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<b>let </b><font color="Maroon" title="c1">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">  <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#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="152_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:152_1"/>
 <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#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><b>then consider </b><font color="Maroon" title="c2">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:152_1"/><i><font color="Green" title="E122">B1</font></i>: 
<font color="Maroon" title="c2">y</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#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/><b>consider </b><font color="Maroon" title="c3">x</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E5:152_1"/>
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font>
 <b>and </b><br/><a NAME="E6:152_1"/><i><font color="Green" title="E123">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#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c1">v</font></span>)</span> &amp; <font color="Maroon" title="c3">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="#E3:152_1"><i><font color="Green" title="E122">B1</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c4">u</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E8:152_1"/><i><font color="Green" title="E124">B4</font></i>: 
( <font color="Maroon" title="c4">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#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c1">v</font></span>)</span> &amp; <font color="Maroon" title="c3">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="c4">u</font> )
 <b>by </b><i><a class="txt" href="#E6:152_1"><i><font color="Green" title="E123">B3</font></i></a></i>;<br/><b>thus </b><a NAME="E9:152_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E8:152_1"><i><font color="Green" title="E124">B4</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="E2:152"/>
 <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#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c1">v</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <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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