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<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">r</font> be   <a href="binarith.html#NM1" title="BINARITH:NM.1">Tuple</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="radix_1.html#K3" title="RADIX_1:func.3">-SD</a> </span>)</span>;<br/>



<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E20">A1</font></i>: 
( <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Maroon" title="c2">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 )
 ;<br/>

<a NAME="E2:20"/><b>then </b><i><font color="Green" title="E21">A2</font></i>: 
<font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="radix_6.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E3:20"/><i><font color="Green" title="E22">A3</font></i>: 
<font color="Maroon" title="c1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="radix_6.html#E1:20"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="finseq_3.html#T10" title="FINSEQ_3:th.10">FINSEQ_3:10</a></i>;<br/>
<span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K2" title="RADIX_6:func.2">M0</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K6" title="RADIX_6:func.6">Mmin</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 0,<span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_6.html#E1:20"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="radix_6.html#T11" target="_self" title="RADIX_6:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K6" title="RADIX_6:func.6">Mmin</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 0
<b>by </b><i><a class="txt" href="radix_6.html#E2:20"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="radix_5.html#T6" title="RADIX_5:th.6">RADIX_5:6</a></i>
;<br/>
<b>then </b><span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K6" title="RADIX_6:func.6">Mmin</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K2" title="RADIX_6:func.2">M0</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p3">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p3">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K2" title="RADIX_6:func.2">M0</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 0,<span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_6.html#E1:20"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="radix_6.html#E2:20"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="radix_6.html#E3:20"><i><font color="Green" title="E22">A3</font></i></a>, <a class="ref" href="radix_5.html#T17" title="RADIX_5:th.17">RADIX_5:17</a></i>
;<br/>
<b>hence </b><a NAME="E6:20"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K2" title="RADIX_6:func.2">M0</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 0,<span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K6" title="RADIX_6:func.6">Mmin</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>
 ;<br/>


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