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

<b>let </b><font color="Maroon" title="c1">V</font> be    <a href="modelc_2.html#L1" title="MODELC_2:struct.1">LTLModelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a> ,the <a href="modelc_2.html#U2" title="MODELC_2:sel.2">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_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font> st <font color="Olive" title="b2">f</font> <a href="modelc_2.html#R4" title="MODELC_2:pred.4">is-Evaluation-for</a> <font color="Olive" title="b1">Kai</font></span><br/><b>let </b><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_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a> ,the <a href="modelc_2.html#U2" title="MODELC_2:sel.2">BasicAssign</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font> st <font color="Olive" title="b1">f</font> <a href="modelc_2.html#R4" title="MODELC_2:pred.4">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font></span><br/>



<b>set </b><font color="Maroon" title="c3">M</font> =  <a href="modelc_2.html#K19" title="MODELC_2:func.19">EvalFamily</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>;<br/>
<a NAME="E1:104"/>
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_2.html#K19" title="MODELC_2:func.19">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="104_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K19" title="MODELC_2:func.19">EvalFamily</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font> implies <font color="Maroon" title="c4">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/>

<b>assume </b><a NAME="E1:104_1"/><i><font color="Green" title="E86">A1</font></i>: 
<font color="Maroon" title="c4">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K19" title="MODELC_2:func.19">EvalFamily</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">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/>

<b>consider </b><font color="Maroon" title="c5">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E3:104_1"/><i><font color="Green" title="E87">A2</font></i>: 
<font color="Maroon" title="c4">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K17" title="MODELC_2:func.17">EvalSet</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c5">n</font>
 <b>by </b><i><a class="txt" href="#E1:104_1"><i><font color="Green" title="E86">A1</font></i></a>, <a class="ref" href="modelc_2.html#D32" target="_self" title="MODELC_2:def.32">Def31</a></i>;<br/>
<b>thus </b><a NAME="E4:104_1"/>
<font color="Maroon" title="c4">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> 
 <b>by </b><i><a class="txt" href="#E3:104_1"><i><font color="Green" title="E87">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c4">Choice</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E3:104"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">Choice</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K19" title="MODELC_2:func.19">EvalFamily</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>
 <b>and </b><br/><a NAME="E4:104"/><i><font color="Green" title="E86">A3</font></i>: 
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_2.html#K19" title="MODELC_2:func.19">EvalFamily</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font> holds <br/><font color="Maroon" title="c4">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>
 <b>by </b><i><a class="ref" href="wellord2.html#T28" title="WELLORD2:th.28">WELLORD2:28</a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  = <font color="Maroon" title="c4">Choice</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K17" title="MODELC_2:func.17">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_2.html#K1" title="MODELC_2:func.1">CastNat</a> $1</span>)</span></span>)</span>;<br/>
<a NAME="E5:104"/><i><font color="Green" title="E87">A4</font></i>: 
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_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">n</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">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="c5">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font> )</span><br/>

<b>assume </b><a NAME="E1:104_2"/><i><font color="Green" title="E88">A5</font></i>: 
<font color="Maroon" title="c5">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font></span><br/>

<b>set </b><font color="Maroon" title="c6">Y</font> = <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>);<br/>
<a NAME="E2:104_2"/>
<font color="Maroon" title="c5">n</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="txt" href="#E1:104_2"><i><font color="Green" title="E88">A5</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">n</font> = <font color="Maroon" title="c5">n</font> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> ;<br/>
<a NAME="E4:104_2"/><i><font color="Green" title="E89">A6</font></i>: 
 <a href="modelc_2.html#K1" title="MODELC_2:func.1">CastNat</a> <font color="Maroon" title="c7">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">n</font>
 
<b>by </b><i><a class="ref" href="modelc_2.html#D1" target="_self" title="MODELC_2:def.1">DefCastNat</a></i>;<br/>
<b>set </b><font color="Maroon" title="c8">Z</font> =  <a href="modelc_2.html#K17" title="MODELC_2:func.17">EvalSet</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c7">n</font>;<br/>
<a NAME="E5:104_2"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K17" title="MODELC_2:func.17">EvalSet</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c7">n</font>
 
