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

<b>thus </b><a NAME="E1:39_2_1"/>
( <font color="Maroon" title="c1">H</font> is <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a> implies  ex <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_1.html#K9" title="MODELC_1:func.9">'&amp;'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_2_1_1"/>
<font color="Maroon" title="c1">H</font> is <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">F</font> being   <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a><b> such that </b><br/><a NAME="E3:39_2_1_1"/><i><font color="Green" title="E36">A2</font></i>: 
<font color="Maroon" title="c2">G</font> <a href="modelc_1.html#K9" title="MODELC_1:func.9">'&amp;'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="ref" href="modelc_1.html#D16" target="_self" title="MODELC_1:def.16">Def16</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">F</font>
;<br/>

<b>thus </b><a NAME="E4:39_2_1_1"/>
 ex <font color="Olive" title="b1">H1</font> being  <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a> st <font color="Olive" title="b1">H1</font> <a href="modelc_1.html#K9" title="MODELC_1:func.9">'&amp;'</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E3:39_2_1_1"><i><font color="Green" title="E36">A2</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:39_2_1"/>
( not <font color="Maroon" title="c1">H</font> is <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a> implies  ex <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">H1</font> being  <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a> st <font color="Olive" title="b2">H1</font> <a href="modelc_1.html#K12" title="MODELC_1:func.12">EU</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_2_1_2"/>
not <font color="Maroon" title="c1">H</font> is <a href="modelc_1.html#V4" title="MODELC_1:attr.4">conjunctive</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">F</font> being   <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a><b> such that </b><br/><a NAME="E3:39_2_1_2"/><i><font color="Green" title="E36">A3</font></i>: 
<font color="Maroon" title="c2">G</font> <a href="modelc_1.html#K12" title="MODELC_1:func.12">EU</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:39"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="modelc_1.html#D19" target="_self" title="MODELC_1:def.19">Def19</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">F</font>
;<br/>

<b>thus </b><a NAME="E4:39_2_1_2"/>
 ex <font color="Olive" title="b1">H1</font> being  <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a> st <font color="Olive" title="b1">H1</font> <a href="modelc_1.html#K12" title="MODELC_1:func.12">EU</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E3:39_2_1_2"><i><font color="Green" title="E36">A3</font></i></a></i>;<br/>


</div><b>end;</b></div>


</div>
