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

<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">V</font> being   <a href="modelc_2.html#L1" title="MODELC_2:struct.1">LTLModelStr</a> <br/> for <font color="Olive" title="b2">Kai</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a> ,the <a href="modelc_2.html#U2" title="MODELC_2:sel.2">BasicAssign</a> of <font color="Olive" title="b1">V</font><br/> for <font color="Olive" title="b3">f1</font>, <font color="Olive" title="b4">f2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b3">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">Kai</font> &amp; <font color="Olive" title="b4">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">Kai</font> holds <br/>for <font color="Olive" title="b5">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Olive" title="b3">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">H</font></span><br/><b>let </b><font color="Maroon" title="c2">V</font> be    <a href="modelc_2.html#L1" title="MODELC_2:struct.1">LTLModelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">Kai</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a> ,the <a href="modelc_2.html#U2" title="MODELC_2:sel.2">BasicAssign</a> of <font color="Maroon" title="c2">V</font><br/> for <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">f2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b2">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">Kai</font> &amp; <font color="Olive" title="b3">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">Kai</font> holds <br/>for <font color="Olive" title="b4">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Olive" title="b2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">H</font></span><br/><b>let </b><font color="Maroon" title="c3">Kai</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a> ,the <a href="modelc_2.html#U2" title="MODELC_2:sel.2">BasicAssign</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">Kai</font> &amp; <font color="Olive" title="b2">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">Kai</font> holds <br/>for <font color="Olive" title="b3">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Olive" title="b1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">H</font></span><br/><b>let </b><font color="Maroon" title="c4">f1</font>, <font color="Maroon" title="c5">f2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">Kai</font> &amp; <font color="Maroon" title="c5">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">Kai</font> implies for <font color="Olive" title="b1">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Maroon" title="c4">f1</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="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> )</span><br/>









<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <b>means </b>( <font color="Maroon" title="c4">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> $1,<font color="Maroon" title="c3">Kai</font> &amp; <font color="Maroon" title="c5">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> $1,<font color="Maroon" title="c3">Kai</font> implies for <font color="Olive" title="b1">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> $1 holds <br/><font color="Maroon" title="c4">f1</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="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> );<br/>
<a NAME="E1:97"/><i><font color="Green" title="E80">A1</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<b>by </b><i><a class="ref" href="modelc_2.html#T3" target="_self" title="MODELC_2:th.3">Thlen01</a></i>;<br/>
<a NAME="E2:97"/><i><font color="Green" title="E81">A2</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] )</span><br/>

<b>assume </b><a NAME="E1:97_1"/><i><font color="Green" title="E82">A3</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">k</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E2:97_1"/><i><font color="Green" title="E83">A4</font></i>: 
<font color="Maroon" title="c4">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1,<font color="Maroon" title="c3">Kai</font>
 <b>and </b><br/><a NAME="E3:97_1"/><i><font color="Green" title="E84">A5</font></i>: 
<font color="Maroon" title="c5">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1,<font color="Maroon" title="c3">Kai</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 holds <br/><font color="Maroon" title="c4">f1</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="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font></span><br/>

<b>let </b><font color="Maroon" title="c7">H</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 implies <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> )</span><br/>

