_4_1_1_1_1_2_2"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="modelc_1.html#E57"><span class="lab"><font color="Green" title="E49">Lm27</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:63_4_1_1_1_1_2_2"/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E12:63_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E73">A22</font></span>: 
( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_1_1_1_1_2_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:63_4_1_1_1_1_2_3"/><span class="lab"><font color="Green" title="E74">A23</font></span>: 
<font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:63_4_1_1_1_1_2_3"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_1.html#E48"><span class="lab"><font color="Green" title="E41">Lm23</font></span></a></span>;<br/>
<a NAME="E3:63_4_1_1_1_1_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A24</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E65">A12</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E4:63_4_1_1_1_1_2_3"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1_1_1_1_2_3"><span class="lab"><font color="Green" title="E74">A23</font></span></a>, <a class="txt" href="modelc_1.html#E48"><span class="lab"><font color="Green" title="E41">Lm23</font></span></a></span>;<br/>
<a NAME="E5:63_4_1_1_1_1_2_3"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E65">A12</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E6:63_4_1_1_1_1_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E76">A25</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1"><span class="lab"><font color="Green" title="E63">A10</font></span></a>, <a class="txt" href="#E9:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="txt" href="modelc_1.html#E57"><span class="lab"><font color="Green" title="E49">Lm27</font></span></a></span>;<br/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> = 
the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="txt" href="#E8:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="txt" href="#E1:63_4_1_1_1_1_2_3"><span class="lab"><font color="Green" title="E74">A23</font></span></a>, <a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></span>
<br/>.= 
the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1"><span class="lab"><font color="Green" title="E63">A10</font></span></a>, <a class="txt" href="#E9:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="txt" href="#E6:63_4_1_1_1_1_2_3"><span class="lab"><font color="Green" title="E76">A25</font></span></a>, <a class="txt" href="#E3:63_4_1_1_1_1_2_3"><span class="lab"><font color="Green" title="E75">A24</font></span></a>, <a class="txt" href="modelc_1.html#E57"><span class="lab"><font color="Green" title="E49">Lm27</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:63_4_1_1_1_1_2_3"/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E13:63_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E74">A26</font></span>: 
( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_1_1_1_1_2_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:63_4_1_1_1_1_2_4"/><span class="lab"><font color="Green" title="E75">A27</font></span>: 
<font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:63_4_1_1_1_1_2_4"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_1.html#E48"><span class="lab"><font color="Green" title="E41">Lm23</font></span></a></span>;<br/>
<a NAME="E3:63_4_1_1_1_1_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E76">A28</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E65">A12</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E4:63_4_1_1_1_1_2_4"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1_1_1_1_2_4"><span class="lab"><font color="Green" title="E75">A27</font></span></a>, <a class="txt" href="modelc_1.html#E48"><span class="lab"><font color="Green" title="E41">Lm23</font></span></a></span>;<br/>
<a NAME="E5:63_4_1_1_1_1_2_4"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E65">A12</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E6:63_4_1_1_1_1_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A29</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1"><span class="lab"><font color="Green" title="E63">A10</font></span></a>, <a class="txt" href="#E9:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="txt" href="modelc_1.html#E57"><span class="lab"><font color="Green" title="E49">Lm27</font></span></a></span>;<br/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> = 
the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="txt" href="#E8:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="txt" href="#E1:63_4_1_1_1_1_2_4"><span class="lab"><font color="Green" title="E75">A27</font></span></a>, <a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></span>
<br/>.= 
the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1"><span class="lab"><font color="Green" title="E63">A10</font></span></a>, <a class="txt" href="#E9:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="txt" href="#E6:63_4_1_1_1_1_2_4"><span class="lab"><font color="Green" title="E77">A29</font></span></a>, <a class="txt" href="#E3:63_4_1_1_1_1_2_4"><span class="lab"><font color="Green" title="E76">A28</font></span></a>, <a class="txt" href="modelc_1.html#E57"><span class="lab"><font color="Green" title="E49">Lm27</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:63_4_1_1_1_1_2_4"/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E14:63_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E75">A30</font></span>: 
( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_1_1_1_1_2_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:63_4_1_1_1_1_2_5"/><span class="lab"><font color="Green" title="E76">A31</font></span>: 
<font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:63_4_1_1_1_1_2_5"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_1.html#E47"><span class="lab"><font color="Green" title="E40">Lm22</font></span></a></span>;<br/>
<a NAME="E3:63_4_1_1_1_1_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A32</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E65">A12</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> = 
the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="txt" href="#E8:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="txt" href="#E1:63_4_1_1_1_1_2_5"><span class="lab"><font color="Green" title="E76">A31</font></span></a>, <a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></span>
<br/>.= 
the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1"><span class="lab"><font color="Green" title="E63">A10</font></span></a>, <a class="txt" href="#E9:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="txt" href="#E3:63_4_1_1_1_1_2_5"><span class="lab"><font color="Green" title="E77">A32</font></span></a>, <a class="txt" href="modelc_1.html#E57"><span class="lab"><font color="Green" title="E49">Lm27</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:63_4_1_1_1_1_2_5"/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E15:63_4_1_1_1_1_2"/>
( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_1_1_1_1_2_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:63_4_1_1_1_1_2_6"/><span class="lab"><font color="Green" title="E76">A33</font></span>: 
<font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:63_4_1_1_1_1_2_6"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_1.html#E47"><span class="lab"><font color="Green" title="E40">Lm22</font></span></a></span>;<br/>
<a NAME="E3:63_4_1_1_1_1_2_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A34</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E65">A12</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> = 
the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="txt" href="#E8:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="txt" href="#E1:63_4_1_1_1_1_2_6"><span class="lab"><font color="Green" title="E76">A33</font></span></a>, <a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></span>
<br/>.= 
the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_4_1"><span class="lab"><font color="Green" title="E63">A10</font></span></a>, <a class="txt" href="#E9:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="txt" href="#E3:63_4_1_1_1_1_2_6"><span class="lab"><font color="Green" title="E77">A34</font></span></a>, <a class="txt" href="modelc_1.html#E57"><span class="lab"><font color="Green" title="E49">Lm27</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:63_4_1_1_1_1_2_6"/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E16:63_4_1_1_1_1_2"/>
( ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="txt" href="#E8:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="txt" href="#E11:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E72">A19</font></span></a>, <a class="txt" href="#E14:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E75">A30</font></span></a>, <a class="txt" href="#E13:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E74">A26</font></span></a>, <a class="txt" href="#E12:63_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E73">A22</font></span></a>, <a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:63_4_1_1"/>
( ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c9">H</font> is  <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:63_4_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:63_4"/>
for <font color="Olive" title="b1">H</font> being  <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/>( ( <font color="Olive" title="b1">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a>  implies <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_1.html#E32"><span class="lab"><font color="Green" title="E25">Lm10</font></span></a></span>;<br/>
<a NAME="E3:63_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A35</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></span>;<br/>
<a NAME="E4:63_4"/>
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="#E3:63_4"><span class="lab"><font color="Green" title="E63">A35</font></span></a>, <a class="txt" href="#E1:63_4"><span class="lab"><font color="Green" title="E62">A9</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E5:63_4"/>
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c7">f</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a> <font color="Olive" title="b1">n</font>,<font color="Maroon" title="c2">Kai</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E14:63"/>
<font color="Maroon" title="c7">f</font> <a href="modelc_1.html#R1" title="MODELC_1:pred.1">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_1.html#E59"><span class="lab"><font color="Green" title="E51">Lm29</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
