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<b>let </b><font color="Maroon" title="c1">n</font> be    <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> ;<br/><b>let </b><font color="Maroon" title="c2">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">A1</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c2">X</font>;<br/>





<b>reconsider </b><font color="Maroon" title="c4">Y</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Olive" title="b1">k</font></span>)</span> where <font color="Olive" title="b1">k</font> is    <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>  : <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> </span>}</span>  as   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c2">X</font> <b>by </b><i><a class="ref" href="setlim_1.html#T33" title="SETLIM_1:th.33">SETLIM_1:33</a></i>;<br/>
<span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c3">A1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font> = 
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c4">Y</font>
<b>by </b><i><a class="ref" href="setlim_1.html#D3" title="SETLIM_1:def.3">SETLIM_1:def 3</a></i>
<br/>.= 
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="kurato_2.html#K3" title="KURATO_2:func.3">^\</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="setlim_1.html#T10" title="SETLIM_1:th.10">SETLIM_1:10</a></i>
;<br/>
<b>hence </b><a NAME="E3:2"/>
<span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c3">A1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="prob_1.html#K2" title="PROB_1:func.2">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="kurato_2.html#K3" title="KURATO_2:func.3">^\</a> <font color="Maroon" title="c1">n</font></span>)</span>
 <b>by </b><i><a class="ref" href="card_3.html#D4" title="CARD_3:def.4">CARD_3:def 4</a></i>;<br/>


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