<b>assume </b><a NAME="E4:97_1"/><i><font color="Green" title="E85">A6</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:97_1_1"/>
( <font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> or <font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> or <font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a> or <font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a> or <font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> or <font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> or <font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> )
 </span><b>by </b><i><a class="ref" href="modelc_2.html#T2" target="_self" title="MODELC_2:th.2">Th2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1"><b>suppose </b></a><a NAME="E1:97_1_1_1"/><i><font color="Green" title="E86">A7</font></i>: 
<font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:97_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <b>by </b><i><a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>;<br/><b>hence </b><a NAME="E3:97_1_1_1"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <b>by </b><i><a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E1:97_1_1_1"><i><font color="Green" title="E86">A7</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_2"><b>suppose </b></a><a NAME="E1:97_1_1_2"/><i><font color="Green" title="E86">A8</font></i>: 
<font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:97_1_1_2"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">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="c7">H</font>
 <b>by </b><i><a class="ref" href="modelc_2.html#T10" target="_self" title="MODELC_2:th.10">ThArg7</a></i>;<br/><a NAME="E3:97_1_1_2"/><b>then </b><i><font color="Green" title="E87">A9</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a></i>;<br/><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> = 
the <a href="modelc_2.html#U5" title="MODELC_2:sel.5">Not</a> of <font color="Maroon" title="c2">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">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:97_1_1_2"><i><font color="Green" title="E86">A8</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>
<br/>.= 
the <a href="modelc_2.html#U5" title="MODELC_2:sel.5">Not</a> of <font color="Maroon" title="c2">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">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:97_1"><i><font color="Green" title="E82">A3</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a>, <a class="txt" href="modelc_2.html#E99"><i><font color="Green" title="E77">Lm25</font></i></a>, <a class="txt" href="#E3:97_1_1_2"><i><font color="Green" title="E87">A9</font></i></a></i>
;<br/><b>hence </b><a NAME="E5:97_1_1_2"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <b>by </b><i><a class="txt" href="#E1:97_1_1_2"><i><font color="Green" title="E86">A8</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_3"><b>suppose </b></a><a NAME="E1:97_1_1_3"/><i><font color="Green" title="E86">A10</font></i>: 
<font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:97_1_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_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">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="c7">H</font>
 <b>by </b><i><a class="ref" href="modelc_2.html#T10" target="_self" title="MODELC_2:th.10">ThArg7</a></i>;<br/><a NAME="E3:97_1_1_3"/><b>then </b><i><font color="Green" title="E87">A11</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a></i>;<br/><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> = 
the <a href="modelc_2.html#U6" title="MODELC_2:sel.6">NEXT</a> of <font color="Maroon" title="c2">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">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:97_1_1_3"><i><font color="Green" title="E86">A10</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>
<br/>.= 
the <a href="modelc_2.html#U6" title="MODELC_2:sel.6">NEXT</a> of <font color="Maroon" title="c2">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">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:97_1_1_3"><i><font color="Green" title="E87">A11</font></i></a>, <a class="txt" href="#E1:97_1"><i><font color="Green" title="E82">A3</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="txt" href="modelc_2.html#E99"><i><font color="Green" title="E77">Lm25</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a></i>
;<br/><b>hence </b><a NAME="E5:97_1_1_3"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <b>by </b><i><a class="txt" href="#E1:97_1_1_3"><i><font color="Green" title="E86">A10</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_4"><b>suppose </b></a><a NAME="E1:97_1_1_4"/><i><font color="Green" title="E86">A14</font></i>: 
<font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:97_1_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_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">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="c7">H</font>
 <b>by </b><i><a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/><a NAME="E3:97_1_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_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a></i>;<br/><a NAME="E4:97_1_1_4"/><b>then </b><i><font color="Green" title="E87">A15</font></i>: 
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:97_1"><i><font color="Green" title="E82">A3</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="txt" href="modelc_2.html#E99"><i><font color="Green" title="E77">Lm25</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a></i>;<br/><a NAME="E5:97_1_1_4"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">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="c7">H</font>
 <b>by </b><i><a class="txt" href="#E1:97_1_1_4"><i><font color="Green" title="E86">A14</font></i></a>, <a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/><a NAME="E6:97_1_1_4"/><b>then </b><i><font color="Green" title="E88">A16</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a></i>;<br/><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> = 
the <a href="modelc_2.html#U3" title="MODELC_2:sel.3">And</a> of <font color="Maroon" title="c2">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">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:97_1_1_4"><i><font color="Green" title="E86">A14</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>
<br/>.= 
the <a href="modelc_2.html#U3" title="MODELC_2:sel.3">And</a> of <font color="Maroon" title="c2">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">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:97_1_1_4"><i><font color="Green" title="E87">A15</font></i></a>, <a class="txt" href="#E6:97_1_1_4"><i><font color="Green" title="E88">A16</font></i></a>, <a class="txt" href="#E1:97_1"><i><font color="Green" title="E82">A3</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="txt" href="modelc_2.html#E99"><i><font color="Green" title="E77">Lm25</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a></i>
;<br/><b>hence </b><a NAME="E8:97_1_1_4"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <b>by </b><i><a class="txt" href="#E1:97_1_1_4"><i><font color="Green" title="E86">A14</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_5"><b>suppose </b></a><a NAME="E1:97_1_1_5"/><i><font color="Green" title="E86">A1401</font></i>: 
<font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:97_1_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_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">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="c7">H</font>
 <b>by </b><i><a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/><a NAME="E3:97_1_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_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a></i>;<br/><a NAME="E4:97_1_1_5"/><b>then </b><i><font color="Green" title="E87">A1501</font></i>: 
