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<b>let </b><font color="Maroon">x</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><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>assume </b><a NAME="E1:25"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2
 ;<br/>

<a NAME="E2:25"/><b>then </b>
<font color="Maroon">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E3:25"/><b>then </b>
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/>
<a NAME="E4:25"/><b>then </b>
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<a NAME="E5:25"/><b>then </b>
2 <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="ref" href="power.html#T40">POWER:40</a></i>;<br/>
<a NAME="E6:25"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="radix_1.html#K1">Radix</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
;<br/>
<a NAME="E7:25"/><b>then </b><i><font color="Green">E37</font></i>: 
<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 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="int_1.html#T79">INT_1:79</a></i>;<br/>
<a NAME="E8:25"/>
 <a href="radix_3.html#K5" target="_self">SDSub_Add_Carry</a> <font color="Maroon">x</font>,<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:25"/><b>then </b><i><font color="Green">E38</font></i>: 
 <a href="radix_3.html#K5" target="_self">SDSub_Add_Carry</a> <font color="Maroon">x</font>,<font color="Maroon">k</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>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E10:25"/><i><font color="Green">E41</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="radix_3.html#K5" target="_self">SDSub_Add_Carry</a> <font color="Maroon">x</font>,<font color="Maroon">k</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E11:25"/>
 <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>  <a href="xcmplx_0.html#K4">-</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/>
<a NAME="E12:25"/><b>then </b><i><font color="Green">E47</font></i>: 
 <a href="radix_3.html#K5" target="_self">SDSub_Add_Carry</a> <font color="Maroon">x</font>,<font color="Maroon">k</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>
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E13:25"/><i><font color="Green">E48</font></i>: 
 <a href="radix_3.html#K5" target="_self">SDSub_Add_Carry</a> <font color="Maroon">x</font>,<font color="Maroon">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="mesfunc1.html#K2">INT</a> 
 
<b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a></i>;<br/>
<b>thus </b><a NAME="E14:25"/>
 <a href="radix_3.html#K5" target="_self">SDSub_Add_Carry</a> <font color="Maroon">x</font>,<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">k</font> <a href="radix_3.html#K3" target="_self">-SD_Sub_S</a> 
 <b>by </b><i>, , </i>;<br/>


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