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<span class="kw">thus </span><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> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  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">b<sub>1</sub></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">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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></span><br/>

<span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E3:39_2_1_1"/><span class="lab"><font color="Green" title="E36">A2</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D16" target="_self" title="MODELC_1:def.16">Def16</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">F</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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></span><br/>

<span class="kw">thus </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_2_1_1"><span class="lab"><font color="Green" title="E36">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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

<span class="kw">thus </span><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> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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></span><br/>

<span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E3:39_2_1_2"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="modelc_1.html#D19" target="_self" title="MODELC_1:def.19">Def19</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">F</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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></span><br/>

<span class="kw">thus </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_2_1_2"><span class="lab"><font color="Green" title="E36">A3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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


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