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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1_1_1"/>
( <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c1">k</font> or <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">k</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_1_1"><b>suppose </b></a><a NAME="E1:29_1_1_1_1"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c1">k</font>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c3">l</font> = <font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">k</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T18" title="INT_1:th.18">INT_1:18</a></i>;<br/><a NAME="E3:29_1_1_1_1"/>
<font color="Maroon" title="c2">n</font> <a href="newton.html#K7" title="NEWTON:func.7">choose</a> <font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K6" title="NEWTON:func.6">!</a> </span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="newton.html#K6" title="NEWTON:func.6">!</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="newton.html#K6" title="NEWTON:func.6">!</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="newton.html#E1:29_1_1_1_1"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="newton.html#D3" target="_self" title="NEWTON:def.3">Def3</a></i>;<br/><b>hence </b><a NAME="E4:29_1_1_1_1"/>
<font color="Maroon" title="c2">n</font> <a href="newton.html#K7" title="NEWTON:func.7">choose</a> <font color="Maroon" title="c1">k</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_1_2"><b>suppose </b></a><a NAME="E1:29_1_1_1_2"/>
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">k</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:29_1_1_1_2"/>
<font color="Maroon" title="c2">n</font> <a href="newton.html#K7" title="NEWTON:func.7">choose</a> <font color="Maroon" title="c1">k</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>
 <b>by </b><i><a class="ref" href="newton.html#D3" target="_self" title="NEWTON:def.3">Def3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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