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

<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="modelc_2.html#NM3" title="MODELC_2:NM.3">LTLModel</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Kai</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>, the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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/><span class="kw">let </span><font color="Maroon" title="c2">Kai</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>, the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">BasicAssign</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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/>



<span class="kw">set </span><font color="Maroon" title="c3">M</font> =  <a href="modelc_2.html#K20" title="MODELC_2:func.20">EvalFamily</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c4">v0</font> =  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>;<br/>
<a NAME="E1:106"/>
 for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="106_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">EvalFamily</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>) implies <font color="Maroon" title="c5">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:106_1"/>
<font color="Maroon" title="c5">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">EvalFamily</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<a NAME="E2:106_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c5">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K18" title="MODELC_2:func.18">EvalSet</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Olive" title="b1">n</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D34" target="_self" onmouseover="rs('modelc_2/D34')" onmouseout="rh()">Def34</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:106_1"/>
<font color="Maroon" title="c5">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">Choice</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E3:106"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c5">Choice</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">EvalFamily</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>)
 <span class="kw">and </span><br/><a NAME="E4:106"/><span class="lab"><font color="Green" title="E73">A1</font></span>: 
 for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K20" title="MODELC_2:func.20">EvalFamily</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>) holds <br/><font color="Maroon" title="c5">Choice</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T111" onmouseover="rs('funct_1/T111')" onmouseout="rh()">FUNCT_1:111</a></span>;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ) <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  = <font color="Maroon" title="c5">Choice</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K18" title="MODELC_2:func.18">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="E5:106"/><span class="lab"><font color="Green" title="E74">A2</font></span>: 
 for <font color="Olive" title="b1">n</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="106_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">n</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  implies <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:106_2"/><span class="lab"><font color="Green" title="E75">A3</font></span>: 
<font color="Maroon" title="c6">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">Y</font> = <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">n</font> = <font color="Maroon" title="c6">n</font> as   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_2"><span class="lab"><font color="Green" title="E75">A3</font></span></a></span>;<br/>
<a NAME="E3:106_2"/>
 <a href="modelc_2.html#K1" title="MODELC_2:func.1">CastNat</a> <font color="Maroon" title="c8">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D1" target="_self" onmouseover="rs('modelc_2/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E4:106_2"/><span class="kw">then </span>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K18" title="MODELC_2:func.18">EvalSet</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c8">n</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:106"><span class="lab"><font color="Green" title="E73">A1</font></span></a>, <a class="txt" href="modelc_2.html#E108"><span class="lab"><font color="Green" title="E71">Lm27</font></span></a></span>;<br/>
<a NAME="E5:106_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">h</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> &amp; <font color="Olive" title="b1">h</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c8">n</font>,<font color="Maroon" title="c2">Kai</font> )
 
;<br/>
<span class="kw">hence </span><a NAME="E6:106_2"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E6:106"/><span class="lab"><font color="Green" title="E75">A4</font></span>: 
 for <font color="Olive" title="b1">n</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">n</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>)
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="106_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">n</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  implies <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E1:106_3"/>
<font color="Maroon" title="c6">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>)</span><br/>

<a NAME="E2:106_3"/><span class="kw">then </span>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:106"><span class="lab"><font color="Green" title="E74">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:106_3"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">n</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T8" onmouseover="rs('funct_2/T8')" onmouseout="rh()">FUNCT_2:8</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">consider </span><font color="Maroon" title="c6">f1</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>)</span>)</span><span class="kw"> such that </span><br/><a NAME="E8:106"/><span class="lab"><font color="Green" title="E76">A5</font></span>: 
 for <font color="Olive" title="b1">n</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds <br/><font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">n</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S2" onmouseover="rs('funct_2/S2')" onmouseout="rh()">FUNCT_2:sch 2</a>(<a class="txt" href="#E6:106"><span class="lab"><font color="Green" title="E75">A4</font></span></a>);<br/></span>
