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

<b>let </b><font color="Maroon" title="c1">V</font> be    <a href="modelc_1.html#L2" title="MODELC_1:struct.2">CTLModelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">Kai</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a> ,the <a href="modelc_1.html#U6" title="MODELC_1:sel.6">BasicAssign</a> of <font color="Maroon" title="c1">V</font>;<br/>



<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ] <b>means </b> ex <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font> st <font color="Olive" title="b1">f</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a> $1,<font color="Maroon" title="c2">Kai</font>;<br/>
<a NAME="E1:57"/><i><font color="Green" title="E51">A1</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c3">v0</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E2:57_1"/><i><font color="Green" title="E52">A2</font></i>: 
<font color="Maroon" title="c3">v0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E3:57_1"/><i><font color="Green" title="E53">A3</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">v0</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E2:57_1"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">f</font> = <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>  <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c3">v0</font>;<br/>
<a NAME="E4:57_1"/><i><font color="Green" title="E54">A4</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>  <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c3">v0</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>  &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>  <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c3">v0</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">v0</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E5:57_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>  <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c3">v0</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E3:57_1"><i><font color="Green" title="E53">A3</font></i></a>, <a class="txt" href="modelc_1.html#E4:57_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">f</font> = <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>  <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c3">v0</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font> <b>by </b><i><a class="ref" href="funct_2.html#T4" title="FUNCT_2:th.4">FUNCT_2:4</a>, <a class="txt" href="modelc_1.html#E4:57_1"><i><font color="Green" title="E54">A4</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">f</font>
;<br/>

<b>thus </b><a NAME="E7:57_1"/>
<font color="Maroon" title="c5">f</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a> 0,<font color="Maroon" title="c2">Kai</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E54"><i><font color="Green" title="E46">Lm24</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:57"/><i><font color="Green" title="E52">A5</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   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="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:57_2"/><i><font color="Green" title="E53">A6</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">k</font>]
 ;<br/>

<b>consider </b><font color="Maroon" title="c4">h</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E3:57_2"/><i><font color="Green" title="E54">A7</font></i>: 
<font color="Maroon" title="c4">h</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a> <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">Kai</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2"><i><font color="Green" title="E53">A6</font></i></a></i>;<br/>
<a NAME="E4:57_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1"><b>proof </b></a><div class="add">

