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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> ;<br/><b>let </b><font color="Maroon" title="c2">A1</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>set </b><font color="Maroon" title="c3">A2</font> =  <a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font>;<br/>
<a NAME="E1:70"/>
 <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K1" title="SETLIM_1:func.1">inferior_setsequence</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="prob_1.html#K4" title="PROB_1:func.4">Intersection</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="setlim_1.html#T59" target="_self" title="SETLIM_1:th.59">Th59</a></i>;<br/>
<a NAME="E2:70"/><b>then </b><i><font color="Green" title="E52">A1</font></i>: 
 <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#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="prob_1.html#K4" title="PROB_1:func.4">Intersection</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font></span>)</span>
 
;<br/>
<a NAME="E3:70"/>
 <a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font>
 
<b>by </b><i><a class="ref" href="setlim_1.html#T55" target="_self" title="SETLIM_1:th.55">Th55</a></i>;<br/>
<a NAME="E4:70"/><b>then </b><i><font color="Green" title="E53">A2</font></i>: 
 <a href="kurato_2.html#K5" title="KURATO_2:func.5">lim_sup</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="prob_1.html#K4" title="PROB_1:func.4">Intersection</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font></span>)</span>
 
;<br/>
<a NAME="E5:70"/><b>then </b>
 <a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font> is <a href="kurato_2.html#V3" title="KURATO_2:attr.3">convergent</a>
 
<b>by </b><i><a class="txt" href="setlim_1.html#E2:70"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="kurato_2.html#D7" title="KURATO_2:def.7">KURATO_2:def 7</a></i>;<br/>
<a NAME="E6:70"/><b>then </b>
 <a href="setlim_1.html#K3" title="SETLIM_1:func.3">lim</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="prob_1.html#K4" title="PROB_1:func.4">Intersection</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="setlim_1.html#E4:70"><i><font color="Green" title="E53">A2</font></i></a>, <a class="ref" href="setlim_1.html#D6" target="_self" title="SETLIM_1:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E7:70"/>
 <a href="kurato_2.html#K5" title="KURATO_2:func.5">lim_sup</a> <font color="Maroon" title="c2">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setlim_1.html#K3" title="SETLIM_1:func.3">lim</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font></span>)</span>
 ;<br/>


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