<span class="kw">deffunc </span><font color="Maroon">H<sub>2</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ) <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  = <span class="p1">(<span class="default"><a href="modelc_2.html#K19" title="MODELC_2:func.19">CastEval</a> (<font color="Maroon" title="c1">V</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="funct_5.html#K10" title="FUNCT_5:func.10">.</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>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1;<br/>
<a NAME="E9:106"/><span class="lab"><font color="Green" title="E77">A6</font></span>: 
 for <font color="Olive" title="b1">H</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T5" onmouseover="rs('funct_2/T5')" onmouseout="rh()">FUNCT_2:5</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E11:106"/><span class="lab"><font color="Green" title="E78">A7</font></span>: 
 for <font color="Olive" title="b1">H</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S2" onmouseover="rs('funct_2/S2')" onmouseout="rh()">FUNCT_2:sch 2</a>(<a class="txt" href="#E9:106"><span class="lab"><font color="Green" title="E77">A6</font></span></a>);<br/></span>
<span class="kw">take </span>
<font color="Maroon" title="c7">f</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E12:106"/>
 for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="106_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>] <span class="kw">means </span><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="E1:106_4"/><span class="lab"><font color="Green" title="E79">A8</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="106_4_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E1:106_4_1"/><span class="lab"><font color="Green" title="E80">A9</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font>]
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/>

<a NAME="E2:106_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> <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="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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="lattices.html#U1" title="LATTICES:sel.1">L_meet</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="lattices.html#U2" title="LATTICES:sel.2">L_join</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#U2" title="MODELC_2:sel.2">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#U3" title="MODELC_2:sel.3">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#U4" title="MODELC_2:sel.4">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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="106_4_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">H</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> <a href="nat_1.html#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="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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="lattices.html#U1" title="LATTICES:sel.1">L_meet</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="lattices.html#U2" title="LATTICES:sel.2">L_join</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#U2" title="MODELC_2:sel.2">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#U3" title="MODELC_2:sel.3">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#U4" title="MODELC_2:sel.4">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/>

<span class="kw">assume </span><a NAME="E1:106_4_1_1"/><span class="lab"><font color="Green" title="E81">A10</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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="lattices.html#U1" title="LATTICES:sel.1">L_meet</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="lattices.html#U2" title="LATTICES:sel.2">L_join</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#U2" title="MODELC_2:sel.2">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#U3" title="MODELC_2:sel.3">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#U4" title="MODELC_2:sel.4">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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="106_4_1_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> &amp; ( <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="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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="lattices.html#U1" title="LATTICES:sel.1">L_meet</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="lattices.html#U2" title="LATTICES:sel.2">L_join</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#U2" title="MODELC_2:sel.2">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#U3" title="MODELC_2:sel.3">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#U4" title="MODELC_2:sel.4">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>) ) ) 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 &amp; ( <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="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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="lattices.html#U1" title="LATTICES:sel.1">L_meet</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="lattices.html#U2" title="LATTICES:sel.2">L_join</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#U2" title="MODELC_2:sel.2">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#U3" title="MODELC_2:sel.3">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#U4" title="MODELC_2:sel.4">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></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="106_4_1_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:106_4_1_1_1_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1"><span class="lab"><font color="Green" title="E81">A10</font></span></a>, <a class="ref" href="nat_1.html#T8" onmouseover="rs('nat_1/T8')" onmouseout="rh()">NAT_1:8</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="106_4_1_1_1_1_1"><span class="kw">case </span></a><a NAME="E1:106_4_1_1_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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="lattices.html#U1" title="LATTICES:sel.1">L_meet</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="lattices.html#U2" title="LATTICES:sel.2">L_join</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#U2" title="MODELC_2:sel.2">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#U3" title="MODELC_2:sel.3">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#U4" title="MODELC_2:sel.4">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"><span