<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E25">Th17</font></span>: <a NAME="T17"><span class="comment"><font color="firebrick">:: INT_7:17</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">m</font> holds <br/> ex <font color="Olive" title="b3">m0</font>, <font color="Olive" title="b4">n0</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <br/>( <font color="Olive" title="b1">n</font> <a href="int_2.html#K2" title="INT_2:func.2">lcm</a> <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">n0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b3">m0</font> &amp; <font color="Olive" title="b4">n0</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Olive" title="b3">m0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b4">n0</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b3">m0</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Olive" title="b2">m</font> &amp; <font color="Olive" title="b4">n0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b3">m0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )</div></div>