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  =  <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><a href="modelc_1.html#K18" title="MODELC_1:func.18">CastCTLformula</a> $1</span>)</span>;<br/>
<a NAME="E1:57_2_1"/><i><font color="Green" title="E55">A8</font></i>: 
for <font color="Olive" title="b1">H</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>  holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">H</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">H</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:57_2_1_1"/><i><font color="Green" title="E56">A9</font></i>: 
<font color="Maroon" title="c5">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c6">H</font> = <font color="Maroon" title="c5">H</font> as   <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a> <b>by </b><i><a class="ref" href="modelc_1.html#T1" target="_self" title="MODELC_1:th.1">Th1</a>, <a class="txt" href="modelc_1.html#E1:57_2_1_1"><i><font color="Green" title="E56">A9</font></i></a></i>;<br/>
<a NAME="E3:57_2_1_1"/><i><font color="Green" title="E57">A10</font></i>: 
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">H</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_1"><i><font color="Green" title="E56">A9</font></i></a>, <a class="ref" href="modelc_1.html#D24" target="_self" title="MODELC_1:def.24">Def24</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_2_1_1_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 or (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 &amp; <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a> ) or (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 &amp; <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a> ) or (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 &amp; <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a> ) or (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 &amp; <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a> ) or (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 &amp; <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a> ) or (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 &amp; <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a> ) or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 )
 </span><b>by </b><i><a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a>, <a class="ref" href="modelc_1.html#T2" target="_self" title="MODELC_1:th.2">Th2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_1_1_1"><b>suppose </b></a><a NAME="E1:57_2_1_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 ;<br/><div class="add"><a NAME="E2:57_2_1_1_1_1"/><b>then </b>
 <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font>
 <b>by </b><i><a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a></i>;<br/><b>hence </b><a NAME="E3:57_2_1_1_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">H</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_1"><i><font color="Green" title="E56">A9</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a>, <a class="txt" href="modelc_1.html#E3:57_2_1_1"><i><font color="Green" title="E57">A10</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_1_1_2"><b>suppose </b></a><a NAME="E1:57_2_1_1_1_2"/><i><font color="Green" title="E58">A11</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 &amp; <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a> )
 ;<br/><div class="add"><a NAME="E2:57_2_1_1_1_2"/><b>then </b><i><font color="Green" title="E59">A12</font></i>: 
<font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a> 
 ;<br/><a NAME="E3:57_2_1_1_1_2"/>
<font color="Maroon" title="c2">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U6" title="MODELC_1:sel.6">BasicAssign</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E2:57_2_1_1_1_2"><i><font color="Green" title="E59">A12</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><a NAME="E4:57_2_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 ;<br/><b>hence </b><a NAME="E5:57_2_1_1_1_2"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">H</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_1_1_2"><i><font color="Green" title="E58">A11</font></i></a>, <a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a>, <a class="txt" href="modelc_1.html#E3:57_2_1_1"><i><font color="Green" title="E57">A10</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_1_1_3"><b>suppose </b></a><a NAME="E1:57_2_1_1_1_3"/><i><font color="Green" title="E58">A13</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 &amp; <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a> )
 ;<br/><div class="add"><a NAME="E2:57_2_1_1_1_3"/>
 <a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_1.html#T1" target="_self" title="MODELC_1:th.1">Th1</a></i>;<br/><a NAME="E3:57_2_1_1_1_3"/><b>then </b><i><font color="Green" title="E59">A14</font></i>: 
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><a NAME="E4:57_2_1_1_1_3"/>
 <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_1_1_3"><i><font color="Green" title="E58">A13</font></i></a>, <a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a></i>;<br/><b>hence </b><a NAME="E5:57_2_1_1_1_3"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">H</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2_1_1_1_3"><i><font color="Green" title="E59">A14</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a>, <a class="txt" href="modelc_1.html#E3:57_2_1_1"><i><font color="Green" title="E57">A10</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_1_1_4"><b>suppose </b></a><a NAME="E1:57_2_1_1_1_4"/><i><font color="Green" title="E58">A15</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 &amp; <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a> )
 ;<br/><div class="add"><a NAME="E2:57_2_1_1_1_4"/>
 <a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_1.html#T1" target="_self" title="MODELC_1:th.1">Th1</a></i>;<br/><a NAME="E3:57_2_1_1_1_4"/><b>then </b><i><font color="Green" title="E59">A16</font></i>: 
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><a NAME="E4:57_2_1_1_1_4"/>
 <a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_1.html#T1" target="_self" title="MODELC_1:th.1">Th1</a></i>;<br/><a NAME="E5:57_2_1_1_1_4"/><b>then </b>
