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<b>let </b><font color="Maroon" title="c1">w</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</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">v</font> being <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st <font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Olive" title="b1">v</font> holds <br/><font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Olive" title="b1">v</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">v</font> be  <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> <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">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">v</font> implies <font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c2">v</font></span>)</span> )</span><br/>



<b>assume </b><a NAME="E1:154"/><i><font color="Green" title="E123">A1</font></i>: 
<font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c2">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="c1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c2">v</font></span>)</span></span><br/>

<b>set </b><font color="Maroon" title="c3">N</font> =  <a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c2">v</font>;<br/>
<a NAME="E2:154"/>
for <font color="Olive" title="b1">H</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</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#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K8" title="MODELC_3:func.8">Seed</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span> holds <br/><font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Olive" title="b1">H</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="154_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">H</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="c4">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K8" title="MODELC_3:func.8">Seed</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span> implies <font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c4">H</font> )</span><br/>

<b>assume </b><a NAME="E1:154_1"/><i><font color="Green" title="E124">B1</font></i>: 
<font color="Maroon" title="c4">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K8" title="MODELC_3:func.8">Seed</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c4">H</font></span><br/>

<b>consider </b><font color="Maroon" title="c5">x</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E3:154_1"/><i><font color="Green" title="E125">B2</font></i>: 
<font color="Maroon" title="c4">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font>
 <b>and </b><br/><a NAME="E4:154_1"/><i><font color="Green" title="E126">B3</font></i>: 
 ex <font color="Olive" title="b1">u</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K8" title="MODELC_3:func.8">Seed</a> <font color="Maroon" title="c2">v</font></span>)</span> &amp; <font color="Maroon" title="c5">x</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="Olive" title="b1">u</font> )
 <b>by </b><i><a class="txt" href="#E1:154_1"><i><font color="Green" title="E124">B1</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">u</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E6:154_1"/><i><font color="Green" title="E127">B4</font></i>: 
( <font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K8" title="MODELC_3:func.8">Seed</a> <font color="Maroon" title="c2">v</font></span>)</span> &amp; <font color="Maroon" title="c5">x</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="c6">u</font> )
 <b>by </b><i><a class="txt" href="#E4:154_1"><i><font color="Green" title="E126">B3</font></i></a></i>;<br/>
<b>thus </b><a NAME="E7:154_1"/>
<font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c4">H</font>
 <b>by </b><i><a class="txt" href="#E6:154_1"><i><font color="Green" title="E127">B4</font></i></a>, <a class="txt" href="#E3:154_1"><i><font color="Green" title="E125">B2</font></i></a>, <a class="txt" href="#E1:154"><i><font color="Green" title="E123">A1</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</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="E3:154"/>
<font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c2">v</font></span>)</span>
 <b>by </b><i><a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</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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