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<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#K5" title="KURATO_2:func.5">lim_sup</a> <font color="Olive" title="b2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K4" title="KURATO_2:func.4">lim_inf</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K7" title="SETLIM_1:func.7">@Complement</a> <font color="Olive" title="b2">S</font></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </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#K5" title="KURATO_2:func.5">lim_sup</a> <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K4" title="KURATO_2:func.4">lim_inf</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K7" title="SETLIM_1:func.7">@Complement</a> <font color="Olive" title="b1">S</font></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </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#K5" title="KURATO_2:func.5">lim_sup</a> <font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K4" title="KURATO_2:func.4">lim_inf</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K7" title="SETLIM_1:func.7">@Complement</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span><br/>





 <a href="kurato_2.html#K4" title="KURATO_2:func.4">lim_inf</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K7" title="SETLIM_1:func.7">@Complement</a> <font color="Maroon" title="c3">S</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="kurato_2.html#K5" title="KURATO_2:func.5">lim_sup</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K7" title="SETLIM_1:func.7">@Complement</a> <span class="p3">(<span class="default"><a href="setlim_1.html#K7" title="SETLIM_1:func.7">@Complement</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
<b>by </b><i><a class="ref" href="setlim_1.html#T71" target="_self" title="SETLIM_1:th.71">Th205</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="kurato_2.html#K5" title="KURATO_2:func.5">lim_sup</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 

;<br/>
<b>hence </b><a NAME="E2:82"/>
 <a href="kurato_2.html#K5" title="KURATO_2:func.5">lim_sup</a> <font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K4" title="KURATO_2:func.4">lim_inf</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K7" title="SETLIM_1:func.7">@Complement</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</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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