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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#NM2" title="MODELC_2:NM.2">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> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> iff <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> )</span><br/>



<b>thus </b><a NAME="E1:49"/>
( <font color="Maroon" title="c1">H</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> implies <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"> ( <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> implies <font color="Maroon" title="c1">H</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:49_1"/>
<font color="Maroon" title="c1">H</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</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"> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font></span><br/>

<a NAME="E2:49_1"/><b>then </b><i><font color="Green" title="E49">A1</font></i>: 
(  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</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="c1">H</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c1">H</font> or  ex <font color="Olive" title="b1">H1</font> being  <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a> st <br/>(  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Olive" title="b1">H1</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c1">H</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Olive" title="b1">H1</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c1">H</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Olive" title="b1">H1</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c1">H</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Olive" title="b1">H1</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c1">H</font> ) )
 
<b>by </b><i><a class="ref" href="modelc_2.html#D21" target="_self" title="MODELC_2:def.21">Def100</a></i>;<br/>
<div><i><font color="Green" title="E50">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:49_1_1"/><i><font color="Green" title="E51">A3</font></i>: 
 <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</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="c1">H</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:49_1_1"/>
( <span class="p1">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <span class="p1">(<span class="default"><a href="modelc_2.html#K3" title="MODELC_2:func.3">'not'</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="modelc_2.html#T12" target="_self" title="MODELC_2:th.12">Th100</a></i>;<br/><b>hence </b><a NAME="E3:49_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="modelc_2.html#E1:49_1_1"><i><font color="Green" title="E51">A3</font></i></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><i><font color="Green" title="E51">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_2"><b>now </b></a><div class="add"><b>given </b><font color="Maroon" title="c3">H1</font> being   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a><b> such that </b><a NAME="E2:49_1_2"/><i><font color="Green" title="E52">A5</font></i>: 
(  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c3">H1</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c1">H</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c3">H1</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H1</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c1">H</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c3">H1</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c1">H</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c3">H1</font> or  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</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"> contradiction</span><br/><a NAME="E3:49_1_2"/>
( <span class="p1">(<span class="default"><a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">H</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="modelc_2.html#K4" title="MODELC_2:func.4">'&amp;'</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">H</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">H</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">H</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="modelc_2.html#K8" title="MODELC_2:func.8">'R'</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 )
 <b>by </b><i><a class="ref" href="modelc_2.html#T12" target="_self" title="MODELC_2:th.12">Th100</a></i>;<br/><b>hence </b><a NAME="E4:49_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:49_1_2"><i><font color="Green" title="E52">A5</font></i></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>thus </b><a NAME="E5:49_1"/>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E2:49_1"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="modelc_2.html#E3:49_1"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="finseq_1.html#T46" title="FINSEQ_1:th.46">FINSEQ_1:46</a>, <a class="txt" href="modelc_2.html#E4:49_1"><i><font color="Green" title="E51">A4</font></i></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>thus </b><a NAME="E2:49"/>
( <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> implies <font color="Maroon" title="c1">H</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">F</font> )
 <b>by </b><i><a class="ref" href="modelc_2.html#D21" target="_self" title="MODELC_2:def.21">Def100</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>
