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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">m</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">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>assume </b><a NAME="E1:36"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">k</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 &amp; <font color="Maroon">m</font> <a href="radix_1.html#R1" target="_self">is_represented_by</a> 1,<font color="Maroon">k</font> &amp; <font color="Maroon">n</font> <a href="radix_1.html#R1" target="_self">is_represented_by</a> 1,<font color="Maroon">k</font> )
 ;<br/>

<b>then </b> <a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">m</font>,1,<font color="Maroon">k</font></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">n</font>,1,<font color="Maroon">k</font></span>)</span>,1</span>)</span></span>)</span> = 
 <a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">n</font>,1,<font color="Maroon">k</font></span>)</span>,1</span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i>, </i>
;<br/>
<b>hence </b><a NAME="E3:36"/>
 <a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">m</font>,1,<font color="Maroon">k</font></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">n</font>,1,<font color="Maroon">k</font></span>)</span>,1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 ;<br/>


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