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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">r</font> being  <a href="finseq_2.html#NM4" title="FINSEQ_2:NM.4">Tuple</a> of <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2,<font color="Maroon" title="c2">k</font> <a href="radix_1.html#K3" title="RADIX_1:func.3">-SD</a>   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/><span class="kw">let </span><font color="Maroon" title="c3">r</font> be   <a href="finseq_2.html#NM4" title="FINSEQ_2:NM.4">Tuple</a> of <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2,<font color="Maroon" title="c2">k</font> <a href="radix_1.html#K3" title="RADIX_1:func.3">-SD</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:28"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <span class="kw">and </span><br/><a NAME="E2:28"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E3:28"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
<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
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="radix_6.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="radix_6.html#T17" target="_self" title="RADIX_6:th.17">Th17</a></span>
<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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="radix_5.html#T6" title="RADIX_5:th.6">RADIX_5:6</a></span>
;<br/>
<a NAME="E5:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A4</font></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#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/>
<span class="kw">assume </span><a NAME="E6:28"/>
 <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="kw">hence </span><a NAME="E7:28"/>
 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:28"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="xreal_1.html#T49" title="XREAL_1:th.49">XREAL_1:49</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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