class="kw">hence </span><a NAME="E2:106_4_1_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="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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="lattices.html#U1" title="LATTICES:sel.1">L_meet</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="lattices.html#U2" title="LATTICES:sel.2">L_join</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#U2" title="MODELC_2:sel.2">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#U3" title="MODELC_2:sel.3">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#U4" title="MODELC_2:sel.4">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1"><span class="lab"><font color="Green" title="E80">A9</font></span></a>, <a class="ref" href="modelc_2.html#D28" target="_self" onmouseover="rs('modelc_2/D28')" onmouseout="rh()">Def28</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="106_4_1_1_1_1_2"><span class="kw">case </span></a><a NAME="E1:106_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E82">A11</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font> <a href="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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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="lattices.html#U1" title="LATTICES:sel.1">L_meet</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="lattices.html#U2" title="LATTICES:sel.2">L_join</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#U2" title="MODELC_2:sel.2">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#U3" title="MODELC_2:sel.3">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#U4" title="MODELC_2:sel.4">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"><span class="kw">set </span><font color="Maroon" title="c10">f2</font> = <font color="Maroon">H<sub>1</sub></font>( <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>);<br/><a NAME="E2:106_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E83">A12</font></span>: 
<font color="Maroon" title="c9">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T1" target="_self" onmouseover="rs('modelc_2/T1')" onmouseout="rh()">Th1</a></span>;<br/><span class="kw">then </span><font color="Maroon" title="c6">f1</font> <a href="funct_5.html#K10" title="FUNCT_5:func.10">.</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="c6">f1</font> <a href="funct_5.html#K10" title="FUNCT_5:func.10">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D25" target="_self" onmouseover="rs('modelc_2/D25')" onmouseout="rh()">Def25</a></span>
<br/>.= 
<font color="Maroon">H<sub>1</sub></font>( <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:106"><span class="lab"><font color="Green" title="E76">A5</font></span></a></span>
;<br/><a NAME="E4:106_4_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A13</font></span>: 
 <a href="modelc_2.html#K19" title="MODELC_2:func.19">CastEval</a> (<font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="funct_5.html#K10" title="FUNCT_5:func.10">.</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>, the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>( <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D33" target="_self" onmouseover="rs('modelc_2/D33')" onmouseout="rh()">Def33</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">f2</font> = <font color="Maroon">H<sub>1</sub></font>( <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font>) as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font> ;<br/><a NAME="E6:106_4_1_1_1_1_2"/>
( <font color="Maroon" title="c11">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Choice</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K18" title="MODELC_2:func.18">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> &amp; <font color="Maroon" title="c5">Choice</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K18" title="MODELC_2:func.18">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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K18" title="MODELC_2:func.18">EvalSet</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">H</font></span>)</span>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:106"><span class="lab"><font color="Green" title="E73">A1</font></span></a>, <a class="ref" href="modelc_2.html#D1" target="_self" onmouseover="rs('modelc_2/D1')" onmouseout="rh()">Def1</a>, <a class="txt" href="modelc_2.html#E108"><span class="lab"><font color="Green" title="E71">Lm27</font></span></a></span>;<br/><a NAME="E7:106_4_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E85">A14</font></span>: 
 ex <font color="Olive" title="b1">h</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Maroon" title="c11">f2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">h</font> &amp; <font color="Olive" title="b1">h</font> <a href="modelc_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> )
 ;<br/><a NAME="E8:106_4_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A15</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E82">A11</font></span></a>, <a class="txt" href="modelc_2.html#E101"><span class="lab"><font color="Green" title="E65">Lm23</font></span></a></span>;<br/><a NAME="E9:106_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E87">A16</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:106"><span class="lab"><font color="Green" title="E78">A7</font></span></a>, <a class="txt" href="#E2:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E83">A12</font></span></a>, <a class="txt" href="#E4:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E84">A13</font></span></a></span>;<br/><a NAME="E10:106_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E88">A17</font></span>: 
( <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#U2" title="MODELC_2:sel.2">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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="106_4_1_1_1_1_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:106_4_1_1_1_1_2_2"/><span class="lab"><font color="Green" title="E89">A18</font></span>: 
<font color="Maroon" title="c9">H</font> is  <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="modelc_2.html#U2" title="MODELC_2:sel.2">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="E2:106_4_1_1_1_1_2_2"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T10" target="_self" onmouseover="rs('modelc_2/T10')" onmouseout="rh()">Th10</a></span>;<br/>
