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

<b>let </b><font color="Maroon">n</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">b1</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b2</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b3</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>;<br/>



<b>assume </b><a NAME="E1:46"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">b1</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">b2</font> &amp; <font color="Maroon">b2</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">b3</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_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="E1:46_1"/>
( <font color="Maroon">b1</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b2</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">k</font> &amp; <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">b3</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">k</font> )
 <b>by </b><i><a class="ref" href="groeb_1.html#T1" target="_self">Th1</a>, <a class="ref" href="polynom1.html#D13">POLYNOM1:def 13</a></i>;<br/><b>hence </b><a NAME="E2:46_1"/>
<font color="Maroon">b1</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b3</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:46"/>
<font color="Maroon">b1</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">b3</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D13">POLYNOM1:def 13</a></i>;<br/>


</div>