<b>by </b><i><a class="txt" href="#E4:104_2"><i><font color="Green" title="E89">A6</font></i></a>, <a class="txt" href="#E4:104"><i><font color="Green" title="E86">A3</font></i></a>, <a class="txt" href="modelc_2.html#E107"><i><font color="Green" title="E84">Lm30</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c9">h</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E7:104_2"/><i><font color="Green" title="E90">A7</font></i>: 
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">h</font>
 <b>and </b><br/><a NAME="E8:104_2"/>
<font color="Maroon" title="c9">h</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c7">n</font>,<font color="Maroon" title="c2">Kai</font>
 ;<br/>
<b>thus </b><a NAME="E9:104_2"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="#E7:104_2"><i><font color="Green" title="E90">A7</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E6:104"/><i><font color="Green" title="E88">A8</font></i>: 
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#K1" title="FUNCT_2:func.1">Funcs</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">n</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">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="c5">n</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font> )</span><br/>

<b>assume </b><a NAME="E1:104_3"/><i><font color="Green" title="E89">A9</font></i>: 
<font color="Maroon" title="c5">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font></span><br/>

<a NAME="E2:104_3"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font>
 
<b>by </b><i><a class="txt" href="#E1:104_3"><i><font color="Green" title="E89">A9</font></i></a>, <a class="txt" href="#E5:104"><i><font color="Green" title="E87">A4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:104_3"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c5">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> , <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E8:104"/><i><font color="Green" title="E89">A10</font></i>: 
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="c5">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>)
 <b>from </b><i><a class="ref" href="funct_2.html#S2" title="FUNCT_2:sch.2">FUNCT_2:sch 2</a>(<a class="txt" href="#E6:104"><i><font color="Green" title="E88">A8</font></i></a>);<br/></i>
<b>consider </b><font color="Maroon" title="c6">v0</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  = <span class="p1">(<span class="default"><a href="modelc_2.html#K18" title="MODELC_2:func.18">CastEval</a> <font color="Maroon" title="c1">V</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">f1</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</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_2.html#K14" title="MODELC_2:func.14">CastLTL</a> $1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c6">v0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1;<br/>
<a NAME="E10:104"/><i><font color="Green" title="E90">A11</font></i>: 
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_2.html#K9" title="MODELC_2:func.9">LTL_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_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/>
<b>consider </b><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_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E12:104"/><i><font color="Green" title="E91">A12</font></i>: 
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_2.html#K9" title="MODELC_2:func.9">LTL_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>)
 <b>from </b><i><a class="ref" href="funct_2.html#S2" title="FUNCT_2:sch.2">FUNCT_2:sch 2</a>(<a class="txt" href="#E10:104"><i><font color="Green" title="E90">A11</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon" title="c7">f</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="modelc_2.html#R4" title="MODELC_2:pred.4">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font></span><br/>

<a NAME="E13:104"/>
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c7">f</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">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="104_4"><b>proof </b></a><div class="add">

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <b>means </b><font color="Maroon" title="c7">f</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> $1,<font color="Maroon" title="c2">Kai</font>;<br/>
<a NAME="E1:104_4"/><i><font color="Green" title="E92">A13</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_4_1"><b>proof </b></a><div class="add">

<a NAME="E1:104_4_1"/>
for <font color="Olive" title="b1">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-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_2.html#V2" title="MODELC_2: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_2.html#V3" title="MODELC_2: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_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">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_2.html#V4" title="MODELC_2: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_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V5" title="MODELC_2:attr.5">disjunctive</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_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V6" title="MODELC_2:attr.6">next</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_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">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_2.html#V7" title="MODELC_2:attr.7">Until</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_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V8" title="MODELC_2:attr.8">Release</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_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) )
 
<b>by </b><i><a class="ref" href="modelc_2.html#T3" target="_self" title="MODELC_2:th.3">Thlen01</a></i>;<br/>
<b>hence </b><a NAME="E2:104_4_1"/>
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 <b>by </b><i><a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E2:104_4"/><i><font color="Green" title="E93">A14</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">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#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_4_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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#K1" title="NAT_1:func.1">+</a> 1] )</span><br/>