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><a NAME="E6:57_2_1_1_1_4"/><b>then </b><i><font color="Green" title="E60">A17</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2_1_1_1_4"><i><font color="Green" title="E59">A16</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/><a NAME="E7:57_2_1_1_1_4"/>
 <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_1_1_4"><i><font color="Green" title="E58">A15</font></i></a>, <a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a></i>;<br/><b>hence </b><a NAME="E8:57_2_1_1_1_4"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">H</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E6:57_2_1_1_1_4"><i><font color="Green" title="E60">A17</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a>, <a class="txt" href="modelc_1.html#E3:57_2_1_1"><i><font color="Green" title="E57">A10</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_1_1_5"><b>suppose </b></a><a NAME="E1:57_2_1_1_1_5"/><i><font color="Green" title="E58">A18</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 &amp; <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a> )
 ;<br/><div class="add"><a NAME="E2:57_2_1_1_1_5"/>
 <a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_1.html#T1" target="_self" title="MODELC_1:th.1">Th1</a></i>;<br/><a NAME="E3:57_2_1_1_1_5"/><b>then </b><i><font color="Green" title="E59">A19</font></i>: 
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><a NAME="E4:57_2_1_1_1_5"/>
 <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_1_1_5"><i><font color="Green" title="E58">A18</font></i></a>, <a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a></i>;<br/><b>hence </b><a NAME="E5:57_2_1_1_1_5"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">H</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2_1_1_1_5"><i><font color="Green" title="E59">A19</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a>, <a class="txt" href="modelc_1.html#E3:57_2_1_1"><i><font color="Green" title="E57">A10</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_1_1_6"><b>suppose </b></a><a NAME="E1:57_2_1_1_1_6"/><i><font color="Green" title="E58">A20</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 &amp; <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a> )
 ;<br/><div class="add"><a NAME="E2:57_2_1_1_1_6"/>
 <a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_1.html#T1" target="_self" title="MODELC_1:th.1">Th1</a></i>;<br/><a NAME="E3:57_2_1_1_1_6"/><b>then </b><i><font color="Green" title="E59">A21</font></i>: 
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><a NAME="E4:57_2_1_1_1_6"/>
 <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_1_1_6"><i><font color="Green" title="E58">A20</font></i></a>, <a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a></i>;<br/><b>hence </b><a NAME="E5:57_2_1_1_1_6"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">H</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2_1_1_1_6"><i><font color="Green" title="E59">A21</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a>, <a class="txt" href="modelc_1.html#E3:57_2_1_1"><i><font color="Green" title="E57">A10</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_1_1_7"><b>suppose </b></a><a NAME="E1:57_2_1_1_1_7"/><i><font color="Green" title="E58">A22</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 &amp; <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a> )
 ;<br/><div class="add"><a NAME="E2:57_2_1_1_1_7"/>
 <a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_1.html#T1" target="_self" title="MODELC_1:th.1">Th1</a></i>;<br/><a NAME="E3:57_2_1_1_1_7"/><b>then </b><i><font color="Green" title="E59">A23</font></i>: 
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><a NAME="E4:57_2_1_1_1_7"/>
 <a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_1.html#T1" target="_self" title="MODELC_1:th.1">Th1</a></i>;<br/><a NAME="E5:57_2_1_1_1_7"/><b>then </b>
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><a NAME="E6:57_2_1_1_1_7"/><b>then </b><i><font color="Green" title="E60">A24</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2_1_1_1_7"><i><font color="Green" title="E59">A23</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/><a NAME="E7:57_2_1_1_1_7"/>
 <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_1_1_7"><i><font color="Green" title="E58">A22</font></i></a>, <a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a></i>;<br/><b>hence </b><a NAME="E8:57_2_1_1_1_7"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">H</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E6:57_2_1_1_1_7"><i><font color="Green" title="E60">A24</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a>, <a class="txt" href="modelc_1.html#E3:57_2_1_1"><i><font color="Green" title="E57">A10</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_1_1_8"><b>suppose </b></a><a NAME="E1:57_2_1_1_1_8"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 ;<br/><div class="add"><a NAME="E2:57_2_1_1_1_8"/><b>then </b>
 <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font>
 <b>by </b><i><a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a></i>;<br/><b>hence </b><a NAME="E3:57_2_1_1_1_8"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">H</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_1"><i><font color="Green" title="E56">A9</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a>, <a class="txt" href="modelc_1.html#E3:57_2_1_1"><i><font color="Green" title="E57">A10</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c5">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E3:57_2_1"/><i><font color="Green" title="E56">A25</font></i>: 
for <font color="Olive" title="b1">H</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>  holds <br/><font color="Maroon" title="c5">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>1</sub></font>(<font color="Olive" title="b1">H</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S2" title="FUNCT_2:sch.2">FUNCT_2:sch 2</a>(<a class="txt" href="modelc_1.html#E1:57_2_1"><i><font color="Green" title="E55">A8</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon" title="c5">f</font>
;<br/>