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:97_1"><i><font color="Green" title="E82">A3</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="txt" href="modelc_2.html#E99"><i><font color="Green" title="E77">Lm25</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a></i>;<br/><a NAME="E5:97_1_1_5"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">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="c7">H</font>
 <b>by </b><i><a class="txt" href="#E1:97_1_1_5"><i><font color="Green" title="E86">A1401</font></i></a>, <a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/><a NAME="E6:97_1_1_5"/><b>then </b><i><font color="Green" title="E88">A1601</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a></i>;<br/><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> = 
the <a href="modelc_2.html#U4" title="MODELC_2:sel.4">Or</a> of <font color="Maroon" title="c2">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">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:97_1_1_5"><i><font color="Green" title="E86">A1401</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>
<br/>.= 
the <a href="modelc_2.html#U4" title="MODELC_2:sel.4">Or</a> of <font color="Maroon" title="c2">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">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:97_1_1_5"><i><font color="Green" title="E87">A1501</font></i></a>, <a class="txt" href="#E6:97_1_1_5"><i><font color="Green" title="E88">A1601</font></i></a>, <a class="txt" href="#E1:97_1"><i><font color="Green" title="E82">A3</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="txt" href="modelc_2.html#E99"><i><font color="Green" title="E77">Lm25</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a></i>
;<br/><b>hence </b><a NAME="E8:97_1_1_5"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <b>by </b><i><a class="txt" href="#E1:97_1_1_5"><i><font color="Green" title="E86">A1401</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_6"><b>suppose </b></a><a NAME="E1:97_1_1_6"/><i><font color="Green" title="E86">A17</font></i>: 
<font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:97_1_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_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">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="c7">H</font>
 <b>by </b><i><a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/><a NAME="E3:97_1_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_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a></i>;<br/><a NAME="E4:97_1_1_6"/><b>then </b><i><font color="Green" title="E87">A18</font></i>: 
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:97_1"><i><font color="Green" title="E82">A3</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="txt" href="modelc_2.html#E99"><i><font color="Green" title="E77">Lm25</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a></i>;<br/><a NAME="E5:97_1_1_6"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">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="c7">H</font>
 <b>by </b><i><a class="txt" href="#E1:97_1_1_6"><i><font color="Green" title="E86">A17</font></i></a>, <a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/><a NAME="E6:97_1_1_6"/><b>then </b><i><font color="Green" title="E88">A19</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a></i>;<br/><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> = 
the <a href="modelc_2.html#U7" title="MODELC_2:sel.7">UNTIL</a> of <font color="Maroon" title="c2">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">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:97_1_1_6"><i><font color="Green" title="E86">A17</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>
<br/>.= 
the <a href="modelc_2.html#U7" title="MODELC_2:sel.7">UNTIL</a> of <font color="Maroon" title="c2">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">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:97_1_1_6"><i><font color="Green" title="E87">A18</font></i></a>, <a class="txt" href="#E6:97_1_1_6"><i><font color="Green" title="E88">A19</font></i></a>, <a class="txt" href="#E1:97_1"><i><font color="Green" title="E82">A3</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="txt" href="modelc_2.html#E99"><i><font color="Green" title="E77">Lm25</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a></i>
;<br/><b>hence </b><a NAME="E8:97_1_1_6"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <b>by </b><i><a class="txt" href="#E1:97_1_1_6"><i><font color="Green" title="E86">A17</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_7"><b>suppose </b></a><a NAME="E1:97_1_1_7"/><i><font color="Green" title="E86">A1701</font></i>: 
<font color="Maroon" title="c7">H</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:97_1_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_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">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="c7">H</font>
 <b>by </b><i><a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/><a NAME="E3:97_1_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_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a></i>;<br/><a NAME="E4:97_1_1_7"/><b>then </b><i><font color="Green" title="E87">A1801</font></i>: 
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:97_1"><i><font color="Green" title="E82">A3</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="txt" href="modelc_2.html#E99"><i><font color="Green" title="E77">Lm25</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a></i>;<br/><a NAME="E5:97_1_1_7"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">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="c7">H</font>
 <b>by </b><i><a class="txt" href="#E1:97_1_1_7"><i><font color="Green" title="E86">A1701</font></i></a>, <a class="ref" href="modelc_2.html#T11" target="_self" title="MODELC_2:th.11">ThArg8</a></i>;<br/><a NAME="E6:97_1_1_7"/><b>then </b><i><font color="Green" title="E88">A1901</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a></i>;<br/><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> = 
the <a href="modelc_2.html#U8" title="MODELC_2:sel.8">RELEASE</a> of <font color="Maroon" title="c2">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">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:97_1_1_7"><i><font color="Green" title="E86">A1701</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>
<br/>.= 
the <a href="modelc_2.html#U8" title="MODELC_2:sel.8">RELEASE</a> of <font color="Maroon" title="c2">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">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:97_1_1_7"><i><font color="Green" title="E87">A1801</font></i></a>, <a class="txt" href="#E6:97_1_1_7"><i><font color="Green" title="E88">A1901</font></i></a>, <a class="txt" href="#E1:97_1"><i><font color="Green" title="E82">A3</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="txt" href="modelc_2.html#E99"><i><font color="Green" title="E77">Lm25</font></i></a>, <a class="txt" href="#E3:97_1"><i><font color="Green" title="E84">A5</font></i></a></i>
;<br/><b>hence </b><a NAME="E8:97_1_1_7"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <b>by </b><i><a class="txt" href="#E1:97_1_1_7"><i><font color="Green" title="E86">A1701</font></i></a>, <a class="txt" href="#E4:97_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="#E2:97_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="ref" href="modelc_2.html#D28" target="_self" title="MODELC_2:def.28">Def27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E3:97"/>
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S2" title="NAT_1:sch.2">NAT_1:sch 2</a>(<a class="txt" href="#E1:97"><i><font color="Green" title="E80">A1</font></i></a>, <a class="txt" href="#E2:97"><i><font color="Green" title="E81">A2</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:97"/>
( <font color="Maroon" title="c4">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">Kai</font> &amp; <font color="Maroon" title="c5">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">Kai</font> implies for <font color="Olive" title="b1">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Maroon" title="c4">f1</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="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
