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<b>let </b><font color="Maroon" title="c1">k</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">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font>;<br/><b>let </b><font color="Maroon" title="c4">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/>







<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">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>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="setlim_2.html#K6" title="SETLIM_2:func.6">(\/)</a> <font color="Maroon" title="c4">A1</font></span>)</span> <a href="kurato_2.html#K3" title="KURATO_2:func.3">^\</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">n</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="setlim_2.html#K6" title="SETLIM_2:func.6">(\/)</a> <font color="Maroon" title="c4">A1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">k</font></span>)</span>
<b>by </b><i><a class="ref" href="kurato_2.html#D2" title="KURATO_2:def.2">KURATO_2:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c3">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="setlim_2.html#D6" target="_self" title="SETLIM_2:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c3">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="kurato_2.html#K3" title="KURATO_2:func.3">^\</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span>
<b>by </b><i><a class="ref" href="kurato_2.html#D2" title="KURATO_2:def.2">KURATO_2:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="setlim_2.html#K6" title="SETLIM_2:func.6">(\/)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="kurato_2.html#K3" title="KURATO_2:func.3">^\</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">n</font>
<b>by </b><i><a class="ref" href="setlim_2.html#D6" target="_self" title="SETLIM_2:def.6">Def6</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:19"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="setlim_2.html#K6" title="SETLIM_2:func.6">(\/)</a> <font color="Maroon" title="c4">A1</font></span>)</span> <a href="kurato_2.html#K3" title="KURATO_2:func.3">^\</a> <font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="setlim_2.html#K6" title="SETLIM_2:func.6">(\/)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="kurato_2.html#K3" title="KURATO_2:func.3">^\</a> <font color="Maroon" title="c1">k</font></span>)</span>
 <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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