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

<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">Si</font> being  <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">S</font> being   <a href="prob_1.html#M1" title="PROB_1:mode.1">SetSequence</a> of <font color="Olive" title="b1">Si</font> holds   <a href="kurato_2.html#K4" title="KURATO_2:func.4">lim_sup</a> <font color="Olive" title="b2">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <font color="Olive" title="b2">S</font></span><br/><b>let </b><font color="Maroon" title="c2">Si</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font>; <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">S</font> being   <a href="prob_1.html#M1" title="PROB_1:mode.1">SetSequence</a> of <font color="Maroon" title="c2">Si</font> holds   <a href="kurato_2.html#K4" title="KURATO_2:func.4">lim_sup</a> <font color="Olive" title="b1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <font color="Olive" title="b1">S</font></span><br/><b>let </b><font color="Maroon" title="c3">S</font> be    <a href="prob_1.html#M1" title="PROB_1:mode.1">SetSequence</a> of <font color="Maroon" title="c2">Si</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="kurato_2.html#K4" title="KURATO_2:func.4">lim_sup</a> <font color="Maroon" title="c3">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <font color="Maroon" title="c3">S</font></span><br/><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_2.html#K4" title="KURATO_2:func.4">lim_sup</a> <font color="Maroon" title="c3">S</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <font color="Maroon" title="c3">S</font> )</span><br/>







<b>assume </b><a NAME="E1:77"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_2.html#K4" title="KURATO_2:func.4">lim_sup</a> <font color="Maroon" title="c3">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <font color="Maroon" title="c3">S</font></span><br/>

<b>then consider </b><font color="Maroon" title="c5">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:77"/><i><font color="Green" title="E56">B</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="setlim_1.html#T66" target="_self" title="SETLIM_1:th.66">Th55</a></i>;<br/>
<b>thus </b><a NAME="E4:77"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <font color="Maroon" title="c3">S</font>
 <b>by </b><i><a class="txt" href="#E3:77"><i><font color="Green" title="E56">B</font></i></a>, <a class="ref" href="prob_1.html#T25" title="PROB_1:th.25">PROB_1:25</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>
