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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E58">Th30</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: NUMBER03:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( 10 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> 10</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 iff  ex <font color="Olive" title="b2">r</font>, <font color="Olive" title="b3">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">10 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">k</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">r</font> &amp; 10 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">r</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> 10</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp;  not  not <font color="Olive" title="b2">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  ...  &amp;  not <font color="Olive" title="b2">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 ) )</div></div>
