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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="modelc_2.html#NM3" title="MODELC_2:NM.3">LTLModel</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#U1" title="MODELC_2:sel.1">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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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/><span class="kw">let </span><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#U1" title="MODELC_2:sel.1">BasicAssign</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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/><span class="kw">let </span><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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>







<span class="kw">assume </span><a NAME="E1:107"/><span class="lab"><font color="Green" title="E74">A1</font></span>: 
( <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> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E2:107"/>
 for <font color="Olive" title="b1">H</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="107_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">H</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E1:107_1"/>
<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">H</font> = <font color="Maroon" title="c5">H</font> as   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T1" target="_self" onmouseover="rs('modelc_2/T1')" onmouseout="rh()">Th1</a></span>;<br/>
<span class="kw">set </span><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="E3:107_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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:107"><span class="lab"><font color="Green" title="E74">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:107_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_2.html#E102"><span class="lab"><font color="Green" title="E66">Lm24</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="E3:107"/>
<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 class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T12" onmouseover="rs('funct_2/T12')" onmouseout="rh()">FUNCT_2:12</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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