<b>assume </b><a NAME="E1:104_4_2"/><i><font color="Green" title="E94">A15</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/>

<a NAME="E2:104_4_2"/>
for <font color="Olive" title="b1">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-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#K1" title="NAT_1:func.1">+</a> 1 holds <br/>( ( <font color="Olive" title="b1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2: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_2.html#V3" title="MODELC_2: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_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">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_2.html#V4" title="MODELC_2: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_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V5" title="MODELC_2:attr.5">disjunctive</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_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V6" title="MODELC_2:attr.6">next</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_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">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_2.html#V7" title="MODELC_2:attr.7">Until</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_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V8" title="MODELC_2:attr.8">Release</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_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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="104_4_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">H</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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#K1" title="NAT_1:func.1">+</a> 1 implies ( ( <font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V2" title="MODELC_2: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_2.html#V3" title="MODELC_2: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_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">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_2.html#V4" title="MODELC_2: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_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V5" title="MODELC_2:attr.5">disjunctive</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_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V6" title="MODELC_2:attr.6">next</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_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">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_2.html#V7" title="MODELC_2:attr.7">Until</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_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V8" title="MODELC_2:attr.8">Release</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_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) ) )</span><br/>

<b>assume </b><a NAME="E1:104_4_2_1"/><i><font color="Green" title="E95">A16</font></i>: 
 <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#K1" title="NAT_1:func.1">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V2" title="MODELC_2: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_2.html#V3" title="MODELC_2: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_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">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_2.html#V4" title="MODELC_2: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_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V5" title="MODELC_2:attr.5">disjunctive</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_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V6" title="MODELC_2:attr.6">next</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_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">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_2.html#V7" title="MODELC_2:attr.7">Until</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_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V8" title="MODELC_2:attr.8">Release</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_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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="104_4_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="104_4_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:104_4_2_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#K1" title="NAT_1:func.1">+</a> 1 )
 </span><b>by </b><i><a class="txt" href="#E1:104_4_2_1"><i><font color="Green" title="E95">A16</font></i></a>, <a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="104_4_2_1_1_1_1"><b>case </b></a><a NAME="E1:104_4_2_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V2" title="MODELC_2: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_2.html#V3" title="MODELC_2: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_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">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_2.html#V4" title="MODELC_2: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_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V5" title="MODELC_2:attr.5">disjunctive</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_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V6" title="MODELC_2:attr.6">next</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_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">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_2.html#V7" title="MODELC_2:attr.7">Until</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_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V8" title="MODELC_2:attr.8">Release</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_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) )</span><br/><div class="add"><b>hence </b><a NAME="E2:104_4_2_1_1_1_1"/>
( ( <font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V2" title="MODELC_2: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_2.html#V3" title="MODELC_2: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_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">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_2.html#V4" title="MODELC_2: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_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V5" title="MODELC_2:attr.5">disjunctive</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_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V6" title="MODELC_2:attr.6">next</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_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">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_2.html#V7" title="MODELC_2:attr.7">Until</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_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V8" title="MODELC_2:attr.8">Release</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_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="#E1:104_4_2"><i><font color="Green" title="E94">A15</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="104_4_2_1_1_1_2"><b>case </b></a><a NAME="E1:104_4_2_1_1_1_2"/><i><font color="Green" title="E96">A17</font></i>: 
