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

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



<b>assume </b><b>that </b><br/><a NAME="E1:125"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">b1</font> <a href="polynom1.html#R3" target="_self">divides</a> <font color="Maroon">b2</font>
 <b>and </b><br/><a NAME="E2:125"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">b2</font> <a href="polynom1.html#K10" target="_self">-'</a> <font color="Maroon">b1</font> <a href="pboole.html#R6">=</a>  <a href="polynom1.html#K16" target="_self">EmptyBag</a> <font color="Maroon">n</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="125_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/><b>assume </b><a NAME="E1:125_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">n</font>
 ;<br/><a NAME="E2:125_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">b1</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b2</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font>
 <b>by </b><i>, </i>;<br/>0 = 
<span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K10" target="_self">-'</a> <font color="Maroon">b1</font></span>)</span> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i/>
;<br/><a NAME="E4:125_1"/><b>then </b>
<font color="Maroon">b2</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b1</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="binarith.html#T54">BINARITH:54</a></i>;<br/><b>hence </b><a NAME="E5:125_1"/>
<font color="Maroon">b2</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">k</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:125"/>
<font color="Maroon">b2</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b1</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


</div>
