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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_3.html#V6" title="MODELC_3:attr.6">Sub_atomic</a> iff ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> or ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> &amp;  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> ) ) )</span><br/>

<b>thus </b><a NAME="E1:135"/>
(  not <font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V6" title="MODELC_3:attr.6">Sub_atomic</a> or <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> or ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> &amp;  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</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#V2" title="MODELC_2:attr.2">atomic</a> or ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> &amp;  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> ) ) implies <font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V6" title="MODELC_3:attr.6">Sub_atomic</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:135_1"/><i><font color="Green" title="E114">A1</font></i>: 
<font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V6" title="MODELC_3:attr.6">Sub_atomic</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#V2" title="MODELC_2:attr.2">atomic</a> or ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> &amp;  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> ) )</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:135_1_1"/>
( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> or  ex <font color="Olive" title="b1">G</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Olive" title="b1">G</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> &amp; <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Olive" title="b1">G</font> ) )
 </span><b>by </b><i><a class="txt" href="#E1:135_1"><i><font color="Green" title="E114">A1</font></i></a>, <a class="ref" href="modelc_3.html#D38" target="_self" title="MODELC_3:def.38">DefSubatomic</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1_1_1"><b>suppose </b></a><a NAME="E1:135_1_1_1"/>
<font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</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#V2" title="MODELC_2:attr.2">atomic</a> or ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> &amp;  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> ) )</span><br/><div class="add"><b>hence </b><a NAME="E2:135_1_1_1"/>
( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> or ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> &amp;  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> ) )
 ; <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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1_1_2"><b>suppose </b></a><a NAME="E1:135_1_1_2"/>
 ex <font color="Olive" title="b1">G</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Olive" title="b1">G</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> &amp; <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Olive" title="b1">G</font> )
 ; <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#V2" title="MODELC_2:attr.2">atomic</a> or ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> &amp;  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> ) )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">G</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E3:135_1_1_2"/><i><font color="Green" title="E115">B1</font></i>: 
( <font color="Maroon" title="c2">G</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> &amp; <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c2">G</font> )
 ;<br/><a NAME="E4:135_1_1_2"/>
<font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a>
 <b>by </b><i><a class="txt" href="#E3:135_1_1_2"><i><font color="Green" title="E115">B1</font></i></a>, <a class="ref" href="modelc_2.html#D12" title="MODELC_2:def.12">MODELC_2:def 12</a></i>;<br/><b>hence </b><a NAME="E5:135_1_1_2"/>
( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> or ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> &amp;  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> ) )
 <b>by </b><i><a class="txt" href="#E3:135_1_1_2"><i><font color="Green" title="E115">B1</font></i></a>, <a class="ref" href="modelc_2.html#D18" title="MODELC_2:def.18">MODELC_2:def 18</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></div><b>end;</b></div>

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

<b>thus </b><a NAME="E2:135"/>
( ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> or ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> &amp;  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> ) ) implies <font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V6" title="MODELC_3:attr.6">Sub_atomic</a> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:135_2"/><i><font color="Green" title="E114">A1</font></i>: 
( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> or ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> &amp;  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</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#V6" title="MODELC_3:attr.6">Sub_atomic</a></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:135_2_1"/>
( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> or ( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> &amp;  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> ) )
 </span><b>by </b><i><a class="txt" href="#E1:135_2"><i><font color="Green" title="E114">A1</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_2_1_1"><b>suppose </b></a><a NAME="E1:135_2_1_1"/>
<font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</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#V6" title="MODELC_3:attr.6">Sub_atomic</a></span><br/><div class="add"><b>hence </b><a NAME="E2:135_2_1_1"/>
<font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V6" title="MODELC_3:attr.6">Sub_atomic</a>
 <b>by </b><i><a class="ref" href="modelc_3.html#D38" target="_self" title="MODELC_3:def.38">DefSubatomic</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_2_1_2"><b>suppose </b></a><a NAME="E1:135_2_1_2"/><i><font color="Green" title="E115">B1</font></i>: 
( <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> &amp;  <a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</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#V6" title="MODELC_3:attr.6">Sub_atomic</a></span><br/><div class="add"><a NAME="E2:135_2_1_2"/><b>then </b>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="modelc_2.html#D18" title="MODELC_2:def.18">MODELC_2:def 18</a></i>;<br/><b>hence </b><a NAME="E3:135_2_1_2"/>
<font color="Maroon" title="c1">H</font> is <a href="modelc_3.html#V6" title="MODELC_3:attr.6">Sub_atomic</a>
 <b>by </b><i><a class="txt" href="#E1:135_2_1_2"><i><font color="Green" title="E115">B1</font></i></a>, <a class="ref" href="modelc_3.html#D38" target="_self" title="MODELC_3:def.38">DefSubatomic</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></div><b>end;</b></div>

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


</div>