 <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#K1" title="NAT_1:func.1">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V2" title="MODELC_2: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_2.html#V3" title="MODELC_2: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_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">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_2.html#V4" title="MODELC_2: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_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V5" title="MODELC_2:attr.5">disjunctive</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_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V6" title="MODELC_2:attr.6">next</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_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">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_2.html#V7" title="MODELC_2:attr.7">Until</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_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V8" title="MODELC_2:attr.8">Release</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_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) )</span><br/><div class="add"><a NAME="E2:104_4_2_1_1_1_2"/><i><font color="Green" title="E97">A18</font></i>: 
<font color="Maroon" title="c9">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_2.html#T1" target="_self" title="MODELC_2:th.1">Th1</a></i>;<br/><i><font color="Green" title="E98">A19</font></i>: <font color="Maroon" title="c5">f1</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</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_2.html#K14" title="MODELC_2:func.14">CastLTL</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c5">f1</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</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>
<b>by </b><i><a class="txt" href="#E2:104_4_2_1_1_1_2"><i><font color="Green" title="E97">A18</font></i></a>, <a class="ref" href="modelc_2.html#D25" target="_self" title="MODELC_2:def.25">Def24</a></i>
<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>)
<b>by </b><i><a class="txt" href="#E8:104"><i><font color="Green" title="E89">A10</font></i></a></i>
;<br/><a NAME="E4:104_4_2_1_1_1_2"/><i><font color="Green" title="E99">A20</font></i>: 
 <a href="modelc_2.html#K18" title="MODELC_2:func.18">CastEval</a> <font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f1</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</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_2.html#K14" title="MODELC_2:func.14">CastLTL</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c6">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>)
 <b>by </b><i><a class="ref" href="modelc_2.html#D31" target="_self" title="MODELC_2:def.31">Def30</a>, <a class="txt" href="#E3:104_4_2_1_1_1_2"><i><font color="Green" title="E98">A19</font></i></a></i>;<br/><b>set </b><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/><b>reconsider </b><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_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font> <b>by </b><i><a class="txt" href="#E4:104_4_2_1_1_1_2"><i><font color="Green" title="E99">A20</font></i></a></i>;<br/><a NAME="E6:104_4_2_1_1_1_2"/><i><font color="Green" title="E100">A21</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="#E12:104"><i><font color="Green" title="E91">A12</font></i></a>, <a class="txt" href="#E2:104_4_2_1_1_1_2"><i><font color="Green" title="E97">A18</font></i></a>, <a class="txt" href="#E4:104_4_2_1_1_1_2"><i><font color="Green" title="E99">A20</font></i></a></i>;<br/><a NAME="E7:104_4_2_1_1_1_2"/><i><font color="Green" title="E101">A22</font></i>: 
<font color="Maroon" title="c11">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Choice</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K17" title="MODELC_2:func.17">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>
 <b>by </b><i><a class="ref" href="modelc_2.html#D1" target="_self" title="MODELC_2:def.1">DefCastNat</a></i>;<br/><a NAME="E8:104_4_2_1_1_1_2"/>
<font color="Maroon" title="c4">Choice</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K17" title="MODELC_2:func.17">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_2.html#K17" title="MODELC_2:func.17">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>
 <b>by </b><i><a class="txt" href="#E4:104"><i><font color="Green" title="E86">A3</font></i></a>, <a class="txt" href="modelc_2.html#E107"><i><font color="Green" title="E84">Lm30</font></i></a></i>;<br/><b>then consider </b><font color="Maroon" title="c12">h</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E10:104_4_2_1_1_1_2"/><i><font color="Green" title="E102">A23</font></i>: 
<font color="Maroon" title="c11">f2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c12">h</font>
 <b>and </b><br/><a NAME="E11:104_4_2_1_1_1_2"/><i><font color="Green" title="E103">A24</font></i>: 
<font color="Maroon" title="c12">h</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">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>
 <b>by </b><i><a class="txt" href="#E7:104_4_2_1_1_1_2"><i><font color="Green" title="E101">A22</font></i></a></i>;<br/><a NAME="E12:104_4_2_1_1_1_2"/><i><font color="Green" title="E104">A25</font></i>: 
<font color="Maroon" title="c11">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c8">k</font>,<font color="Maroon" title="c2">Kai</font>
 <b>by </b><i><a class="txt" href="#E10:104_4_2_1_1_1_2"><i><font color="Green" title="E102">A23</font></i></a>, <a class="txt" href="#E11:104_4_2_1_1_1_2"><i><font color="Green" title="E103">A24</font></i></a>, <a class="txt" href="#E1:104_4_2_1_1_1_2"><i><font color="Green" title="E96">A17</font></i></a>, <a class="txt" href="modelc_2.html#E99"><i><font color="Green" title="E77">Lm25</font></i></a></i>;<br/><a NAME="E13:104_4_2_1_1_1_2"/><i><font color="Green" title="E105">A26</font></i>: 
( <font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V3" title="MODELC_2: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_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">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="104_4_2_1_1_1_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:104_4_2_1_1_1_2_2"/><i><font color="Green" title="E106">A27</font></i>: 
<font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:104_4_2_1_1_1_2_2"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">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>
 
