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<div class="add">

<b>let </b><font color="Maroon">S</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">R</font> be  <a href="partfun1.html#V1">total</a>  <a href="relset_1.html#M2">Relation</a> of <font color="Maroon">S</font>,<font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">BASSIGN</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">S</font></span>)</span>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="modelc_1.html#NM2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K50" target="_self">CTLModel</a> <font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font></span>)</span>, <font color="Maroon">g</font> be   <a href="modelc_1.html#NM2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K50" target="_self">CTLModel</a> <font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font></span>)</span>;<br/>







<b>assume </b><a NAME="E1:167"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">s</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font> holds <br/> ( <font color="Olive">s</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">g</font> iff <font color="Olive">s</font> <a href="modelc_1.html#R3" target="_self">|=</a>  <a href="modelc_1.html#K55" target="_self">Fax</a> <font color="Maroon">f</font>,<font color="Maroon">g</font> )
 ;<br/>

<a NAME="E2:167"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">s</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font>  st <font color="Olive">s</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">g</font> holds <br/><font color="Olive">s</font> <a href="modelc_1.html#R3" target="_self">|=</a>  <a href="modelc_1.html#K27" target="_self">EX</a> <font color="Maroon">g</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="167_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">s</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E1:167_1"/>
<font color="Maroon">s</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">g</font>
 ;<br/>

<a NAME="E2:167_1"/><b>then </b>
<font color="Maroon">s</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">f</font> <a href="modelc_1.html#K26" target="_self">'&amp;'</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K27" target="_self">EX</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E37"><i><font color="Green">Lemma127</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:167_1"/>
<font color="Maroon">s</font> <a href="modelc_1.html#R3" target="_self">|=</a>  <a href="modelc_1.html#K27" target="_self">EX</a> <font color="Maroon">g</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E3:167"/>
for <font color="Olive">s0</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font>  st <font color="Olive">s0</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">g</font> holds <br/><font color="Olive">s0</font> <a href="modelc_1.html#R3" target="_self">|=</a>  <a href="modelc_1.html#K28" target="_self">EG</a> <font color="Maroon">f</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="167_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">s0</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E1:167_2"/>
<font color="Maroon">s0</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">g</font>
 ;<br/>

<b>then consider </b><font color="Maroon">pai</font> being    <a href="modelc_1.html#M1" target="_self">inf_path</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:167_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">pai</font> <a href="funct_2.html#K3">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">s0</font>
 <b>and </b><br/><a NAME="E4:167_2"/><i><font color="Green">E52</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">pai</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E38"><i><font color="Green">Lemma128</font></i></a>, <a class="txt" href="modelc_1.html#E35"><i><font color="Green">Lemma125</font></i></a></i>;<br/>
<a NAME="E5:167_2"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">pai</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">f</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="167_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<a NAME="E1:167_2_1"/>
<font color="Maroon">pai</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E40"><i><font color="Green">Lemma130</font></i></a></i>;<br/>
<a NAME="E2:167_2_1"/><b>then </b>
<font color="Maroon">pai</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">f</font> <a href="modelc_1.html#K26" target="_self">'&amp;'</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K27" target="_self">EX</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E37"><i><font color="Green">Lemma127</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:167_2_1"/>
<font color="Maroon">pai</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">f</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:167_2"/>
<font color="Maroon">s0</font> <a href="modelc_1.html#R3" target="_self">|=</a>  <a href="modelc_1.html#K28" target="_self">EG</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E39"><i><font color="Green">Lemma129</font></i></a>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:167"/>
for <font color="Olive">s</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font>  st <font color="Olive">s</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">g</font> holds <br/><font color="Olive">s</font> <a href="modelc_1.html#R3" target="_self">|=</a>  <a href="modelc_1.html#K28" target="_self">EG</a> <font color="Maroon">f</font>
 ;<br/>


</div>
