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<b>let </b><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">i1</font> be   <a href="int_1.html#NM1">Integer</a>;<br/>



<b>assume </b><a NAME="E1:2"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">k</font> <a href="radix_3.html#K3">-SD_Sub_S</a> 
 ;<br/>

<a NAME="E2:2"/>
<font color="Maroon">k</font> <a href="radix_3.html#K3">-SD_Sub_S</a>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">e</font> where <font color="Olive">e</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="mesfunc1.html#K2">INT</a>  : (  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">e</font> &amp; <font color="Olive">e</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="radix_3.html#D1">RADIX_3:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="mesfunc1.html#K2">INT</a> <b> such that </b><br/><a NAME="E4:2"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font>
 <b>and </b><br/><a NAME="E5:2"/><i><font color="Green">E33</font></i>: 
(  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E6:2"/>
( <font color="Maroon">i1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon">i1</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 )
 <b>by </b><i>, </i>;<br/>


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