<a NAME="E4:57_2_1"/><i><font color="Green" title="E57">A26</font></i>: 
for <font color="Olive" title="b1">H</font> being  <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">H</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 holds <br/><font color="Maroon" title="c5">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="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">H</font> be   <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a>;<br/>

<b>assume </b><a NAME="E1:57_2_1_2"/><i><font color="Green" title="E58">A27</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 ;<br/>

<a NAME="E2:57_2_1_2"/><i><font color="Green" title="E59">A28</font></i>: 
<font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 
<b>by </b><i><a class="ref" href="modelc_1.html#T1" target="_self" title="MODELC_1:th.1">Th1</a></i>;<br/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> = 
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">H</font>)
<b>by </b><i><a class="txt" href="modelc_1.html#E2:57_2_1_2"><i><font color="Green" title="E59">A28</font></i></a>, <a class="txt" href="modelc_1.html#E3:57_2_1"><i><font color="Green" title="E56">A25</font></i></a></i>
<br/>.= 
 <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font>
<b>by </b><i><a class="txt" href="modelc_1.html#E2:57_2_1_2"><i><font color="Green" title="E59">A28</font></i></a>, <a class="ref" href="modelc_1.html#D24" target="_self" title="MODELC_1:def.24">Def24</a></i>
;<br/>
<b>hence </b><a NAME="E4:57_2_1_2"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font>
 <b>by </b><i><a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a>, <a class="txt" href="modelc_1.html#E1:57_2_1_2"><i><font color="Green" title="E58">A27</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:57_2_1"/>
<font color="Maroon" title="c5">f</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1,<font color="Maroon" title="c2">Kai</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:57_2_1_3"/>
for <font color="Olive" title="b1">H</font> being  <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 holds <br/>( ( <font color="Olive" title="b1">H</font> is <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> ) &amp; ( <font color="Olive" title="b1">H</font> is <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">H</font> be   <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a>;<br/>

<b>assume </b><a NAME="E1:57_2_1_3_1"/><i><font color="Green" title="E58">A29</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 ;<br/>

<a NAME="E2:57_2_1_3_1"/><i><font color="Green" title="E59">A30</font></i>: 
<font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> 
 
<b>by </b><i><a class="ref" href="modelc_1.html#T1" target="_self" title="MODELC_1:th.1">Th1</a></i>;<br/>
<i><font color="Green" title="E60">A31</font></i>: <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> = 
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">H</font>)
<b>by </b><i><a class="txt" href="modelc_1.html#E2:57_2_1_3_1"><i><font color="Green" title="E59">A30</font></i></a>, <a class="txt" href="modelc_1.html#E3:57_2_1"><i><font color="Green" title="E56">A25</font></i></a></i>
<br/>.= 
 <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font>
<b>by </b><i><a class="txt" href="modelc_1.html#E2:57_2_1_3_1"><i><font color="Green" title="E59">A30</font></i></a>, <a class="ref" href="modelc_1.html#D24" target="_self" title="MODELC_1:def.24">Def24</a></i>
;<br/>
<a NAME="E4:57_2_1_3_1"/><i><font color="Green" title="E61">A32</font></i>: 
( <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">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="c6">H</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1_3_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:57_2_1_3_1_2"/><i><font color="Green" title="E62">A33</font></i>: 
<font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_2_1_3_1_2_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 )
 </span><b>by </b><i><a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1"><i><font color="Green" title="E58">A29</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_2_1_1"><b>suppose </b></a><a NAME="E1:57_2_1_3_1_2_1_1"/><i><font color="Green" title="E63">A34</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 ;<br/><div class="add"><a NAME="E2:57_2_1_3_1_2_1_1"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>then </b><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> = 
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font>
<b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c2">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font>
<b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2"><i><font color="Green" title="E54">A7</font></i></a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_2"><i><font color="Green" title="E62">A33</font></i></a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_2_1_1"><i><font color="Green" title="E63">A34</font></i></a>, <a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></i>
;<br/><b>hence </b><a NAME="E4:57_2_1_3_1_2_1_1"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">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="c6">H</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_2_1_2"><b>suppose </b></a><a NAME="E1:57_2_1_3_1_2_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:57_2_1_3_1_2_1_2"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">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="c6">H</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_3_1_2"><i><font color="Green" title="E62">A33</font></i></a>, <a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a>, <a class="txt" href="modelc_1.html#E3:57_2_1_3_1"><i><font color="Green" title="E60">A31</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E5:57_2_1_3_1"/><i><font color="Green" title="E62">A35</font></i>: 
( <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1_3_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:57_2_1_3_1_3"/><i><font color="Green" title="E63">A36</font></i>: 
<font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a>
 ;<br/>