<a NAME="E3:106_4_1_1_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E90">A19</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E82">A11</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> = 
 the <a href="modelc_2.html#U2" title="MODELC_2:sel.2">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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E87">A16</font></span></a>, <a class="txt" href="#E7:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E85">A14</font></span></a>, <a class="txt" href="#E1:106_4_1_1_1_1_2_2"><span class="lab"><font color="Green" title="E89">A18</font></span></a></span>
<br/>.= 
 the <a href="modelc_2.html#U2" title="MODELC_2:sel.2">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1"><span class="lab"><font color="Green" title="E80">A9</font></span></a>, <a class="txt" href="#E8:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E86">A15</font></span></a>, <a class="txt" href="#E3:106_4_1_1_1_1_2_2"><span class="lab"><font color="Green" title="E90">A19</font></span></a>, <a class="txt" href="modelc_2.html#E102"><span class="lab"><font color="Green" title="E66">Lm24</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:106_4_1_1_1_1_2_2"/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="modelc_2.html#U2" title="MODELC_2:sel.2">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E11:106_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E89">A20</font></span>: 
( <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#U4" title="MODELC_2:sel.4">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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="106_4_1_1_1_1_2_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:106_4_1_1_1_1_2_3"/><span class="lab"><font color="Green" title="E90">A21</font></span>: 
<font color="Maroon" title="c9">H</font> is  <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="modelc_2.html#U4" title="MODELC_2:sel.4">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="E2:106_4_1_1_1_1_2_3"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E3:106_4_1_1_1_1_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A22</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E82">A11</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E4:106_4_1_1_1_1_2_3"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2_3"><span class="lab"><font color="Green" title="E90">A21</font></span></a>, <a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E5:106_4_1_1_1_1_2_3"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E82">A11</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E6:106_4_1_1_1_1_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E92">A23</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1"><span class="lab"><font color="Green" title="E80">A9</font></span></a>, <a class="txt" href="#E8:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E86">A15</font></span></a>, <a class="txt" href="modelc_2.html#E102"><span class="lab"><font color="Green" title="E66">Lm24</font></span></a></span>;<br/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> = 
 the <a href="modelc_2.html#U4" title="MODELC_2:sel.4">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>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E87">A16</font></span></a>, <a class="txt" href="#E7:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E85">A14</font></span></a>, <a class="txt" href="#E1:106_4_1_1_1_1_2_3"><span class="lab"><font color="Green" title="E90">A21</font></span></a></span>
<br/>.= 
 the <a href="modelc_2.html#U4" title="MODELC_2:sel.4">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1"><span class="lab"><font color="Green" title="E80">A9</font></span></a>, <a class="txt" href="#E8:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E86">A15</font></span></a>, <a class="txt" href="#E6:106_4_1_1_1_1_2_3"><span class="lab"><font color="Green" title="E92">A23</font></span></a>, <a class="txt" href="#E3:106_4_1_1_1_1_2_3"><span class="lab"><font color="Green" title="E91">A22</font></span></a>, <a class="txt" href="modelc_2.html#E102"><span class="lab"><font color="Green" title="E66">Lm24</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:106_4_1_1_1_1_2_3"/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="modelc_2.html#U4" title="MODELC_2:sel.4">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E12:106_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E90">A24</font></span>: 
( <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#U3" title="MODELC_2:sel.3">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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="106_4_1_1_1_1_2_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:106_4_1_1_1_1_2_4"/><span class="lab"><font color="Green" title="E91">A25</font></span>: 
<font color="Maroon" title="c9">H</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="modelc_2.html#U3" title="MODELC_2:sel.3">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="E2:106_4_1_1_1_1_2_4"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E3:106_4_1_1_1_1_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E92">A26</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E82">A11</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E4:106_4_1_1_1_1_2_4"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2_4"><span class="lab"><font color="Green" title="E91">A25</font></span></a>, <a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E5:106_4_1_1_1_1_2_4"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E82">A11</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E6:106_4_1_1_1_1_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A27</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1"><span class="lab"><font color="Green" title="E80">A9</font></span></a>, <a class="txt" href="#E8:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E86">A15</font></span></a>, <a class="txt" href="modelc_2.html#E102"><span class="lab"><font color="Green" title="E66">Lm24</font></span></a></span>;<br/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> = 
