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<b>let </b><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">b</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>assume </b><a NAME="E1:10"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_1"/>
( <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or <font color="Maroon" title="c1">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1"><b>suppose </b></a><a NAME="E1:10_1_1"/>
<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:10_1_1"/><b>then </b>
 <a href="numeral1.html#K2" title="NUMERAL1:func.2">digits</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">&lt;%</a><span class="default">0</span><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">%&gt;</a></span>
 <b>by </b><i><a class="txt" href="numeral1.html#E1:10"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="numeral1.html#D2" target="_self" title="NUMERAL1:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E3:10_1_1"/>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="numeral1.html#K2" title="NUMERAL1:func.2">digits</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="afinsq_1.html#T37" title="AFINSQ_1:th.37">AFINSQ_1:37</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_2"><b>suppose </b></a><a NAME="E1:10_1_2"/>
<font color="Maroon" title="c1">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:10_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="numeral1.html#K2" title="NUMERAL1:func.2">digits</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="stirl2_1.html#K8" title="STIRL2_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="numeral1.html#K2" title="NUMERAL1:func.2">digits</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="numeral1.html#E1:10"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="numeral1.html#D2" target="_self" title="NUMERAL1:def.2">Def2</a></i>;<br/><a NAME="E3:10_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="numeral1.html#K2" title="NUMERAL1:func.2">digits</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="numeral1.html#K2" title="NUMERAL1:func.2">digits</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_1.html#D4" title="FUNCT_1:def.4">FUNCT_1:def 4</a></i>;<br/><a NAME="E4:10_1_2"/><b>then </b>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="numeral1.html#K2" title="NUMERAL1:func.2">digits</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 <b>by </b><i><a class="ref" href="afinsq_1.html#D1" title="AFINSQ_1:def.1">AFINSQ_1:def 1</a></i>;<br/><b>hence </b><a NAME="E5:10_1_2"/>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="numeral1.html#K2" title="NUMERAL1:func.2">digits</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T14" title="NAT_1:th.14">NAT_1:14</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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