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<b>let </b><font color="Maroon" title="c1">H</font>, <font color="Maroon" title="c2">F</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> &amp; <font color="Maroon" title="c2">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c1">H</font> implies <font color="Maroon" title="c2">F</font> is <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> )</span><br/>



<b>assume </b><a NAME="E1:134"/><i><font color="Green" title="E113">A1</font></i>: 
( <font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> &amp; <font color="Maroon" title="c2">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c1">H</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">F</font> is <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a></span><br/>

<a NAME="E2:134"/>
for <font color="Olive" title="b1">G</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st <font color="Olive" title="b1">G</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Olive" title="b1">G</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> holds <br/> <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Olive" title="b1">G</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="134_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">G</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">G</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Maroon" title="c3">G</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> implies  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c3">G</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> )</span><br/>

<b>assume </b><a NAME="E1:134_1"/><i><font color="Green" title="E114">B1</font></i>: 
<font color="Maroon" title="c3">G</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">G</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> or  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c3">G</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> )</span><br/>

<a NAME="E2:134_1"/>
<font color="Maroon" title="c3">G</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c1">H</font>
 
<b>by </b><i><a class="txt" href="#E1:134"><i><font color="Green" title="E113">A1</font></i></a>, <a class="txt" href="#E1:134_1"><i><font color="Green" title="E114">B1</font></i></a>, <a class="ref" href="modelc_2.html#T35" title="MODELC_2:th.35">MODELC_2:35</a></i>;<br/>
<b>hence </b><a NAME="E3:134_1"/>
(  not <font color="Maroon" title="c3">G</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> or  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c3">G</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> )
 <b>by </b><i><a class="txt" href="#E1:134"><i><font color="Green" title="E113">A1</font></i></a>, <a class="ref" href="modelc_3.html#D37" target="_self" title="MODELC_3:def.37">DefNegIM</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="E3:134"/>
<font color="Maroon" title="c2">F</font> is <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a>
 <b>by </b><i><a class="ref" href="modelc_3.html#D37" target="_self" title="MODELC_3:def.37">DefNegIM</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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