<b>by </b><i><a class="ref" href="modelc_2.html#T10" target="_self" title="MODELC_2:th.10">ThArg7</a></i>;<br/>
<a NAME="E3:104_4_2_1_1_1_2_2"/><b>then </b><i><font color="Green" title="E107">A28</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2"><i><font color="Green" title="E96">A17</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<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_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E6:104_4_2_1_1_1_2"><i><font color="Green" title="E100">A21</font></i></a>, <a class="txt" href="#E10:104_4_2_1_1_1_2"><i><font color="Green" title="E102">A23</font></i></a>, <a class="txt" href="#E11:104_4_2_1_1_1_2"><i><font color="Green" title="E103">A24</font></i></a>, <a class="txt" href="#E1:104_4_2_1_1_1_2_2"><i><font color="Green" title="E106">A27</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>
<br/>.= 
the <a href="modelc_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E12:104_4_2_1_1_1_2"><i><font color="Green" title="E104">A25</font></i></a>, <a class="txt" href="#E1:104_4_2"><i><font color="Green" title="E94">A15</font></i></a>, <a class="txt" href="modelc_2.html#E101"><i><font color="Green" title="E79">Lm27</font></i></a>, <a class="txt" href="#E3:104_4_2_1_1_1_2_2"><i><font color="Green" title="E107">A28</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E5:104_4_2_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_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E14:104_4_2_1_1_1_2"/><i><font color="Green" title="E106">A29</font></i>: 
( <font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</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_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">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="104_4_2_1_1_1_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:104_4_2_1_1_1_2_3"/><i><font color="Green" title="E107">A30</font></i>: 
<font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:104_4_2_1_1_1_2_3"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">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>
 
<b>by </b><i><a class="ref" href="modelc_2.html#T10" target="_self" title="MODELC_2:th.10">ThArg7</a></i>;<br/>
<a NAME="E3:104_4_2_1_1_1_2_3"/><b>then </b><i><font color="Green" title="E108">A31</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2"><i><font color="Green" title="E96">A17</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<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_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E6:104_4_2_1_1_1_2"><i><font color="Green" title="E100">A21</font></i></a>, <a class="txt" href="#E10:104_4_2_1_1_1_2"><i><font color="Green" title="E102">A23</font></i></a>, <a class="txt" href="#E11:104_4_2_1_1_1_2"><i><font color="Green" title="E103">A24</font></i></a>, <a class="txt" href="#E1:104_4_2_1_1_1_2_3"><i><font color="Green" title="E107">A30</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>
<br/>.= 
the <a href="modelc_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E12:104_4_2_1_1_1_2"><i><font color="Green" title="E104">A25</font></i></a>, <a class="txt" href="#E1:104_4_2"><i><font color="Green" title="E94">A15</font></i></a>, <a class="txt" href="modelc_2.html#E101"><i><font color="Green" title="E79">Lm27</font></i></a>, <a class="txt" href="#E3:104_4_2_1_1_1_2_3"><i><font color="Green" title="E108">A31</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E5:104_4_2_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_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E15:104_4_2_1_1_1_2"/><i><font color="Green" title="E107">A35</font></i>: 
( <font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V4" title="MODELC_2: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_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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="104_4_2_1_1_1_2_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:104_4_2_1_1_1_2_4"/><i><font color="Green" title="E108">A36</font></i>: 
<font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:104_4_2_1_1_1_2_4"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">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>
 
