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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:27_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="27_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:27_1_1_1_1"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">n</font> <a href="newton.html#K6" title="NEWTON:func.6">choose</a> <font color="Maroon" title="c1">k</font> is  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a> </span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T5" title="INT_1:th.5">INT_1:5</a></span>;<br/><a NAME="E3:27_1_1_1_1"/>
<font color="Maroon" title="c2">n</font> <a href="newton.html#K6" title="NEWTON:func.6">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#K5" title="NEWTON:func.5">!</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#K5" title="NEWTON:func.5">!</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#K5" title="NEWTON:func.5">!</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_1_1_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="newton.html#D3" target="_self" title="NEWTON:def.3">Def3</a></span>;<br/><span class="kw">hence </span><a NAME="E4:27_1_1_1_1"/>
<font color="Maroon" title="c2">n</font> <a href="newton.html#K6" title="NEWTON:func.6">choose</a> <font color="Maroon" title="c1">k</font> is  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:27_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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">n</font> <a href="newton.html#K6" title="NEWTON:func.6">choose</a> <font color="Maroon" title="c1">k</font> is  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a> </span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:27_1_1_1_2"/>
<font color="Maroon" title="c2">n</font> <a href="newton.html#K6" title="NEWTON:func.6">choose</a> <font color="Maroon" title="c1">k</font> is  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#D3" target="_self" title="NEWTON:def.3">Def3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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