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<div><span class="kw">theorem </span><a NAME="T27"><span class="comment"><font color="firebrick">:: NUMBER03:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">k</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Olive" title="b2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b3">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b4">k</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">b</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b4">k</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="power.html#K2" title="POWER:func.2">to_power</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">a</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b4">k</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">b</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b4">k</font></span>)</span></span>)</span> <a href="power.html#K2" title="POWER:func.2">to_power</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b4">k</font></div></div>
