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

<b>set </b><font color="Maroon" title="c1">X</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">x</font> where <font color="Olive" title="b1">x</font> is   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> : <font color="Olive" title="b1">x</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> </span>}</span> ;<br/>
<a NAME="E1:90_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive" title="b1">x</font> where <font color="Olive" title="b1">x</font> is   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> : <font color="Olive" title="b1">x</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">y</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="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">x</font> where <font color="Olive" title="b1">x</font> is   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> : <font color="Olive" title="b1">x</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> </span>}</span>  or <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  )</span><br/>

<b>assume </b><a NAME="E1:90_1_1_1"/>
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">x</font> where <font color="Olive" title="b1">x</font> is   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> : <font color="Olive" title="b1">x</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> </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="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> </span><br/>

<a NAME="E2:90_1_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">x</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> &amp; <font color="Olive" title="b1">x</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> )
 
;<br/>
<b>hence </b><a NAME="E3:90_1_1_1"/>
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 <b>by </b><i><a class="ref" href="modelc_2.html#T1" target="_self" title="MODELC_2:th.1">Th1</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>hence </b><a NAME="E2:90_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive" title="b1">x</font> where <font color="Olive" title="b1">x</font> is   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> : <font color="Olive" title="b1">x</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> </span>}</span>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
