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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:26"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font> )
 ;<br/>

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E2:26"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 ;<br/>

<a NAME="E3:26"/><b>then </b><i><font color="Green">E23</font></i>: 
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a</font> =  <a href="radix_5.html#K1" target="_self">SDMinDigit</a> <font color="Maroon">m</font>,<font color="Maroon">k</font>,<font color="Maroon">i</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="mesfunc1.html#K2">INT</a>  ;<br/>
<b>reconsider </b><font color="Maroon">b</font> =  <a href="radix_5.html#K3" target="_self">SDMaxDigit</a> <font color="Maroon">m</font>,<font color="Maroon">k</font>,<font color="Maroon">i</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="mesfunc1.html#K2">INT</a>  ;<br/>
<a NAME="E6:26"/><i><font color="Green">E30</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">n</font>,<font color="Maroon">m</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="radix_5.html#K1" target="_self">SDMinDigit</a> <font color="Maroon">m</font>,<font color="Maroon">k</font>,<font color="Maroon">i</font>
 
<b>by </b><i><a class="ref" href="radix_5.html#T2" target="_self">Th2</a>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_1_1"/>
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font> or <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">m</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_1_1"><b>suppose </b></a><a NAME="E1:26_1_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font>
 ;<br/><div class="add"><b>then </b><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font>
<b>by </b><i><a class="txt" href="radix_5.html#E3:26"><i><font color="Green">E23</font></i></a>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E3:26"><i><font color="Green">E23</font></i></a>, , <a class="ref" href="radix_5.html#T3" target="_self">Th3</a>, </i>
<br/>.= 
0

;<br/><b>hence </b><a NAME="E3:26_1_1_1"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">n</font>,<font color="Maroon">m</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">n</font>,<font color="Maroon">m</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="radix_5.html#T2" target="_self">Th2</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_1_2"><b>suppose </b></a><a NAME="E1:26_1_1_2"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">m</font>
 ;<br/><div class="add"><b>then </b><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font> = 
0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font>
<b>by </b><i><a class="txt" href="radix_5.html#E3:26"><i><font color="Green">E23</font></i></a>, </i>
<br/>.= 
0 <a href="nat_1.html#K1">+</a> 0
<b>by </b><i><a class="txt" href="radix_5.html#E3:26"><i><font color="Green">E23</font></i></a>, <a class="ref" href="radix_5.html#T3" target="_self">Th3</a>, </i>
;<br/><b>hence </b><a NAME="E3:26_1_1_2"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">n</font>,<font color="Maroon">m</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">n</font>,<font color="Maroon">m</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="radix_5.html#T2" target="_self">Th2</a>, , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E8:26"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">n</font>,<font color="Maroon">m</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">n</font>,<font color="Maroon">m</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/>


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