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<b>let </b><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>let </b><font color="Maroon">r</font> be   <a href="binarith.html#NM1">Tuple</a> of <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="radix_1.html#K3">-SD</a> </span>)</span>;<br/>



<b>assume </b><a NAME="E1:24"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">m</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 )
 ;<br/>

<b>set </b><font color="Maroon">MLow</font> =  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K6" target="_self">Mmin</a> <font color="Maroon">r</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">MHigh</font> =  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K4" target="_self">Mmax</a> <font color="Maroon">r</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">MZero</font> =  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">R</font> =  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_1_1"/>
(  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span> or  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1"><b>suppose </b></a><a NAME="E1:24_1_1_1"/>
 <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:24_1_1_1"/>
( (  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> &amp;  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K4" target="_self">Mmax</a> <font color="Maroon">r</font></span>)</span> ) or (  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K6" target="_self">Mmin</a> <font color="Maroon">r</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> &amp;  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span> ) )
 <b>by </b><i><a class="ref" href="radix_6.html#T1" target="_self">Th1</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_2"><b>suppose </b></a><a NAME="E1:24_1_1_2"/>
 <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:24_1_1_2"/>
( (  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> &amp;  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K4" target="_self">Mmax</a> <font color="Maroon">r</font></span>)</span> ) or (  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K6" target="_self">Mmin</a> <font color="Maroon">r</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> &amp;  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span> ) )
 <b>by </b><i><a class="ref" href="radix_6.html#T1" target="_self">Th1</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:24"/>
( (  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> &amp;  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K4" target="_self">Mmax</a> <font color="Maroon">r</font></span>)</span> ) or (  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K6" target="_self">Mmin</a> <font color="Maroon">r</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> &amp;  <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">r</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span> ) )
 ;<br/>


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