<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">b1</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">X</font>, <font color="Maroon">b2</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">X</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">b2</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">b1</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:13_1_1"/>
<font color="Maroon">b2</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b1</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">k</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#D13">POLYNOM1:def 13</a></i>;<br/><b>hence </b><a NAME="E2:13_1_1"/>
<font color="Maroon">b1</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="xxreal_0.html#K4">max</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="xxreal_0.html#D9">XXREAL_0:def 9</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:13_1"/>
 <a href="groeb_2.html#K2" target="_self">lcm</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b1</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:13"/>
( <font color="Maroon">b2</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">b1</font> iff  <a href="groeb_2.html#K2" target="_self">lcm</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b1</font> )
 <b>by </b><i/>;<br/>


</div>
