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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="E1:20"/><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/>

<a NAME="E2:20"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i/>;<br/>
<a NAME="E3:20"/>
<font color="Maroon">m</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="radix_6.html#E1:20"><i><font color="Green">E20</font></i></a></i>;<br/>
<a NAME="E4:20"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T10">FINSEQ_3:10</a></i>;<br/>
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2">SDMin</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">m</font>,<font color="Maroon">k</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K6" target="_self">Mmin</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> 0,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_6.html#E1:20"><i><font color="Green">E20</font></i></a>, <a class="txt" href="radix_6.html#E1"><i><font color="Green">Lemma18</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K6" target="_self">Mmin</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0
<b>by </b><i><a class="ref" href="radix_6.html#T1" target="_self">Th1</a>, <a class="ref" href="radix_5.html#T6">RADIX_5:6</a></i>
;<br/>
<b>then </b><span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K6" target="_self">Mmin</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K4">SDMax</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">m</font>,<font color="Maroon">k</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span></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#K8">SDDec</a> <span class="p3">(<span class="default"><a href="radix_5.html#K4">SDMax</a> <span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">m</font>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p3">(<span class="default"><a href="radix_5.html#K2">SDMin</a> <span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">m</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> 0,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_6.html#E1:20"><i><font color="Green">E20</font></i></a>, <a class="ref" href="radix_6.html#T1" target="_self">Th1</a>, , <a class="ref" href="radix_5.html#T17">RADIX_5:17</a></i>
;<br/>
<b>hence </b><a NAME="E7:20"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K2" target="_self">M0</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> 0,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K6" target="_self">Mmin</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K4">SDMax</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">m</font>,<font color="Maroon">k</font></span>)</span></span>)</span>
 ;<br/>


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