<a NAME="E2:57_2_1_3_1_3"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">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="c6">H</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E47"><i><font color="Green" title="E40">Lm22</font></i></a></i>;<br/>
<a NAME="E3:57_2_1_3_1_3"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_3_1"><i><font color="Green" title="E58">A29</font></i></a>, <a class="txt" href="modelc_1.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E4:57_2_1_3_1_3"/><b>then </b><i><font color="Green" title="E64">A37</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_2_1_3_1_3_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 )
 </span><b>by </b><i><a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1"><i><font color="Green" title="E58">A29</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_3_1_1"><b>suppose </b></a><a NAME="E1:57_2_1_3_1_3_1_1"/><i><font color="Green" title="E65">A38</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 ;<br/><div class="add"><a NAME="E2:57_2_1_3_1_3_1_1"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>then </b><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> = 
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font>
<b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>
<br/>.= 
the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2"><i><font color="Green" title="E54">A7</font></i></a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_3"><i><font color="Green" title="E63">A36</font></i></a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_3_1_1"><i><font color="Green" title="E65">A38</font></i></a>, <a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></i>
;<br/><b>hence </b><a NAME="E4:57_2_1_3_1_3_1_1"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1_3_1_3"><i><font color="Green" title="E64">A37</font></i></a>, <a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_3_1_2"><b>suppose </b></a><a NAME="E1:57_2_1_3_1_3_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 ;<br/><div class="add"><b>then </b> <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font> = 
the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_3"><i><font color="Green" title="E63">A36</font></i></a></i>
<br/>.= 
the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1_3_1_3"><i><font color="Green" title="E64">A37</font></i></a>, <a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>
;<br/><b>hence </b><a NAME="E3:57_2_1_3_1_3_1_2"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2_1_3_1"><i><font color="Green" title="E60">A31</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E6:57_2_1_3_1"/><i><font color="Green" title="E63">A39</font></i>: 
( <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1_3_1_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:57_2_1_3_1_4"/><i><font color="Green" title="E64">A40</font></i>: 
<font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>
 ;<br/>

