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<b>let </b><font color="Maroon" title="c1">H</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_2.html#V4" title="MODELC_2:attr.4">conjunctive</a> or <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> or <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> or <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> ) &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> implies (  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> &amp;  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> ) )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:138"/><i><font color="Green" title="E115">A1</font></i>: 
( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a> or <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> or <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> or <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> )
 <b>and </b><br/><a NAME="E2:138"/><i><font color="Green" title="E116">A2</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> &amp;  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> )</span><br/>

<b>set </b><font color="Maroon" title="c2">F1</font> =  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font>;<br/>
<b>set </b><font color="Maroon" title="c3">F2</font> =  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font>;<br/>
<a NAME="E3:138"/><i><font color="Green" title="E117">A3</font></i>: 
 <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</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="#E1:138"><i><font color="Green" title="E115">A1</font></i></a>, <a class="ref" href="modelc_2.html#T31" title="MODELC_2:th.31">MODELC_2:31</a></i>;<br/>
<a NAME="E4:138"/><i><font color="Green" title="E118">A4</font></i>: 
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>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</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="138_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">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="c4">G</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> &amp; <font color="Maroon" title="c4">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="c4">G</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> )</span><br/>

<b>assume </b><a NAME="E1:138_1"/><i><font color="Green" title="E119">B1</font></i>: 
<font color="Maroon" title="c4">G</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_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"> (  not <font color="Maroon" title="c4">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="c4">G</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> )</span><br/>

<a NAME="E2:138_1"/>
<font color="Maroon" title="c4">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="#E3:138"><i><font color="Green" title="E117">A3</font></i></a>, <a class="txt" href="#E1:138_1"><i><font color="Green" title="E119">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="E3:138_1"/>
(  not <font color="Maroon" title="c4">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="c4">G</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> )
 <b>by </b><i><a class="txt" href="#E2:138"><i><font color="Green" title="E116">A2</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>
<a NAME="E5:138"/><i><font color="Green" title="E119">A5</font></i>: 
 <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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="#E1:138"><i><font color="Green" title="E115">A1</font></i></a>, <a class="ref" href="modelc_2.html#T31" title="MODELC_2:th.31">MODELC_2:31</a></i>;<br/>
<a NAME="E6:138"/>
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>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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="138_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">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="c4">G</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> &amp; <font color="Maroon" title="c4">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="c4">G</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> )</span><br/>

<b>assume </b><a NAME="E1:138_2"/><i><font color="Green" title="E120">B1</font></i>: 
<font color="Maroon" title="c4">G</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_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"> (  not <font color="Maroon" title="c4">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="c4">G</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> )</span><br/>

<a NAME="E2:138_2"/>
<font color="Maroon" title="c4">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="#E5:138"><i><font color="Green" title="E119">A5</font></i></a>, <a class="txt" href="#E1:138_2"><i><font color="Green" title="E120">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="E3:138_2"/>
(  not <font color="Maroon" title="c4">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="c4">G</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> )
 <b>by </b><i><a class="txt" href="#E2:138"><i><font color="Green" title="E116">A2</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="E7:138"/>
(  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> &amp;  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> )
 <b>by </b><i><a class="txt" href="#E4:138"><i><font color="Green" title="E118">A4</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>
