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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:9_1_1_1"/>
( <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1_1_1_1"><b>suppose </b></a><a NAME="E1:9_1_1_1_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">n</font>;<br/><b>thus </b><a NAME="E2:9_1_1_1_1"/>
<font color="Maroon">k</font> is <a href="ordinal1.html#V7">natural</a>
 <b>by </b><i>, <a class="ref" href="subset_1.html#D2">SUBSET_1:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1_1_1_2"><b>suppose </b></a><a NAME="E1:9_1_1_1_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">n</font>;<br/><a NAME="E2:9_1_1_1_2"/>
( <font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</font> is   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a>  )
 <b>by </b><i>, </i>;<br/><a NAME="E3:9_1_1_1_2"/><b>then </b>
<font color="Maroon">k</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> 
 ;<br/><b>hence </b><a NAME="E4:9_1_1_1_2"/>
<font color="Maroon">k</font> is <a href="ordinal1.html#V7">natural</a>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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