<b>by </b><i><a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/>
<a NAME="E3:104_4_2_1_1_1_2_4"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2"><i><font color="Green" title="E96">A17</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E4:104_4_2_1_1_1_2_4"/><b>then </b><i><font color="Green" title="E109">A37</font></i>: 
<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_2.html#K11" title="MODELC_2:func.11">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_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E12:104_4_2_1_1_1_2"><i><font color="Green" title="E104">A25</font></i></a>, <a class="txt" href="#E1:104_4_2"><i><font color="Green" title="E94">A15</font></i></a>, <a class="txt" href="modelc_2.html#E101"><i><font color="Green" title="E79">Lm27</font></i></a></i>;<br/>
<a NAME="E5:104_4_2_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_2.html#K12" title="MODELC_2:func.12">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2_4"><i><font color="Green" title="E108">A36</font></i></a>, <a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/>
<a NAME="E6:104_4_2_1_1_1_2_4"/><b>then </b><i><font color="Green" title="E110">A38</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2"><i><font color="Green" title="E96">A17</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<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_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E6:104_4_2_1_1_1_2"><i><font color="Green" title="E100">A21</font></i></a>, <a class="txt" href="#E10:104_4_2_1_1_1_2"><i><font color="Green" title="E102">A23</font></i></a>, <a class="txt" href="#E11:104_4_2_1_1_1_2"><i><font color="Green" title="E103">A24</font></i></a>, <a class="txt" href="#E1:104_4_2_1_1_1_2_4"><i><font color="Green" title="E108">A36</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>
<br/>.= 
the <a href="modelc_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:104_4_2_1_1_1_2_4"><i><font color="Green" title="E109">A37</font></i></a>, <a class="txt" href="#E6:104_4_2_1_1_1_2_4"><i><font color="Green" title="E110">A38</font></i></a>, <a class="txt" href="#E12:104_4_2_1_1_1_2"><i><font color="Green" title="E104">A25</font></i></a>, <a class="txt" href="#E1:104_4_2"><i><font color="Green" title="E94">A15</font></i></a>, <a class="txt" href="modelc_2.html#E101"><i><font color="Green" title="E79">Lm27</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E8:104_4_2_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_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E16:104_4_2_1_1_1_2"/><i><font color="Green" title="E108">A3501</font></i>: 
( <font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</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_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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="104_4_2_1_1_1_2_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:104_4_2_1_1_1_2_5"/><i><font color="Green" title="E109">A3601</font></i>: 
<font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:104_4_2_1_1_1_2_5"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">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>
 
<b>by </b><i><a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/>
<a NAME="E3:104_4_2_1_1_1_2_5"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2"><i><font color="Green" title="E96">A17</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E4:104_4_2_1_1_1_2_5"/><b>then </b><i><font color="Green" title="E110">A3701</font></i>: 
<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_2.html#K11" title="MODELC_2:func.11">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_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E12:104_4_2_1_1_1_2"><i><font color="Green" title="E104">A25</font></i></a>, <a class="txt" href="#E1:104_4_2"><i><font color="Green" title="E94">A15</font></i></a>, <a class="txt" href="modelc_2.html#E101"><i><font color="Green" title="E79">Lm27</font></i></a></i>;<br/>
<a NAME="E5:104_4_2_1_1_1_2_5"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2_5"><i><font color="Green" title="E109">A3601</font></i></a>, <a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/>
<a NAME="E6:104_4_2_1_1_1_2_5"/><b>then </b><i><font color="Green" title="E111">A3801</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2"><i><font color="Green" title="E96">A17</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<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_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E6:104_4_2_1_1_1_2"><i><font color="Green" title="E100">A21</font></i></a>, <a class="txt" href="#E10:104_4_2_1_1_1_2"><i><font color="Green" title="E102">A23</font></i></a>, <a class="txt" href="#E11:104_4_2_1_1_1_2"><i><font color="Green" title="E103">A24</font></i></a>, <a class="txt" href="#E1:104_4_2_1_1_1_2_5"><i><font color="Green" title="E109">A3601</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>
<br/>.= 
the <a href="modelc_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:104_4_2_1_1_1_2_5"><i><font color="Green" title="E110">A3701</font></i></a>, <a class="txt" href="#E6:104_4_2_1_1_1_2_5"><i><font color="Green" title="E111">A3801</font></i></a>, <a class="txt" href="#E12:104_4_2_1_1_1_2"><i><font color="Green" title="E104">A25</font></i></a>, <a class="txt" href="#E1:104_4_2"><i><font color="Green" title="E94">A15</font></i></a>, <a class="txt" href="modelc_2.html#E101"><i><font color="Green" title="E79">Lm27</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E8:104_4_2_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_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E17:104_4_2_1_1_1_2"/><i><font color="Green" title="E109">A3900</font></i>: 
( <font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</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_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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="104_4_2_1_1_1_2_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:104_4_2_1_1_1_2_6"/><i><font color="Green" title="E110">A39</font></i>: 
<font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:104_4_2_1_1_1_2_6"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">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>
 
