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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E31">Def10</font></span>   defines <a href="number14.html#K4" title="NUMBER14:func.4">numberR0</a> <a onclick="hs(this)" href="javascript:()">NUMBER14:def 10 : <br/></a><span> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> holds <br/> ( ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="number14.html#R5" title="NUMBER14:pred.5">give_three_different_remainders_upon_dividing_by</a> 3 implies  <a href="number14.html#K4" title="NUMBER14:func.4">numberR0</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) &amp; ( ( <font color="Olive" title="b1">a</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 3 or <font color="Olive" title="b1">a</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 3 ) implies  <a href="number14.html#K4" title="NUMBER14:func.4">numberR0</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 3</span>)</span> ) &amp; ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="number14.html#R5" title="NUMBER14:pred.5">give_three_different_remainders_upon_dividing_by</a> 3 or <font color="Olive" title="b1">a</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 3 or <font color="Olive" title="b1">a</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 3 or  <a href="number14.html#K4" title="NUMBER14:func.4">numberR0</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 3</span>)</span> ) );<br/></span></div>
