<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E32">Th61</font></span>: <a NAME="T61"><span class="comment"><font color="firebrick">:: NAT_D:61</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">k</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> holds <br/> ( ( <font color="Olive" title="b1">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">k</font></span>)</span></span>)</span> <a href="int_1.html#K4" title="INT_1:func.4">div</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="int_1.html#K4" title="INT_1:func.4">div</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b3">k</font> ) &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">k</font></span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b1">n</font> )</div></div>
