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<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">r</font> being  <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>  st <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 &amp;  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K8" title="RADIX_6:func.8">Mmask</a> <font color="Olive" title="b1">r</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K2" title="RADIX_6:func.2">M0</a> <font color="Olive" title="b1">r</font></span>)</span></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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 &amp;  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K8" title="RADIX_6:func.8">Mmask</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <font color="Maroon" title="c3">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<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><br/>



<b>assume </b><a NAME="E1:28"/><i><font color="Green" title="E24">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 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K8" title="RADIX_6:func.8">Mmask</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <font color="Maroon" title="c3">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<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><br/>

<a NAME="E2:28"/><b>then </b><i><font color="Green" title="E25">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/>
<b>assume </b><a NAME="E3:28"/><i><font color="Green" title="E26">A3</font></i>: 
 <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K8" title="RADIX_6:func.8">Mmask</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <font color="Maroon" title="c3">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<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><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_6.html#K8" title="RADIX_6:func.8">Mmask</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <font color="Maroon" title="c3">r</font></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> <a href="numbers.html#K6" title="NUMBERS:func.6">0</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="c2">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:28"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="radix_6.html#T17" target="_self" title="RADIX_6:th.17">Th17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="#E2:28"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="radix_5.html#T6" title="RADIX_5:th.6">RADIX_5:6</a></i>
;<br/>
<a NAME="E5:28"/><b>then </b>
<span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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#K2" title="RADIX_6:func.2">M0</a> <font color="Maroon" title="c3">r</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#K8" title="RADIX_6:func.8">Mmask</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
;<br/>
<b>hence </b><a NAME="E6:28"/>
 <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <font color="Maroon" title="c3">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<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>
 <b>by </b><i><a class="txt" href="#E3:28"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="xreal_1.html#T49" title="XREAL_1:th.49">XREAL_1:49</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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