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

<b>let </b><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">v</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"> for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s0</font>, <font color="Olive" title="b3">s2</font> being <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c3">v</font>  st <font color="Olive" title="b1">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Olive" title="b2">s0</font> &amp; <font color="Olive" title="b3">s2</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Olive" title="b1">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Olive" title="b1">s1</font> &amp; not <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Olive" title="b1">s1</font> holds <br/>( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Olive" title="b1">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Olive" title="b3">s2</font> )</span><br/><b>let </b><font color="Maroon" title="c4">s1</font>, <font color="Maroon" title="c5">s0</font>, <font color="Maroon" title="c6">s2</font> be  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c3">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">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Maroon" title="c5">s0</font> &amp; <font color="Maroon" title="c6">s2</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> &amp; not <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> implies ( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> ) )</span><br/>











<b>assume </b><b>that </b><br/><a NAME="E1:97"/><i><font color="Green" title="E86">A1</font></i>: 
<font color="Maroon" title="c4">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Maroon" title="c5">s0</font>
 <b>and </b><br/><a NAME="E2:97"/><i><font color="Green" title="E87">A2</font></i>: 
<font color="Maroon" title="c6">s2</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Maroon" title="c4">s1</font>
 <b>and </b><br/><a NAME="E3:97"/><i><font color="Green" title="E88">A3</font></i>: 
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> or ( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> ) )</span><br/>

<b>consider </b><font color="Maroon" title="c7">L</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E5:97"/><i><font color="Green" title="E89">A4</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">L</font> &amp; <font color="Maroon" title="c7">L</font> <a href="modelc_3.html#R5" title="MODELC_3:pred.5">is_Finseq_for</a> <font color="Maroon" title="c3">v</font> &amp; <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c5">s0</font> &amp; <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s1</font> )
 <b>by </b><i><a class="ref" href="modelc_3.html#D20" target="_self" title="MODELC_3:def.20">Def215</a>, <a class="txt" href="#E1:97"><i><font color="Green" title="E86">A1</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c8">n</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">L</font>;<br/>
<a NAME="E6:97"/><i><font color="Green" title="E90">A501</font></i>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">L</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s1</font>
 
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a>, <a class="txt" href="#E5:97"><i><font color="Green" title="E89">A4</font></i></a></i>;<br/>
<a NAME="E7:97"/><b>then </b><i><font color="Green" title="E91">A502</font></i>: 
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">L</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c3">v</font>
 
<b>by </b><i><a class="ref" href="modelc_3.html#D11" target="_self" title="MODELC_3:def.11">Defelementary</a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">F1</font> = <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font>;<br/>
<a NAME="E8:97"/><i><font color="Green" title="E92">a5</font></i>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c5">s0</font>
 
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a>, <a class="txt" href="#E5:97"><i><font color="Green" title="E89">A4</font></i></a></i>;<br/>
<a NAME="E9:97"/>
1 <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">L</font>
 
<b>by </b><i><a class="txt" href="#E5:97"><i><font color="Green" title="E89">A4</font></i></a>, <a class="txt" href="#E3:97"><i><font color="Green" title="E88">A3</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c10">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E11:97"/><i><font color="Green" title="E93">A7</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">m</font> &amp; <font color="Maroon" title="c10">m</font> <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">L</font> )
 <b>and </b><br/><a NAME="E12:97"/><i><font color="Green" title="E94">A8</font></i>: 
not <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
 <b>and </b><br/><a NAME="E13:97"/><i><font color="Green" title="E95">A9</font></i>: 
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
 <b>by </b><i><a class="ref" href="modelc_3.html#T27" target="_self" title="MODELC_3:th.27">ThSucc03</a>, <a class="txt" href="#E5:97"><i><font color="Green" title="E89">A4</font></i></a>, <a class="txt" href="#E8:97"><i><font color="Green" title="E92">a5</font></i></a>, <a class="txt" href="#E3:97"><i><font color="Green" title="E88">A3</font></i></a>, <a class="txt" href="#E6:97"><i><font color="Green" title="E90">A501</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">N1</font>, <font color="Maroon" title="c12">N2</font> being  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c3">v</font><b> such that </b><br/><a NAME="E15:97"/><i><font color="Green" title="E96">A10</font></i>: 
( <font color="Maroon" title="c11">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font> &amp; <font color="Maroon" title="c12">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Maroon" title="c12">N2</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c11">N1</font> )
 <b>by </b><i><a class="txt" href="#E5:97"><i><font color="Green" title="E89">A4</font></i></a>, <a class="txt" href="#E11:97"><i><font color="Green" title="E93">A7</font></i></a>, <a class="ref" href="modelc_3.html#D19" target="_self" title="MODELC_3:def.19">DefFinseq</a></i>;<br/>
<a NAME="E16:97"/><i><font color="Green" title="E97">A101</font></i>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">N1</font>
 