<a NAME="E2:57_2_1_3_1_4"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">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="c6">H</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E48"><i><font color="Green" title="E41">Lm23</font></i></a></i>;<br/>
<a NAME="E3:57_2_1_3_1_4"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_3_1"><i><font color="Green" title="E58">A29</font></i></a>, <a class="txt" href="modelc_1.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E4:57_2_1_3_1_4"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E5:57_2_1_3_1_4"/><b>then </b><i><font color="Green" title="E65">A41</font></i>: 
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>;<br/>
<a NAME="E6:57_2_1_3_1_4"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">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="c6">H</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_3_1_4"><i><font color="Green" title="E64">A40</font></i></a>, <a class="txt" href="modelc_1.html#E48"><i><font color="Green" title="E41">Lm23</font></i></a></i>;<br/>
<a NAME="E7:57_2_1_3_1_4"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_3_1"><i><font color="Green" title="E58">A29</font></i></a>, <a class="txt" href="modelc_1.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E8:57_2_1_3_1_4"/><b>then </b><i><font color="Green" title="E66">A42</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_2_1_3_1_4_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 )
 </span><b>by </b><i><a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1"><i><font color="Green" title="E58">A29</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_4_1_1"><b>suppose </b></a><a NAME="E1:57_2_1_3_1_4_1_1"/><i><font color="Green" title="E67">A43</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 ;<br/><div class="add"><a NAME="E2:57_2_1_3_1_4_1_1"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>then </b><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> = 
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font>
<b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>
<br/>.= 
the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2"><i><font color="Green" title="E54">A7</font></i></a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_4"><i><font color="Green" title="E64">A40</font></i></a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_4_1_1"><i><font color="Green" title="E67">A43</font></i></a>, <a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></i>
;<br/><b>hence </b><a NAME="E4:57_2_1_3_1_4_1_1"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E5:57_2_1_3_1_4"><i><font color="Green" title="E65">A41</font></i></a>, <a class="txt" href="modelc_1.html#E8:57_2_1_3_1_4"><i><font color="Green" title="E66">A42</font></i></a>, <a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_4_1_2"><b>suppose </b></a><a NAME="E1:57_2_1_3_1_4_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 ;<br/><div class="add"><b>then </b> <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font> = 
the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_4"><i><font color="Green" title="E64">A40</font></i></a></i>
<br/>.= 
the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="modelc_1.html#E5:57_2_1_3_1_4"><i><font color="Green" title="E65">A41</font></i></a>, <a class="txt" href="modelc_1.html#E8:57_2_1_3_1_4"><i><font color="Green" title="E66">A42</font></i></a>, <a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>
;<br/><b>hence </b><a NAME="E3:57_2_1_3_1_4_1_2"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2_1_3_1"><i><font color="Green" title="E60">A31</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E7:57_2_1_3_1"/><i><font color="Green" title="E64">A44</font></i>: 
( <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1_3_1_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:57_2_1_3_1_5"/><i><font color="Green" title="E65">A45</font></i>: 
<font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a>
 ;<br/>

<a NAME="E2:57_2_1_3_1_5"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">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="c6">H</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E47"><i><font color="Green" title="E40">Lm22</font></i></a></i>;<br/>
<a NAME="E3:57_2_1_3_1_5"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_3_1"><i><font color="Green" title="E58">A29</font></i></a>, <a class="txt" href="modelc_1.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E4:57_2_1_3_1_5"/><b>then </b><i><font color="Green" title="E66">A46</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_5_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_2_1_3_1_5_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 )
 </span><b>by </b><i><a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1"><i><font color="Green" title="E58">A29</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_5_1_1"><b>suppose </b></a><a NAME="E1:57_2_1_3_1_5_1_1"/><i><font color="Green" title="E67">A47</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 ;<br/><div class="add"><a NAME="E2:57_2_1_3_1_5_1_1"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>then </b><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> = 
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font>
<b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>
<br/>.= 
the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2"><i><font color="Green" title="E54">A7</font></i></a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_5"><i><font color="Green" title="E65">A45</font></i></a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_5_1_1"><i><font color="Green" title="E67">A47</font></i></a>, <a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></i>
;<br/><b>hence </b><a NAME="E4:57_2_1_3_1_5_1_1"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1_3_1_5"><i><font color="Green" title="E66">A46</font></i></a>, <a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_5_1_2"><b>suppose </b></a><a NAME="E1:57_2_1_3_1_5_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 ;<br/><div class="add"><b>then </b> <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font> = 
the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_5"><i><font color="Green" title="E65">A45</font></i></a></i>
<br/>.= 
the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1_3_1_5"><i><font color="Green" title="E66">A46</font></i></a>, <a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>
;<br/><b>hence </b><a NAME="E3:57_2_1_3_1_5_1_2"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2_1_3_1"><i><font color="Green" title="E60">A31</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E8:57_2_1_3_1"/><i><font color="Green" title="E65">A48</font></i>: 
( <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1_3_1_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:57_2_1_3_1_6"/><i><font color="Green" title="E66">A49</font></i>: 
<font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a>
 ;<br/>

