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

<b>set </b><font color="Maroon" title="c2">X</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ,<span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> :  ex <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">s1</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="c1">v</font> ex <font color="Olive" title="b4">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">s</font>,<font color="Olive" title="b4">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">s1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b3">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Olive" title="b2">s</font> &amp; <font color="Olive" title="b4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K29" title="MODELC_3:func.29">Label_</a> <font color="Olive" title="b3">s1</font> ) </span>}</span> ;<br/>
<a NAME="E1:143_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ,<span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> :  ex <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">s1</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="c1">v</font> ex <font color="Olive" title="b4">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">s</font>,<font color="Olive" title="b4">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">s1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b3">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Olive" title="b2">s</font> &amp; <font color="Olive" title="b4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K29" title="MODELC_3:func.29">Label_</a> <font color="Olive" title="b3">s1</font> ) </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ,<span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="143_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ,<span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> :  ex <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">s1</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="c1">v</font> ex <font color="Olive" title="b4">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">s</font>,<font color="Olive" title="b4">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">s1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b3">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Olive" title="b2">s</font> &amp; <font color="Olive" title="b4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K29" title="MODELC_3:func.29">Label_</a> <font color="Olive" title="b3">s1</font> ) </span>}</span>  or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ,<span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> )</span><br/>

<b>assume </b><a NAME="E1:143_1_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ,<span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> :  ex <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">s1</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="c1">v</font> ex <font color="Olive" title="b4">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">s</font>,<font color="Olive" title="b4">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">s1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b3">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Olive" title="b2">s</font> &amp; <font color="Olive" title="b4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K29" title="MODELC_3:func.29">Label_</a> <font color="Olive" title="b3">s1</font> ) </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ,<span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span></span><br/>

<b>then consider </b><font color="Maroon" title="c4">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ,<span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span><b> such that </b><br/><a NAME="E3:143_1_1_1"/><i><font color="Green" title="E116">B1</font></i>: 
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> &amp;  ex <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">s1</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="c1">v</font> ex <font color="Olive" title="b3">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">s</font>,<font color="Olive" title="b3">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b2">s1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b2">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Olive" title="b1">s</font> &amp; <font color="Olive" title="b3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K29" title="MODELC_3:func.29">Label_</a> <font color="Olive" title="b2">s1</font> ) )
 ;<br/>
<b>thus </b><a NAME="E4:143_1_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ,<span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 <b>by </b><i><a class="txt" href="#E3:143_1_1_1"><i><font color="Green" title="E116">B1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E2:143_1_1"/><b>then </b>
<span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ,<span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> :  ex <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">s1</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="c1">v</font> ex <font color="Olive" title="b4">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">s</font>,<font color="Olive" title="b4">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">s1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b3">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Olive" title="b2">s</font> &amp; <font color="Olive" title="b4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K29" title="MODELC_3:func.29">Label_</a> <font color="Olive" title="b3">s1</font> ) </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D3" title="ZFMISC_1:def.3">ZFMISC_1:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">X</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ,<span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> :  ex <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">s1</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="c1">v</font> ex <font color="Olive" title="b4">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">s</font>,<font color="Olive" title="b4">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">s1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b3">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Olive" title="b2">s</font> &amp; <font color="Olive" title="b4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K29" title="MODELC_3:func.29">Label_</a> <font color="Olive" title="b3">s1</font> ) </span>}</span>  as    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, <a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font> <b>by </b><i><a class="ref" href="relset_1.html#D1" title="RELSET_1:def.1">RELSET_1:def 1</a></i>;<br/>
<a NAME="E4:143_1_1"/>
<font color="Maroon" title="c3">X</font> is    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, <a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font>
 
;<br/>
<b>hence </b><a NAME="E5:143_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ,<span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> :  ex <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">s1</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="c1">v</font> ex <font color="Olive" title="b4">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">s</font>,<font color="Olive" title="b4">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">s1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b3">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Olive" title="b2">s</font> &amp; <font color="Olive" title="b4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K29" title="MODELC_3:func.29">Label_</a> <font color="Olive" title="b3">s1</font> ) </span>}</span>  is    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font></span>)</span>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, <a href="modelc_3.html#K23" title="MODELC_3:func.23">LTLStates</a> <font color="Maroon" title="c1">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