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a>, <a class="txt" href="#E15:97"><i><font color="Green" title="E96">A10</font></i></a></i>;<br/>
<a NAME="E17:97"/><i><font color="Green" title="E98">A102</font></i>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">N2</font>
 
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a>, <a class="txt" href="#E15:97"><i><font color="Green" title="E96">A10</font></i></a></i>;<br/>
<a NAME="E18:97"/><i><font color="Green" title="E99">A11</font></i>: 
<font color="Maroon" title="c12">N2</font> <a href="modelc_3.html#R1" title="MODELC_3:pred.1">is_succ_of</a> <font color="Maroon" title="c11">N1</font>,<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font>
 
<b>by </b><i><a class="txt" href="#E12:97"><i><font color="Green" title="E94">A8</font></i></a>, <a class="txt" href="#E13:97"><i><font color="Green" title="E95">A9</font></i></a>, <a class="txt" href="#E16:97"><i><font color="Green" title="E97">A101</font></i></a>, <a class="txt" href="#E17:97"><i><font color="Green" title="E98">A102</font></i></a>, <a class="txt" href="#E15:97"><i><font color="Green" title="E96">A10</font></i></a>, <a class="ref" href="modelc_3.html#T28" target="_self" title="MODELC_3:th.28">ThSucc04</a></i>;<br/>
<a NAME="E19:97"/><i><font color="Green" title="E100">A1201</font></i>: 
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 
<b>by </b><i><a class="txt" href="#E5:97"><i><font color="Green" title="E89">A4</font></i></a>, <a class="txt" href="#E11:97"><i><font color="Green" title="E93">A7</font></i></a>, <a class="ref" href="modelc_3.html#T31" target="_self" title="MODELC_3:th.31">ThSucc07</a>, <a class="txt" href="#E6:97"><i><font color="Green" title="E90">A501</font></i></a>, <a class="txt" href="#E16:97"><i><font color="Green" title="E97">A101</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c13">m1</font> = <font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1;<br/>
<a NAME="E20:97"/><i><font color="Green" title="E101">A120101</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">L</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">L</font> &amp; <font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">L</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 
<b>by </b><i><a class="txt" href="#E11:97"><i><font color="Green" title="E93">A7</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E21:97"/><b>then </b><i><font color="Green" title="E102">A1202</font></i>: 
the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c12">N2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c4">s1</font>
 
<b>by </b><i><a class="txt" href="#E5:97"><i><font color="Green" title="E89">A4</font></i></a>, <a class="ref" href="modelc_3.html#T31" target="_self" title="MODELC_3:th.31">ThSucc07</a>, <a class="txt" href="#E6:97"><i><font color="Green" title="E90">A501</font></i></a>, <a class="txt" href="#E17:97"><i><font color="Green" title="E98">A102</font></i></a></i>;<br/>
<a NAME="E22:97"/><i><font color="Green" title="E103">A1203</font></i>: 
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c12">N2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 
<b>by </b><i><a class="txt" href="#E5:97"><i><font color="Green" title="E89">A4</font></i></a>, <a class="txt" href="#E20:97"><i><font color="Green" title="E101">A120101</font></i></a>, <a class="txt" href="#E7:97"><i><font color="Green" title="E91">A502</font></i></a>, <a class="ref" href="modelc_3.html#T34" target="_self" title="MODELC_3:th.34">ThSucc10</a>, <a class="txt" href="#E17:97"><i><font color="Green" title="E98">A102</font></i></a>, <a class="txt" href="#E6:97"><i><font color="Green" title="E90">A501</font></i></a></i>;<br/>
<a NAME="E23:97"/><i><font color="Green" title="E104">A13</font></i>: 
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>
 