<a NAME="E2:57_2_1_3_1_6"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">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="c6">H</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E47"><i><font color="Green" title="E40">Lm22</font></i></a></i>;<br/>
<a NAME="E3:57_2_1_3_1_6"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_3_1"><i><font color="Green" title="E58">A29</font></i></a>, <a class="txt" href="modelc_1.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E4:57_2_1_3_1_6"/><b>then </b><i><font color="Green" title="E67">A50</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_6_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_2_1_3_1_6_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 )
 </span><b>by </b><i><a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1"><i><font color="Green" title="E58">A29</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_6_1_1"><b>suppose </b></a><a NAME="E1:57_2_1_3_1_6_1_1"/><i><font color="Green" title="E68">A51</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 ;<br/><div class="add"><a NAME="E2:57_2_1_3_1_6_1_1"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>then </b><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> = 
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font>
<b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>
<br/>.= 
the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2"><i><font color="Green" title="E54">A7</font></i></a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_6"><i><font color="Green" title="E66">A49</font></i></a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_6_1_1"><i><font color="Green" title="E68">A51</font></i></a>, <a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></i>
;<br/><b>hence </b><a NAME="E4:57_2_1_3_1_6_1_1"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1_3_1_6"><i><font color="Green" title="E67">A50</font></i></a>, <a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_6_1_2"><b>suppose </b></a><a NAME="E1:57_2_1_3_1_6_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 ;<br/><div class="add"><b>then </b> <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font> = 
the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_6"><i><font color="Green" title="E66">A49</font></i></a></i>
<br/>.= 
the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1_3_1_6"><i><font color="Green" title="E67">A50</font></i></a>, <a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>
;<br/><b>hence </b><a NAME="E3:57_2_1_3_1_6_1_2"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2_1_3_1"><i><font color="Green" title="E60">A31</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E9:57_2_1_3_1"/>
( <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1_3_1_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:57_2_1_3_1_7"/><i><font color="Green" title="E66">A52</font></i>: 
<font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a>
 ;<br/>

