<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">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"> for <font color="Olive" title="b1">W</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K13" title="MODELC_2:func.13">Subformulae</a> <font color="Maroon" title="c1">H</font></span>)</span>  st  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Olive" title="b1">W</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 holds <br/><font color="Olive" title="b1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c1">H</font></span><br/><b>let </b><font color="Maroon" title="c2">W</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K13" title="MODELC_2:func.13">Subformulae</a> <font color="Maroon" title="c1">H</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c2">W</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 implies <font color="Maroon" title="c2">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c1">H</font> )</span><br/>



<b>assume </b><a NAME="E1:67"/><i><font color="Green" title="E57">A1</font></i>: 
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c2">W</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c1">H</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_1"/>
<font color="Maroon" title="c2">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="modelc_3.html#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c1">H</font>
 ; <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="c3">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:67_1"/><i><font color="Green" title="E58">B1</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/><a NAME="E4:67_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="#E3:67_1"><i><font color="Green" title="E58">B1</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c4">x</font> = <font color="Maroon" title="c3">x</font> as   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> <b>by </b><i><a class="ref" href="modelc_2.html#T1" title="MODELC_2:th.1">MODELC_2:1</a></i>;<br/><b>set </b><font color="Maroon" title="c5">X</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/><a NAME="E6:67_1"/><i><font color="Green" title="E59">B2</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">W</font>
 <b>by </b><i><a class="txt" href="#E3:67_1"><i><font color="Green" title="E58">B1</font></i></a>, <a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/><a NAME="E7:67_1"/>
<font color="Maroon" title="c4">x</font> <a href="modelc_2.html#R2" title="MODELC_2:pred.2">is_subformula_of</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="#E3:67_1"><i><font color="Green" title="E58">B1</font></i></a>, <a class="ref" href="modelc_2.html#T45" title="MODELC_2:th.45">MODELC_2:45</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c6">X</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">x</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">H</font></span>)</span> <b>by </b><i><a class="txt" href="modelc_3.html#E9"><i><font color="Green" title="E9">Lem104</font></i></a></i>;<br/><a NAME="E9:67_1"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c6">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">x</font>
 <b>by </b><i><a class="ref" href="modelc_3.html#T14" target="_self" title="MODELC_3:th.14">Thlen11</a></i>;<br/><a NAME="E10:67_1"/><b>then </b><i><font color="Green" title="E60">B3</font></i>: 
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c6">X</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="modelc_2.html#T3" title="MODELC_2:th.3">MODELC_2:3</a></i>;<br/><a NAME="E11:67_1"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c6">X</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c2">W</font>
 <b>by </b><i><a class="txt" href="#E6:67_1"><i><font color="Green" title="E59">B2</font></i></a>, <a class="ref" href="modelc_3.html#T15" target="_self" title="MODELC_3:th.15">Thlen12</a></i>;<br/><b>hence </b><a NAME="E12:67_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E10:67_1"><i><font color="Green" title="E60">B3</font></i></a>, <a class="txt" href="#E1:67"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</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="E3:67"/>
<font color="Maroon" title="c2">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c1">H</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
