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<b>let </b><font color="Maroon" title="c1">V</font> be    <a href="modelc_2.html#L1" title="MODELC_2:struct.1">LTLModelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">Kai</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a> ,the <a href="modelc_2.html#U2" title="MODELC_2:sel.2">BasicAssign</a> of <font color="Maroon" title="c1">V</font><br/> for <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">f2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font>  st <font color="Olive" title="b2">f1</font> <a href="modelc_2.html#R4" title="MODELC_2:pred.4">is-Evaluation-for</a> <font color="Olive" title="b1">Kai</font> &amp; <font color="Olive" title="b3">f2</font> <a href="modelc_2.html#R4" title="MODELC_2:pred.4">is-Evaluation-for</a> <font color="Olive" title="b1">Kai</font> holds <br/><font color="Olive" title="b2">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">f2</font></span><br/><b>let </b><font color="Maroon" title="c2">Kai</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a> ,the <a href="modelc_2.html#U2" title="MODELC_2:sel.2">BasicAssign</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font>  st <font color="Olive" title="b1">f1</font> <a href="modelc_2.html#R4" title="MODELC_2:pred.4">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font> &amp; <font color="Olive" title="b2">f2</font> <a href="modelc_2.html#R4" title="MODELC_2:pred.4">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font> holds <br/><font color="Olive" title="b1">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">f2</font></span><br/><b>let </b><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> ,the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">Assignations</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">f1</font> <a href="modelc_2.html#R4" title="MODELC_2:pred.4">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font> &amp; <font color="Maroon" title="c4">f2</font> <a href="modelc_2.html#R4" title="MODELC_2:pred.4">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font> implies <font color="Maroon" title="c3">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f2</font> )</span><br/>







<b>assume </b><b>that </b><br/><a NAME="E1:106"/><i><font color="Green" title="E87">A1</font></i>: 
<font color="Maroon" title="c3">f1</font> <a href="modelc_2.html#R4" title="MODELC_2:pred.4">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font>
 <b>and </b><br/><a NAME="E2:106"/><i><font color="Green" title="E88">A2</font></i>: 
<font color="Maroon" title="c4">f2</font> <a href="modelc_2.html#R4" title="MODELC_2:pred.4">is-Evaluation-for</a> <font color="Maroon" title="c2">Kai</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f2</font></span><br/>

<a NAME="E3:106"/>
for <font color="Olive" title="b1">H</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  holds <br/><font color="Maroon" title="c3">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">H</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>  implies <font color="Maroon" title="c3">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">H</font> )</span><br/>

<b>assume </b><a NAME="E1:106_1"/><i><font color="Green" title="E89">A3</font></i>: 
<font color="Maroon" title="c5">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">H</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c6">H</font> = <font color="Maroon" title="c5">H</font> as   <a href="modelc_2.html#NM2" title="MODELC_2:NM.2">LTL-formula</a> <b>by </b><i><a class="txt" href="modelc_2.html#E1:106_1"><i><font color="Green" title="E89">A3</font></i></a>, <a class="ref" href="modelc_2.html#T1" target="_self" title="MODELC_2:th.1">Th1</a></i>;<br/>
<b>set </b><font color="Maroon" title="c7">n</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font>;<br/>
<a NAME="E3:106_1"/>
( <font color="Maroon" title="c3">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c2">Kai</font> &amp; <font color="Maroon" title="c4">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c2">Kai</font> )
 
<b>by </b><i><a class="txt" href="modelc_2.html#E100"><i><font color="Green" title="E78">Lm26</font></i></a>, <a class="txt" href="modelc_2.html#E1:106"><i><font color="Green" title="E87">A1</font></i></a>, <a class="txt" href="modelc_2.html#E2:106"><i><font color="Green" title="E88">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:106_1"/>
<font color="Maroon" title="c3">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">H</font>
 <b>by </b><i><a class="txt" href="modelc_2.html#E101"><i><font color="Green" title="E79">Lm27</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>hence </b><a NAME="E4:106"/>
<font color="Maroon" title="c3">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18" title="FUNCT_2:th.18">FUNCT_2:18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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