<b>by </b><i><a class="ref" href="modelc_2.html#D16" title="MODELC_2:def.16">MODELC_2:def 16</a></i>;<br/>
<a NAME="E24:97"/><b>then </b><i><font color="Green" title="E105">A1301</font></i>: 
 <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font>
 
<b>by </b><i><a class="ref" href="modelc_2.html#D19" title="MODELC_2:def.19">MODELC_2:def 19</a></i>;<br/>
<a NAME="E25:97"/><i><font color="Green" title="E106">A1302</font></i>: 
 <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font>
 
<b>by </b><i><a class="txt" href="#E23:97"><i><font color="Green" title="E104">A13</font></i></a>, <a class="ref" href="modelc_2.html#D20" title="MODELC_2:def.20">MODELC_2:def 20</a></i>;<br/>
<a NAME="E26:97"/><i><font color="Green" title="E107">A14</font></i>: 
 <a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">F</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="#E23:97"><i><font color="Green" title="E104">A13</font></i></a>, <a class="txt" href="#E24:97"><i><font color="Green" title="E105">A1301</font></i></a>, <a class="ref" href="modelc_3.html#D1" target="_self" title="MODELC_3:def.1">Def203</a></i>;<br/>
<a NAME="E27:97"/><i><font color="Green" title="E108">A15</font></i>: 
 <a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">G</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="#E23:97"><i><font color="Green" title="E104">A13</font></i></a>, <a class="txt" href="#E25:97"><i><font color="Green" title="E106">A1302</font></i></a>, <a class="ref" href="modelc_3.html#D2" target="_self" title="MODELC_3:def.2">Def204</a></i>;<br/>
<a NAME="E28:97"/><i><font color="Green" title="E109">A16</font></i>: 
 <a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="#E23:97"><i><font color="Green" title="E104">A13</font></i></a>, <a class="ref" href="modelc_3.html#D3" target="_self" title="MODELC_3:def.3">Def205</a></i>;<br/>
<a NAME="E29:97"/>
( not <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> implies ( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:97_1"/><i><font color="Green" title="E110">B0</font></i>: 
not <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:97_1_1_1"/>
( ( <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c11">N1</font> &amp; <font color="Maroon" title="c12">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>,<font color="Maroon" title="c11">N1</font> ) or ( <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c11">N1</font> &amp; ( <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> or <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> or <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> ) &amp; <font color="Maroon" title="c12">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>,<font color="Maroon" title="c11">N1</font> ) )
 </span><b>by </b><i><a class="txt" href="#E18:97"><i><font color="Green" title="E99">A11</font></i></a>, <a class="ref" href="modelc_3.html#D6" target="_self" title="MODELC_3:def.6">DefSucc01</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1"><b>suppose </b></a><a NAME="E1:97_1_1_1_1"/><i><font color="Green" title="E111">B2</font></i>: 
( <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c11">N1</font> &amp; <font color="Maroon" title="c12">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>,<font color="Maroon" title="c11">N1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> )</span><br/><div class="add"><a NAME="E2:97_1_1_1_1"/><b>then </b>
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c12">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c11">N1</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font></span>)</span>
 <b>by </b><i><a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def206</a></i>;<br/><a NAME="E3:97_1_1_1_1"/><b>then </b><i><font color="Green" title="E112">C1</font></i>: 
<span class="p1">(<span class="default"><a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c12">N2</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><a NAME="E4:97_1_1_1_1"/><i><font color="Green" title="E113">C2</font></i>: 
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_1_1_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:97_1_1_1_1_1_1_1"/>
( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font> or  not <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:97_1_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font></span><br/><div class="add"><b>hence </b><a NAME="E2:97_1_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 <b>by </b><i><a class="txt" href="#E19:97"><i><font color="Green" title="E100">A1201</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:97_1_1_1_1_1_1_1_2"/><i><font color="Green" title="E114">D1</font></i>: 
not <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font></span><br/><div class="add"><a NAME="E2:97_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E26:97"><i><font color="Green" title="E107">A14</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:97_1_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font>
 <b>by </b><i><a class="txt" href="#E1:97_1_1_1_1_1_1_1_2"><i><font color="Green" title="E114">D1</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/><a NAME="E4:97_1_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c12">N2</font>
 <b>by </b><i><a class="txt" href="#E3:97_1_1_1_1"><i><font color="Green" title="E112">C1</font></i></a></i>;<br/><b>hence </b><a NAME="E5:97_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 <b>by </b><i><a class="txt" href="#E22:97"><i><font color="Green" title="E103">A1203</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:97_1_1_1_1_1"/>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E5:97_1_1_1_1"/>
