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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> <a href="modelc_2.html#R3" title="MODELC_2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">F</font> implies  ex <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#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font> )</span><br/>



<b>assume </b><a NAME="E1:68"/>
<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="c2">F</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="modelc_2.html#D23" target="_self" title="MODELC_2:def.23">MODELC_2:def 23</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c1">H</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">F</font> 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 <font color="Olive" title="b1">G</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font> )</span><br/>

<b>then consider </b><font color="Maroon" title="c3">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>, <font color="Maroon" title="c4">L</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E3:68"/><i><font color="Green" title="E66">A1</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">n</font> &amp; <font color="Maroon" title="c4">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> &amp; <font color="Maroon" title="c4">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> )
 <b>and </b><br/><a NAME="E4:68"/><i><font color="Green" title="E67">A2</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">n</font> holds <br/> ex <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">F1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Maroon" title="c4">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H1</font> &amp; <font color="Maroon" title="c4">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">F1</font> &amp; <font color="Olive" title="b2">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Olive" title="b3">F1</font> )
 <b>by </b><i><a class="ref" href="modelc_2.html#D22" target="_self" title="MODELC_2:def.22">Def101</a></i>;<br/>
<b>assume </b><a NAME="E5:68"/>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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">  ex <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#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font></span><br/>

<a NAME="E6:68"/><b>then </b>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">n</font>
 
<b>by </b><i><a class="txt" href="#E3:68"><i><font color="Green" title="E66">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>
<a NAME="E7:68"/><b>then </b>
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">n</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E9:68"/><i><font color="Green" title="E68">A3</font></i>: 
<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T10" title="NAT_1:th.10">NAT_1:10</a></i>;<br/>
<a NAME="E10:68"/>
<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
;<br/>
<a NAME="E11:68"/><b>then </b>
( 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">n</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font> )
 
<b>by </b><i><a class="txt" href="#E9:68"><i><font color="Green" title="E68">A3</font></i></a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">H1</font>, <font color="Maroon" title="c7">F1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E13:68"/><i><font color="Green" title="E69">A4</font></i>: 
( <font color="Maroon" title="c4">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">H1</font> &amp; <font color="Maroon" title="c4">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F1</font> &amp; <font color="Maroon" title="c6">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c7">F1</font> )
 <b>by </b><i><a class="txt" href="#E4:68"><i><font color="Green" title="E67">A2</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">H1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font></span><br/>

<b>thus </b><a NAME="E14:68"/>
<font color="Maroon" title="c6">H1</font> <a href="modelc_2.html#R1" title="MODELC_2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">F</font>
 <b>by </b><i><a class="txt" href="#E3:68"><i><font color="Green" title="E66">A1</font></i></a>, <a class="txt" href="#E9:68"><i><font color="Green" title="E68">A3</font></i></a>, <a class="txt" href="#E13:68"><i><font color="Green" title="E69">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/>


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