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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th19</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: RADIX_1:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i1</font>, <font color="Olive" title="b2">i2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/>  for <font color="Olive" title="b3">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 &amp; <font color="Olive" title="b1">i1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">k</font> <a href="radix_1.html#K3" title="RADIX_1:func.3">-SD</a>  &amp; <font color="Olive" title="b2">i2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">k</font> <a href="radix_1.html#K3" title="RADIX_1:func.3">-SD</a>  holds <br/>( <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Olive" title="b3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">i1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">i2</font></span>)</span>,<font color="Olive" title="b3">k</font>) &amp;  <a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">i1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">i2</font></span>)</span>,<font color="Olive" title="b3">k</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Olive" title="b3">k</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2 )</div></div>