<a NAME="E2:57_2_1_3_1_7"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">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="c6">H</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E48"><i><font color="Green" title="E41">Lm23</font></i></a></i>;<br/>
<a NAME="E3:57_2_1_3_1_7"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_3_1"><i><font color="Green" title="E58">A29</font></i></a>, <a class="txt" href="modelc_1.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E4:57_2_1_3_1_7"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E5:57_2_1_3_1_7"/><b>then </b><i><font color="Green" title="E67">A53</font></i>: 
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>;<br/>
<a NAME="E6:57_2_1_3_1_7"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">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="c6">H</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E48"><i><font color="Green" title="E41">Lm23</font></i></a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_7"><i><font color="Green" title="E66">A52</font></i></a></i>;<br/>
<a NAME="E7:57_2_1_3_1_7"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E1:57_2_1_3_1"><i><font color="Green" title="E58">A29</font></i></a>, <a class="txt" href="modelc_1.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E8:57_2_1_3_1_7"/><b>then </b><i><font color="Green" title="E68">A54</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_7_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_2_1_3_1_7_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 )
 </span><b>by </b><i><a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1"><i><font color="Green" title="E58">A29</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_7_1_1"><b>suppose </b></a><a NAME="E1:57_2_1_3_1_7_1_1"/><i><font color="Green" title="E69">A55</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 ;<br/><div class="add"><a NAME="E2:57_2_1_3_1_7_1_1"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>then </b><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> = 
<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font>
<b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>
<br/>.= 
the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2"><i><font color="Green" title="E54">A7</font></i></a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_7"><i><font color="Green" title="E66">A52</font></i></a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_7_1_1"><i><font color="Green" title="E69">A55</font></i></a>, <a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></i>
;<br/><b>hence </b><a NAME="E4:57_2_1_3_1_7_1_1"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E5:57_2_1_3_1_7"><i><font color="Green" title="E67">A53</font></i></a>, <a class="txt" href="modelc_1.html#E8:57_2_1_3_1_7"><i><font color="Green" title="E68">A54</font></i></a>, <a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_1_3_1_7_1_2"><b>suppose </b></a><a NAME="E1:57_2_1_3_1_7_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 ;<br/><div class="add"><b>then </b> <a href="modelc_1.html#K20" title="MODELC_1:func.20">GraftEval</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">Kai</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c6">H</font> = 
the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="modelc_1.html#D28" target="_self" title="MODELC_1:def.28">Def28</a>, <a class="txt" href="modelc_1.html#E1:57_2_1_3_1_7"><i><font color="Green" title="E66">A52</font></i></a></i>
<br/>.= 
the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="modelc_1.html#E5:57_2_1_3_1_7"><i><font color="Green" title="E67">A53</font></i></a>, <a class="txt" href="modelc_1.html#E8:57_2_1_3_1_7"><i><font color="Green" title="E68">A54</font></i></a>, <a class="txt" href="modelc_1.html#E4:57_2_1"><i><font color="Green" title="E57">A26</font></i></a></i>
;<br/><b>hence </b><a NAME="E3:57_2_1_3_1_7_1_2"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E3:57_2_1_3_1"><i><font color="Green" title="E60">A31</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E10:57_2_1_3_1"/>
( ( <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">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="c6">H</font> ) &amp; ( <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V3" title="MODELC_1:attr.3">negative</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U8" title="MODELC_1:sel.8">Not</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U7" title="MODELC_1:sel.7">And</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V5" title="MODELC_1:attr.5">ExistNext</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U9" title="MODELC_1:sel.9">EneXt</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V6" title="MODELC_1:attr.6">ExistGlobal</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U10" title="MODELC_1:sel.10">EGlobal</a> of <font color="Maroon" title="c1">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K15" title="MODELC_1:func.15">the_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c6">H</font> is <a href="modelc_1.html#V7" title="MODELC_1:attr.7">ExistUntill</a> implies <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_1.html#U11" title="MODELC_1:sel.11">EUntill</a> of <font color="Maroon" title="c1">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K16" title="MODELC_1:func.16">the_left_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K17" title="MODELC_1:func.17">the_right_argument_of</a> <font color="Maroon" title="c6">H</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="modelc_1.html#E4:57_2_1_3_1"><i><font color="Green" title="E61">A32</font></i></a>, <a class="txt" href="modelc_1.html#E5:57_2_1_3_1"><i><font color="Green" title="E62">A35</font></i></a>, <a class="txt" href="modelc_1.html#E6:57_2_1_3_1"><i><font color="Green" title="E63">A39</font></i></a>, <a class="txt" href="modelc_1.html#E7:57_2_1_3_1"><i><font color="Green" title="E64">A44</font></i></a>, <a class="txt" href="modelc_1.html#E8:57_2_1_3_1"><i><font color="Green" title="E65">A48</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:57_2_1_3"/>
<font color="Maroon" title="c5">f</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1,<font color="Maroon" title="c2">Kai</font>
 <b>by </b><i><a class="ref" href="modelc_1.html#D27" target="_self" title="MODELC_1:def.27">Def27</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:57_2_1"/>
<font color="Maroon" title="c5">f</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a> <font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1,<font color="Maroon" title="c2">Kai</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:57_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1]
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:57"/>
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="modelc_1.html#E1:57"><i><font color="Green" title="E51">A1</font></i></a>, <a class="txt" href="modelc_1.html#E2:57"><i><font color="Green" title="E52">A5</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:57"/>
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   ex <font color="Olive" title="b2">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a> ,the <a href="modelc_1.html#U5" title="MODELC_1:sel.5">Assignations</a> of <font color="Maroon" title="c1">V</font> st <font color="Olive" title="b2">f</font> <a href="modelc_1.html#R2" title="MODELC_1:pred.2">is-PreEvaluation-for</a> <font color="Olive" title="b1">n</font>,<font color="Maroon" title="c2">Kai</font>
 ;<br/>


</div>