 the <a href="modelc_2.html#U3" title="MODELC_2:sel.3">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>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E87">A16</font></span></a>, <a class="txt" href="#E7:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E85">A14</font></span></a>, <a class="txt" href="#E1:106_4_1_1_1_1_2_4"><span class="lab"><font color="Green" title="E91">A25</font></span></a></span>
<br/>.= 
 the <a href="modelc_2.html#U3" title="MODELC_2:sel.3">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1"><span class="lab"><font color="Green" title="E80">A9</font></span></a>, <a class="txt" href="#E8:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E86">A15</font></span></a>, <a class="txt" href="#E6:106_4_1_1_1_1_2_4"><span class="lab"><font color="Green" title="E93">A27</font></span></a>, <a class="txt" href="#E3:106_4_1_1_1_1_2_4"><span class="lab"><font color="Green" title="E92">A26</font></span></a>, <a class="txt" href="modelc_2.html#E102"><span class="lab"><font color="Green" title="E66">Lm24</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:106_4_1_1_1_1_2_4"/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="modelc_2.html#U3" title="MODELC_2:sel.3">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E13:106_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E91">A28</font></span>: 
( <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="lattices.html#U2" title="LATTICES:sel.2">L_join</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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="106_4_1_1_1_1_2_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:106_4_1_1_1_1_2_5"/><span class="lab"><font color="Green" title="E92">A29</font></span>: 
<font color="Maroon" title="c9">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</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="E2:106_4_1_1_1_1_2_5"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E3:106_4_1_1_1_1_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A30</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E82">A11</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E4:106_4_1_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#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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2_5"><span class="lab"><font color="Green" title="E92">A29</font></span></a>, <a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E5:106_4_1_1_1_1_2_5"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E82">A11</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E6:106_4_1_1_1_1_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A31</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1"><span class="lab"><font color="Green" title="E80">A9</font></span></a>, <a class="txt" href="#E8:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E86">A15</font></span></a>, <a class="txt" href="modelc_2.html#E102"><span class="lab"><font color="Green" title="E66">Lm24</font></span></a></span>;<br/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> = 
 the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</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>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E87">A16</font></span></a>, <a class="txt" href="#E7:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E85">A14</font></span></a>, <a class="txt" href="#E1:106_4_1_1_1_1_2_5"><span class="lab"><font color="Green" title="E92">A29</font></span></a></span>
<br/>.= 
 the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1"><span class="lab"><font color="Green" title="E80">A9</font></span></a>, <a class="txt" href="#E8:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E86">A15</font></span></a>, <a class="txt" href="#E6:106_4_1_1_1_1_2_5"><span class="lab"><font color="Green" title="E94">A31</font></span></a>, <a class="txt" href="#E3:106_4_1_1_1_1_2_5"><span class="lab"><font color="Green" title="E93">A30</font></span></a>, <a class="txt" href="modelc_2.html#E102"><span class="lab"><font color="Green" title="E66">Lm24</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:106_4_1_1_1_1_2_5"/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E14:106_4_1_1_1_1_2"/><span class="lab"><font color="Green" title="E92">A32</font></span>: 
( <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="lattices.html#U1" title="LATTICES:sel.1">L_meet</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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="106_4_1_1_1_1_2_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:106_4_1_1_1_1_2_6"/><span class="lab"><font color="Green" title="E93">A33</font></span>: 
<font color="Maroon" title="c9">H</font> is  <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</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="E2:106_4_1_1_1_1_2_6"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E3:106_4_1_1_1_1_2_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A34</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E82">A11</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E4:106_4_1_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#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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2_6"><span class="lab"><font color="Green" title="E93">A33</font></span></a>, <a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E5:106_4_1_1_1_1_2_6"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E82">A11</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E6:106_4_1_1_1_1_2_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E95">A35</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1"><span class="lab"><font color="Green" title="E80">A9</font></span></a>, <a class="txt" href="#E8:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E86">A15</font></span></a>, <a class="txt" href="modelc_2.html#E102"><span class="lab"><font color="Green" title="E66">Lm24</font></span></a></span>;<br/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> = 
 the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</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>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E87">A16</font></span></a>, <a class="txt" href="#E7:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E85">A14</font></span></a>, <a class="txt" href="#E1:106_4_1_1_1_1_2_6"><span class="lab"><font color="Green" title="E93">A33</font></span></a></span>
<br/>.= 
