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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:138"/><span class="lab"><font color="Green" title="E115">A1</font></span>: 
( <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>  )
 <span class="kw">and </span><br/><a NAME="E2:138"/><span class="lab"><font color="Green" title="E116">A2</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">set </span><font color="Maroon" title="c2">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"/><span class="lab"><font color="Green" title="E117">A3</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:138"><span class="lab"><font color="Green" title="E115">A1</font></span></a>, <a class="ref" href="modelc_2.html#T31" title="MODELC_2:th.31">MODELC_2:31</a></span>;<br/>
<a NAME="E4:138"/><span class="lab"><font color="Green" title="E118">A4</font></span>: 
 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_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>  <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="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/>

<span class="kw">assume </span><a NAME="E1:138_1"/>
<font color="Maroon" title="c3">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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E2:138_1"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:138"><span class="lab"><font color="Green" title="E117">A3</font></span></a>, <a class="ref" href="modelc_2.html#T35" title="MODELC_2:th.35">MODELC_2:35</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:138_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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:138"><span class="lab"><font color="Green" title="E116">A2</font></span></a>, <a class="ref" href="modelc_3.html#D37" target="_self" title="MODELC_3:def.37">Def37</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">set </span><font color="Maroon" title="c3">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/>
<a NAME="E5:138"/><span class="lab"><font color="Green" title="E119">A5</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:138"><span class="lab"><font color="Green" title="E115">A1</font></span></a>, <a class="ref" href="modelc_2.html#T31" title="MODELC_2:th.31">MODELC_2:31</a></span>;<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#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_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E1:138_2"/>
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:138"><span class="lab"><font color="Green" title="E119">A5</font></span></a>, <a class="ref" href="modelc_2.html#T35" title="MODELC_2:th.35">MODELC_2:35</a></span>;<br/>
<span class="kw">hence </span><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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:138"><span class="lab"><font color="Green" title="E116">A2</font></span></a>, <a class="ref" href="modelc_3.html#D37" target="_self" title="MODELC_3:def.37">Def37</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">hence </span><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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:138"><span class="lab"><font color="Green" title="E118">A4</font></span></a>, <a class="ref" href="modelc_3.html#D37" target="_self" title="MODELC_3:def.37">Def37</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>