the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c12">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c11">N1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:97_1_1_1_1"><i><font color="Green" title="E111">B2</font></i></a>, <a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def206</a></i>;<br/><a NAME="E6:97_1_1_1_1"/><b>then </b><i><font color="Green" title="E114">C3</font></i>: 
 <a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c12">N2</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><a NAME="E7:97_1_1_1_1"/>
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E28:97"><i><font color="Green" title="E109">A16</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E8:97_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c12">N2</font>
 <b>by </b><i><a class="txt" href="#E6:97_1_1_1_1"><i><font color="Green" title="E114">C3</font></i></a></i>;<br/><a NAME="E9:97_1_1_1_1"/><b>then </b><i><font color="Green" title="E115">C4</font></i>: 
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c4">s1</font>
 <b>by </b><i><a class="txt" href="#E21:97"><i><font color="Green" title="E102">A1202</font></i></a></i>;<br/><a NAME="E10:97_1_1_1_1"/>
the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c4">s1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font>
 <b>by </b><i><a class="ref" href="modelc_3.html#T37" target="_self" title="MODELC_3:th.37">ThNext01</a>, <a class="txt" href="#E2:97"><i><font color="Green" title="E87">A2</font></i></a></i>;<br/><b>hence </b><a NAME="E11:97_1_1_1_1"/>
( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> )
 <b>by </b><i><a class="txt" href="#E9:97_1_1_1_1"><i><font color="Green" title="E115">C4</font></i></a>, <a class="txt" href="#E4:97_1_1_1_1"><i><font color="Green" title="E113">C2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_2"><b>suppose </b></a><a NAME="E1:97_1_1_1_2"/>
( <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c11">N1</font> &amp; ( <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> or <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> or <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> ) &amp; <font color="Maroon" title="c12">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>,<font color="Maroon" title="c11">N1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> )</span><br/><div class="add"><a NAME="E2:97_1_1_1_2"/><b>then </b>
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c12">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c11">N1</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font></span>)</span>
 <b>by </b><i><a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def207</a></i>;<br/><a NAME="E3:97_1_1_1_2"/><b>then </b><i><font color="Green" title="E111">C1</font></i>: 
<span class="p1">(<span class="default"><a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c12">N2</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><a NAME="E4:97_1_1_1_2"/>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_1_2_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_1_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_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="E1:97_1_1_1_2_1_1_1"/>
( <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font> or  not <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_2_1_1_1_1"><b>suppose </b></a><a NAME="E1:97_1_1_1_2_1_1_1_1"/>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font></span><br/><div class="add"><b>hence </b><a NAME="E2:97_1_1_1_2_1_1_1_1"/>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 <b>by </b><i><a class="txt" href="#E19:97"><i><font color="Green" title="E100">A1201</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_2_1_1_1_2"><b>suppose </b></a><a NAME="E1:97_1_1_1_2_1_1_1_2"/><i><font color="Green" title="E112">D1</font></i>: 
not <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font></span><br/><div class="add"><a NAME="E2:97_1_1_1_2_1_1_1_2"/>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E27:97"><i><font color="Green" title="E108">A15</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:97_1_1_1_2_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font>
 <b>by </b><i><a class="txt" href="#E1:97_1_1_1_2_1_1_1_2"><i><font color="Green" title="E112">D1</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/><a NAME="E4:97_1_1_1_2_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c12">N2</font>
 <b>by </b><i><a class="txt" href="#E3:97_1_1_1_2"><i><font color="Green" title="E111">C1</font></i></a></i>;<br/><b>hence </b><a NAME="E5:97_1_1_1_2_1_1_1_2"/>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 <b>by </b><i><a class="txt" href="#E22:97"><i><font color="Green" title="E103">A1203</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:97_1_1_1_2_1"/>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:97_1_1_1_2"/>
( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> )
 <b>by </b><i><a class="txt" href="#E1:97_1"><i><font color="Green" title="E110">B0</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:97_1"/>
( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E30:97"/>
( <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> or ( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
