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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E16">Def3</font></span>   defines <a href="radix_3.html#K5" title="RADIX_3:func.5">SDSub_Add_Carry</a> <a onclick="hs(this)" href="javascript:()">RADIX_3:def 3 : <br/></a><span> for <font color="Olive" title="b1">x</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/>  for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( (  <a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">x</font> implies  <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="b2">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Olive" title="b1">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> implies  <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="b2">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 ) &amp; (  not  <a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">x</font> &amp;  not <font color="Olive" title="b1">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> implies  <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="b2">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) );<br/></span></div>
