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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">Th2</font></span>: <a NAME="T2"><span class="comment"><font color="firebrick">:: RADIX_4:2</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</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 3 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">k</font> holds <br/> <a href="radix_3.html#K5" title="RADIX_3:func.5">SDSub_Add_Carry</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K5" title="RADIX_3:func.5">SDSub_Add_Carry</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">k</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5" title="RADIX_3:func.5">SDSub_Add_Carry</a> (<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">k</font>)</span>)</span></span>)</span>,<font color="Olive" title="b3">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> </div></div>