 the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1"><span class="lab"><font color="Green" title="E80">A9</font></span></a>, <a class="txt" href="#E8:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E86">A15</font></span></a>, <a class="txt" href="#E6:106_4_1_1_1_1_2_6"><span class="lab"><font color="Green" title="E95">A35</font></span></a>, <a class="txt" href="#E3:106_4_1_1_1_1_2_6"><span class="lab"><font color="Green" title="E94">A34</font></span></a>, <a class="txt" href="modelc_2.html#E102"><span class="lab"><font color="Green" title="E66">Lm24</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:106_4_1_1_1_1_2_6"/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E15:106_4_1_1_1_1_2"/>
( <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="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="106_4_1_1_1_1_2_7"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:106_4_1_1_1_1_2_7"/><span class="lab"><font color="Green" title="E93">A36</font></span>: 
<font color="Maroon" title="c9">H</font> is  <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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="E2:106_4_1_1_1_1_2_7"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T10" target="_self" onmouseover="rs('modelc_2/T10')" onmouseout="rh()">Th10</a></span>;<br/>
<a NAME="E3:106_4_1_1_1_1_2_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A37</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E82">A11</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">H</font> = 
 the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E87">A16</font></span></a>, <a class="txt" href="#E7:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E85">A14</font></span></a>, <a class="txt" href="#E1:106_4_1_1_1_1_2_7"><span class="lab"><font color="Green" title="E93">A36</font></span></a></span>
<br/>.= 
 the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_4_1"><span class="lab"><font color="Green" title="E80">A9</font></span></a>, <a class="txt" href="#E8:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E86">A15</font></span></a>, <a class="txt" href="#E3:106_4_1_1_1_1_2_7"><span class="lab"><font color="Green" title="E94">A37</font></span></a>, <a class="txt" href="modelc_2.html#E102"><span class="lab"><font color="Green" title="E66">Lm24</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:106_4_1_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="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E16:106_4_1_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="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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="lattices.html#U1" title="LATTICES:sel.1">L_meet</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="lattices.html#U2" title="LATTICES:sel.2">L_join</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#U2" title="MODELC_2:sel.2">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#U3" title="MODELC_2:sel.3">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#U4" title="MODELC_2:sel.4">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E9:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E87">A16</font></span></a>, <a class="txt" href="#E7:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E85">A14</font></span></a>, <a class="txt" href="#E10:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E88">A17</font></span></a>, <a class="txt" href="#E14:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E92">A32</font></span></a>, <a class="txt" href="#E13:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E91">A28</font></span></a>, <a class="txt" href="#E12:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E90">A24</font></span></a>, <a class="txt" href="#E11:106_4_1_1_1_1_2"><span class="lab"><font color="Green" title="E89">A20</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:106_4_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="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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="lattices.html#U1" title="LATTICES:sel.1">L_meet</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="lattices.html#U2" title="LATTICES:sel.2">L_join</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#U2" title="MODELC_2:sel.2">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#U3" title="MODELC_2:sel.3">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#U4" title="MODELC_2:sel.4">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:106_4_1"/>
<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 class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D28" target="_self" onmouseover="rs('modelc_2/D28')" onmouseout="rh()">Def28</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:106_4"/>
 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#K5" title="NUMBERS:func.5">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="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</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="lattices.html#U1" title="LATTICES:sel.1">L_meet</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="lattices.html#U2" title="LATTICES:sel.2">L_join</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#U2" title="MODELC_2:sel.2">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#U3" title="MODELC_2:sel.3">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#U4" title="MODELC_2:sel.4">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>) ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T3" target="_self" onmouseover="rs('modelc_2/T3')" onmouseout="rh()">Th3</a></span>;<br/>
<a NAME="E3:106_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A38</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> ]
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D28" target="_self" onmouseover="rs('modelc_2/D28')" onmouseout="rh()">Def28</a></span>;<br/>
<a NAME="E4:106_4"/>
 for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S2" onmouseover="rs('nat_1/S2')" onmouseout="rh()">NAT_1:sch 2</a>(<a class="txt" href="#E3:106_4"><span class="lab"><font color="Green" title="E80">A38</font></span></a>, <a class="txt" href="#E1:106_4"><span class="lab"><font color="Green" title="E79">A8</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E5:106_4"/>
 for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E13:106"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="modelc_2.html#E104"><span class="lab"><font color="Green" title="E68">Lm26</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
