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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>assume </b><a NAME="E1:60"/>
<font color="Maroon" title="c2">A1</font> is <a href="prob_1.html#V2" title="PROB_1:attr.2">non-increasing</a>
 ;<br/>

<a NAME="E2:60"/><b>then </b>
for <font color="Olive" title="b1">n</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>  holds  <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#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">n</font>
 
<b>by </b><i><a class="ref" href="setlim_1.html#T54" target="_self" title="SETLIM_1:th.54">Th54</a></i>;<br/>
<b>hence </b><a NAME="E3:60"/>
 <a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">A1</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


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