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

<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">BASSIGN</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span><br/> for <font color="Olive" title="b2">t</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b3">f</font> being  <a href="modelc_2.html#NM3" title="MODELC_2:NM.3">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K45" title="MODELC_2:func.45">LTLModel</a> <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">BASSIGN</font></span>)</span> holds <br/> ( <font color="Olive" title="b2">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <font color="Olive" title="b3">f</font> iff <font color="Olive" title="b2">t</font> <a href="modelc_2.html#NR7" title="MODELC_2:NR.7">|/=</a> <font color="Olive" title="b3">f</font> )</span><br/><b>let </b><font color="Maroon" title="c2">BASSIGN</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span>; <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">t</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">f</font> being  <a href="modelc_2.html#NM3" title="MODELC_2:NM.3">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K45" title="MODELC_2:func.45">LTLModel</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">BASSIGN</font></span>)</span> holds <br/> ( <font color="Olive" title="b1">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <font color="Olive" title="b2">f</font> iff <font color="Olive" title="b1">t</font> <a href="modelc_2.html#NR7" title="MODELC_2:NR.7">|/=</a> <font color="Olive" title="b2">f</font> )</span><br/><b>let </b><font color="Maroon" title="c3">t</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</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">f</font> being  <a href="modelc_2.html#NM3" title="MODELC_2:NM.3">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K45" title="MODELC_2:func.45">LTLModel</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">BASSIGN</font></span>)</span> holds <br/> ( <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <font color="Olive" title="b1">f</font> iff <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#NR7" title="MODELC_2:NR.7">|/=</a> <font color="Olive" title="b1">f</font> )</span><br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="modelc_2.html#NM3" title="MODELC_2:NM.3">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K45" title="MODELC_2:func.45">LTLModel</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">BASSIGN</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">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <font color="Maroon" title="c4">f</font> iff <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#NR7" title="MODELC_2:NR.7">|/=</a> <font color="Maroon" title="c4">f</font> )</span><br/>







<b>set </b><font color="Maroon" title="c5">V</font> =  <a href="modelc_2.html#K45" title="MODELC_2:func.45">LTLModel</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">BASSIGN</font>;<br/>
<b>set </b><font color="Maroon" title="c6">S1</font> =  <a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font>;<br/>
<a NAME="E1:152"/><i><font color="Green" title="E124">A1</font></i>: 
 <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K33" title="MODELC_2:func.33">Not_0</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">S</font>
 
<b>by </b><i><a class="ref" href="modelc_2.html#D47" target="_self" title="MODELC_2:def.47">Def43</a></i>;<br/>
<b>thus </b><a NAME="E2:152"/>
( <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <font color="Maroon" title="c4">f</font> implies <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#NR7" title="MODELC_2:NR.7">|/=</a> <font color="Maroon" title="c4">f</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#NR7" title="MODELC_2:NR.7">|/=</a> <font color="Maroon" title="c4">f</font> implies <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <font color="Maroon" title="c4">f</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="152_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:152_1"/>
<font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <font color="Maroon" title="c4">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#NR7" title="MODELC_2:NR.7">|/=</a> <font color="Maroon" title="c4">f</font></span><br/>

<a NAME="E2:152_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <font color="Maroon" title="c4">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
<b>by </b><i><a class="ref" href="modelc_2.html#D59" target="_self" title="MODELC_2:def.59">Def59</a></i>;<br/>
<a NAME="E3:152_1"/><b>then </b>
 <a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K4" title="MODELC_1:func.4">Castboolean</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c4">f</font>,<span class="p4">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
<b>by </b><i><a class="txt" href="modelc_2.html#E1:152"><i><font color="Green" title="E124">A1</font></i></a>, <a class="ref" href="modelc_2.html#D46" target="_self" title="MODELC_2:def.46">Def42</a></i>;<br/>
<a NAME="E4:152_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c4">f</font>,<span class="p2">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 
<b>by </b><i><a class="ref" href="modelc_1.html#D4" title="MODELC_1:def.4">MODELC_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E5:152_1"/>
<font color="Maroon" title="c3">t</font> <a href="modelc_2.html#NR7" title="MODELC_2:NR.7">|/=</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="ref" href="modelc_2.html#D59" target="_self" title="MODELC_2:def.59">Def59</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>

<b>assume </b><a NAME="E3:152"/>
<font color="Maroon" title="c3">t</font> <a href="modelc_2.html#NR7" title="MODELC_2:NR.7">|/=</a> <font color="Maroon" title="c4">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <font color="Maroon" title="c4">f</font></span><br/>

<a NAME="E4:152"/><b>then </b>
not <span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c4">f</font>,<span class="p2">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
<b>by </b><i><a class="ref" href="modelc_2.html#D59" target="_self" title="MODELC_2:def.59">Def59</a></i>;<br/>
<a NAME="E5:152"/><b>then </b>
not  <a href="modelc_1.html#K4" title="MODELC_1:func.4">Castboolean</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c4">f</font>,<span class="p3">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
<b>by </b><i><a class="ref" href="modelc_1.html#D4" title="MODELC_1:def.4">MODELC_1:def 4</a></i>;<br/>
<a NAME="E6:152"/><b>then </b>
 <a href="modelc_1.html#K4" title="MODELC_1:func.4">Castboolean</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c4">f</font>,<span class="p3">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 
<b>by </b><i><a class="ref" href="xboolean.html#D3" title="XBOOLEAN:def.3">XBOOLEAN:def 3</a></i>;<br/>
<a NAME="E7:152"/><b>then </b>
 <a href="xboolean.html#K3" title="XBOOLEAN:func.3">'not'</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K4" title="MODELC_1:func.4">Castboolean</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <font color="Maroon" title="c4">f</font>,<span class="p4">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">t</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
;<br/>
<a NAME="E8:152"/><b>then </b>
<span class="p1">(<span class="default"><a href="modelc_1.html#K33" title="MODELC_1:func.33">Fid</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <font color="Maroon" title="c4">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
<b>by </b><i><a class="ref" href="modelc_2.html#D46" target="_self" title="MODELC_2:def.46">Def42</a>, <a class="txt" href="modelc_2.html#E1:152"><i><font color="Green" title="E124">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:152"/>
<font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K21" title="MODELC_2:func.21">'not'</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="ref" href="modelc_2.html#D59" target="_self" title="MODELC_2:def.59">Def59</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>
