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

<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#NM2" title="MODELC_2:NM.2">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#K24" title="MODELC_2:func.24">'X'</a> <font color="Olive" title="b3">f</font> iff  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Olive" title="b2">t</font>,1 <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Olive" title="b3">f</font> )</span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#NM2" title="MODELC_2:NM.2">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#K24" title="MODELC_2:func.24">'X'</a> <font color="Olive" title="b2">f</font> iff  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Olive" title="b1">t</font>,1 <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Olive" title="b2">f</font> )</span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">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#K24" title="MODELC_2:func.24">'X'</a> <font color="Olive" title="b1">f</font> iff  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">t</font>,1 <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Olive" title="b1">f</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K24" title="MODELC_2:func.24">'X'</a> <font color="Maroon" title="c4">f</font> iff  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">t</font>,1 <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Maroon" title="c4">f</font> )</span><br/>







<span class="kw">set </span><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/>
<span class="kw">set </span><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/>
<span class="kw">set </span><font color="Maroon" title="c7">t1</font> =  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">t</font>,1;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">t1p</font> =  <a href="modelc_2.html#K31" title="MODELC_2:func.31">Shift</a> <font color="Maroon" title="c3">t</font>,1,<font color="Maroon" title="c1">S</font>;<br/>
<a NAME="E1:153"/><span class="lab"><font color="Green" title="E126">A1</font></span>: 
 <a href="modelc_2.html#K24" title="MODELC_2:func.24">'X'</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K36" title="MODELC_2:func.36">Next_0</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D50" target="_self" title="MODELC_2:def.50">Def50</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:153"/>
( <font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K24" title="MODELC_2:func.24">'X'</a> <font color="Maroon" title="c4">f</font> implies  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">t</font>,1 <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Maroon" title="c4">f</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">t</font>,1 <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</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#K24" title="MODELC_2:func.24">'X'</a> <font color="Maroon" title="c4">f</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="153_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:153_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#K24" title="MODELC_2:func.24">'X'</a> <font color="Maroon" title="c4">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">t</font>,1 <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Maroon" title="c4">f</font></span><br/>

<a NAME="E2:153_1"/><span class="kw">then </span>
<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#K36" title="MODELC_2:func.36">Next_0</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">S</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:153"><span class="lab"><font color="Green" title="E126">A1</font></span></a>, <a class="ref" href="modelc_2.html#D59" target="_self" title="MODELC_2:def.59">Def59</a></span>;<br/>
<a NAME="E3:153_1"/><span class="kw">then </span>
 <a href="modelc_2.html#K35" title="MODELC_2:func.35">Next_univ</a> <font color="Maroon" title="c3">t</font>,<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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D49" target="_self" title="MODELC_2:def.49">Def49</a></span>;<br/>
<a NAME="E4:153_1"/><span class="kw">then </span>
<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> <span class="p1">(<span class="default"><a href="modelc_2.html#K31" title="MODELC_2:func.31">Shift</a> <font color="Maroon" title="c3">t</font>,1,<font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D48" target="_self" title="MODELC_2:def.48">Def48</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:153_1"/>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">t</font>,1 <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Maroon" title="c4">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D59" target="_self" title="MODELC_2:def.59">Def59</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E3:153"/>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">t</font>,1 <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a> <font color="Maroon" title="c4">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K24" title="MODELC_2:func.24">'X'</a> <font color="Maroon" title="c4">f</font></span><br/>

<a NAME="E4:153"/><span class="kw">then </span>
<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> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c3">t</font>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D59" target="_self" title="MODELC_2:def.59">Def59</a></span>;<br/>
<a NAME="E5:153"/><span class="kw">then </span>
 <a href="modelc_2.html#K35" title="MODELC_2:func.35">Next_univ</a> <font color="Maroon" title="c3">t</font>,<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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D48" target="_self" title="MODELC_2:def.48">Def48</a></span>;<br/>
<a NAME="E6:153"/><span class="kw">then </span>
<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#K24" title="MODELC_2:func.24">'X'</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:153"><span class="lab"><font color="Green" title="E126">A1</font></span></a>, <a class="ref" href="modelc_2.html#D49" target="_self" title="MODELC_2:def.49">Def49</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:153"/>
<font color="Maroon" title="c3">t</font> <a href="modelc_2.html#R6" title="MODELC_2:pred.6">|=</a>  <a href="modelc_2.html#K24" title="MODELC_2:func.24">'X'</a> <font color="Maroon" title="c4">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D59" target="_self" title="MODELC_2:def.59">Def59</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