<b>by </b><i><a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/>
<a NAME="E3:104_4_2_1_1_1_2_6"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2"><i><font color="Green" title="E96">A17</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E4:104_4_2_1_1_1_2_6"/><b>then </b><i><font color="Green" title="E111">A40</font></i>: 
<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_2.html#K11" title="MODELC_2:func.11">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_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E12:104_4_2_1_1_1_2"><i><font color="Green" title="E104">A25</font></i></a>, <a class="txt" href="#E1:104_4_2"><i><font color="Green" title="E94">A15</font></i></a>, <a class="txt" href="modelc_2.html#E101"><i><font color="Green" title="E79">Lm27</font></i></a></i>;<br/>
<a NAME="E5:104_4_2_1_1_1_2_6"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2_6"><i><font color="Green" title="E110">A39</font></i></a>, <a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/>
<a NAME="E6:104_4_2_1_1_1_2_6"/><b>then </b><i><font color="Green" title="E112">A41</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2"><i><font color="Green" title="E96">A17</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<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_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E6:104_4_2_1_1_1_2"><i><font color="Green" title="E100">A21</font></i></a>, <a class="txt" href="#E10:104_4_2_1_1_1_2"><i><font color="Green" title="E102">A23</font></i></a>, <a class="txt" href="#E11:104_4_2_1_1_1_2"><i><font color="Green" title="E103">A24</font></i></a>, <a class="txt" href="#E1:104_4_2_1_1_1_2_6"><i><font color="Green" title="E110">A39</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>
<br/>.= 
the <a href="modelc_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:104_4_2_1_1_1_2_6"><i><font color="Green" title="E111">A40</font></i></a>, <a class="txt" href="#E6:104_4_2_1_1_1_2_6"><i><font color="Green" title="E112">A41</font></i></a>, <a class="txt" href="#E12:104_4_2_1_1_1_2"><i><font color="Green" title="E104">A25</font></i></a>, <a class="txt" href="#E1:104_4_2"><i><font color="Green" title="E94">A15</font></i></a>, <a class="txt" href="modelc_2.html#E101"><i><font color="Green" title="E79">Lm27</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E8:104_4_2_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_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E18:104_4_2_1_1_1_2"/>
( <font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</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_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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="104_4_2_1_1_1_2_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:104_4_2_1_1_1_2_7"/><i><font color="Green" title="E110">A3901</font></i>: 
<font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:104_4_2_1_1_1_2_7"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">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>
 
<b>by </b><i><a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/>
<a NAME="E3:104_4_2_1_1_1_2_7"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2"><i><font color="Green" title="E96">A17</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E4:104_4_2_1_1_1_2_7"/><b>then </b><i><font color="Green" title="E111">A4001</font></i>: 
<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_2.html#K11" title="MODELC_2:func.11">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_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E12:104_4_2_1_1_1_2"><i><font color="Green" title="E104">A25</font></i></a>, <a class="txt" href="#E1:104_4_2"><i><font color="Green" title="E94">A15</font></i></a>, <a class="txt" href="modelc_2.html#E101"><i><font color="Green" title="E79">Lm27</font></i></a></i>;<br/>
<a NAME="E5:104_4_2_1_1_1_2_7"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2_7"><i><font color="Green" title="E110">A3901</font></i></a>, <a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/>
<a NAME="E6:104_4_2_1_1_1_2_7"/><b>then </b><i><font color="Green" title="E112">A4101</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">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>
 
