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<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="binarith.html#NM1">Tuple</a> of 1,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="radix_1.html#K3">-SD</a> </span>)</span>;<br/>



<a NAME="E1:7"/><i><font color="Green">E29</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:7"/>
1 <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E3:7"/><b>then </b><i><font color="Green">E33</font></i>: 
1 <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<a NAME="E4:7"/><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><a href="radix_1.html#K7">DigitSD</a> <font color="Maroon">x</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K6">SubDigit</a> <font color="Maroon">x</font>,1,<font color="Maroon">k</font>
 
<b>by </b><i>, <a class="ref" href="radix_1.html#D6">RADIX_1:def 6</a></i>;<br/>
<a NAME="E5:7"/><i><font color="Green">E35</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7">DigitSD</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E6:7"/><b>then </b>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7">DigitSD</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E7:7"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><a href="radix_1.html#K7">DigitSD</a> <font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K6">SubDigit</a> <font color="Maroon">x</font>,1,<font color="Maroon">k</font>
 
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<b>thus </b> <a href="radix_1.html#K8">SDDec</a> <font color="Maroon">x</font> = 
 <a href="wsierp_1.html#K6">Sum</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7">DigitSD</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="radix_1.html#D7">RADIX_1:def 7</a></i>
<br/>.= 
 <a href="wsierp_1.html#K6">Sum</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K6">SubDigit</a> <font color="Maroon">x</font>,1,<font color="Maroon">k</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
<b>by </b><i>, , <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>
<br/>.= 
 <a href="radix_1.html#K6">SubDigit</a> <font color="Maroon">x</font>,1,<font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="rvsum_1.html#T103">RVSUM_1:103</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font></span>)</span> <a href="wsierp_1.html#K2">|^</a> 0</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_1.html#K5">DigB</a> <font color="Maroon">x</font>,1</span>)</span>
<b>by </b><i>, <a class="ref" href="radix_1.html#D5">RADIX_1:def 5</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_1.html#K5">DigB</a> <font color="Maroon">x</font>,1</span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T9">NEWTON:9</a></i>
<br/>.= 
 <a href="radix_1.html#K4">DigA</a> <font color="Maroon">x</font>,1
<b>by </b><i><a class="ref" href="radix_1.html#D4">RADIX_1:def 4</a></i>
;<br/>


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