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<b>set </b><font color="Maroon" title="c4">Old</font> = the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<b>set </b><font color="Maroon" title="c5">NewA</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<b>set </b><font color="Maroon" title="c6">NewB</font> = <span class="p1">(<span class="default"><a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font>;<br/>
<b>set </b><font color="Maroon" title="c7">NewC</font> = <span class="p1">(<span class="default">the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c8">NextD</font> = the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <font color="Maroon" title="c3">H</font></span>)</span>;<br/>
<a NAME="E1:17_1_1"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font>
 
<b>by </b><i><a class="txt" href="#E1:17"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c9">Old</font> = the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span> <b>by </b><i><a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">F</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E4:17_1_1"/><i><font color="Green" title="E19">A9</font></i>: 
<font color="Maroon" title="c3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">F</font>
 <b>and </b><br/><a NAME="E5:17_1_1"/><i><font color="Green" title="E20">A10</font></i>: 
<font color="Maroon" title="c10">F</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c1">v</font>
 <b>by </b><i><a class="txt" href="#E1:17"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="modelc_2.html#D24" title="MODELC_2:def.24">MODELC_2:def 24</a></i>;<br/>
<a NAME="E6:17_1_1"/><i><font color="Green" title="E21">A11</font></i>: 
 <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c3">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font>
 
<b>by </b><i><a class="txt" href="#E4:17_1_1"><i><font color="Green" title="E19">A9</font></i></a>, <a class="txt" href="#E5:17_1_1"><i><font color="Green" title="E20">A10</font></i></a>, <a class="ref" href="modelc_2.html#T46" title="MODELC_2:th.46">MODELC_2:46</a></i>;<br/>
<a NAME="E7:17_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c11">NewC</font> = <span class="p1">(<span class="default">the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font></span>)</span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span> <b>by </b><i><a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E9:17_1_1"/>
 <a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <font color="Maroon" title="c3">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font>
 
<b>by </b><i><a class="txt" href="#E6:17_1_1"><i><font color="Green" title="E21">A11</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c12">NextD</font> = the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <font color="Maroon" title="c3">H</font></span>)</span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span> <b>by </b><i><a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>
<b>set </b><font color="Maroon" title="c13">IT</font> =  <a href="modelc_3.html#G1" title="MODELC_3:aggr.1">LTLnode</a>(# <font color="Maroon" title="c9">Old</font>,<font color="Maroon" title="c11">NewC</font>,<font color="Maroon" title="c12">NextD</font> #);<br/>
<b>take </b>
 <a href="modelc_3.html#G1" title="MODELC_3:aggr.1">LTLnode</a>(# <font color="Maroon" title="c9">Old</font>,<font color="Maroon" title="c11">NewC</font>,<font color="Maroon" title="c12">NextD</font> #)
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <a href="modelc_3.html#G1" title="MODELC_3:aggr.1">LTLnode</a>(# <font color="Maroon" title="c9">Old</font>,<font color="Maroon" title="c11">NewC</font>,<font color="Maroon" title="c12">NextD</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <a href="modelc_3.html#G1" title="MODELC_3:aggr.1">LTLnode</a>(# <font color="Maroon" title="c9">Old</font>,<font color="Maroon" title="c11">NewC</font>,<font color="Maroon" title="c12">NextD</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font></span>)</span> &amp; the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <a href="modelc_3.html#G1" title="MODELC_3:aggr.1">LTLnode</a>(# <font color="Maroon" title="c9">Old</font>,<font color="Maroon" title="c11">NewC</font>,<font color="Maroon" title="c12">NextD</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <font color="Maroon" title="c3">H</font></span>)</span> )</span><br/>

<b>thus </b><a NAME="E11:17_1_1"/>
( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <a href="modelc_3.html#G1" title="MODELC_3:aggr.1">LTLnode</a>(# <font color="Maroon" title="c9">Old</font>,<font color="Maroon" title="c11">NewC</font>,<font color="Maroon" title="c12">NextD</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <a href="modelc_3.html#G1" title="MODELC_3:aggr.1">LTLnode</a>(# <font color="Maroon" title="c9">Old</font>,<font color="Maroon" title="c11">NewC</font>,<font color="Maroon" title="c12">NextD</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font></span>)</span> &amp; the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <a href="modelc_3.html#G1" title="MODELC_3:aggr.1">LTLnode</a>(# <font color="Maroon" title="c9">Old</font>,<font color="Maroon" title="c11">NewC</font>,<font color="Maroon" title="c12">NextD</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <font color="Maroon" title="c3">H</font></span>)</span> )
 ; <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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