<b>by </b><i><a class="txt" href="#E1:104_4_2_1_1_1_2"><i><font color="Green" title="E96">A17</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<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_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E6:104_4_2_1_1_1_2"><i><font color="Green" title="E100">A21</font></i></a>, <a class="txt" href="#E10:104_4_2_1_1_1_2"><i><font color="Green" title="E102">A23</font></i></a>, <a class="txt" href="#E11:104_4_2_1_1_1_2"><i><font color="Green" title="E103">A24</font></i></a>, <a class="txt" href="#E1:104_4_2_1_1_1_2_7"><i><font color="Green" title="E110">A3901</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>
<br/>.= 
the <a href="modelc_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:104_4_2_1_1_1_2_7"><i><font color="Green" title="E111">A4001</font></i></a>, <a class="txt" href="#E6:104_4_2_1_1_1_2_7"><i><font color="Green" title="E112">A4101</font></i></a>, <a class="txt" href="#E12:104_4_2_1_1_1_2"><i><font color="Green" title="E104">A25</font></i></a>, <a class="txt" href="#E1:104_4_2"><i><font color="Green" title="E94">A15</font></i></a>, <a class="txt" href="modelc_2.html#E101"><i><font color="Green" title="E79">Lm27</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E8:104_4_2_1_1_1_2_7"/>
<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_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E19:104_4_2_1_1_1_2"/>
( ( <font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V2" title="MODELC_2: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_2.html#V3" title="MODELC_2: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_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">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_2.html#V4" title="MODELC_2: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_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V5" title="MODELC_2:attr.5">disjunctive</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_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V6" title="MODELC_2:attr.6">next</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_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">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_2.html#V7" title="MODELC_2:attr.7">Until</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_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V8" title="MODELC_2:attr.8">Release</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_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="#E6:104_4_2_1_1_1_2"><i><font color="Green" title="E100">A21</font></i></a>, <a class="txt" href="#E10:104_4_2_1_1_1_2"><i><font color="Green" title="E102">A23</font></i></a>, <a class="txt" href="#E11:104_4_2_1_1_1_2"><i><font color="Green" title="E103">A24</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a>, <a class="txt" href="#E13:104_4_2_1_1_1_2"><i><font color="Green" title="E105">A26</font></i></a>, <a class="txt" href="#E14:104_4_2_1_1_1_2"><i><font color="Green" title="E106">A29</font></i></a>, <a class="txt" href="#E15:104_4_2_1_1_1_2"><i><font color="Green" title="E107">A35</font></i></a>, <a class="txt" href="#E16:104_4_2_1_1_1_2"><i><font color="Green" title="E108">A3501</font></i></a>, <a class="txt" href="#E17:104_4_2_1_1_1_2"><i><font color="Green" title="E109">A3900</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:104_4_2_1"/>
( ( <font color="Maroon" title="c9">H</font> is <a href="modelc_2.html#V2" title="MODELC_2: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_2.html#V3" title="MODELC_2: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_2.html#U5" title="MODELC_2:sel.5">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_2.html#K10" title="MODELC_2:func.10">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_2.html#V4" title="MODELC_2: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_2.html#U3" title="MODELC_2:sel.3">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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V5" title="MODELC_2:attr.5">disjunctive</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_2.html#U4" title="MODELC_2:sel.4">Or</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V6" title="MODELC_2:attr.6">next</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_2.html#U6" title="MODELC_2:sel.6">NEXT</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_2.html#K10" title="MODELC_2:func.10">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_2.html#V7" title="MODELC_2:attr.7">Until</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_2.html#U7" title="MODELC_2:sel.7">UNTIL</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">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_2.html#V8" title="MODELC_2:attr.8">Release</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_2.html#U8" title="MODELC_2:sel.8">RELEASE</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_2.html#K11" title="MODELC_2:func.11">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_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c9">H</font></span>)</span></span>)</span> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:104_4_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 <b>by </b><i><a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:104_4"/>
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S2" title="NAT_1:sch.2">NAT_1:sch 2</a>(<a class="txt" href="#E1:104_4"><i><font color="Green" title="E92">A13</font></i></a>, <a class="txt" href="#E2:104_4"><i><font color="Green" title="E93">A14</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:104_4"/>
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c7">f</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E14:104"/>
<font color="Maroon" title="c7">f</font> <a href="modelc_2.html#R4" title="MODELC_2:pred.4">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E103"><i><font color="Green" title="E81">Lm29</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
