<?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>set </b><font color="Maroon">BO</font> =  <a href="polynom1.html#K17" target="_self">BagOrder</a> <font color="Maroon">n</font>;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_2.html#D8">RELAT_2:def 8</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:132"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font> )
 <b>and </b><br/><a NAME="E2:132"/><i><font color="Green">E42</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K17" target="_self">BagOrder</a> <font color="Maroon">n</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K17" target="_self">BagOrder</a> <font color="Maroon">n</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">b1</font> = <font color="Maroon">x</font>, <font color="Maroon">b2</font> = <font color="Maroon">y</font> as   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> <b>by </b><i>, <a class="ref" href="polynom1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E4:132"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">b1</font> <a href="polynom1.html#R2" target="_self">&lt;='</a> <font color="Maroon">b2</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#T9" target="_self">Th9</a>, <a class="ref" href="polynom1.html#T8" target="_self">Th8</a></i>;<br/>
<b>reconsider </b><font color="Maroon">b1'</font> = <font color="Maroon">y</font>, <font color="Maroon">b2'</font> = <font color="Maroon">z</font> as   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> <b>by </b><i>, <a class="ref" href="polynom1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E6:132"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">b1'</font> <a href="polynom1.html#R2" target="_self">&lt;='</a> <font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#T9" target="_self">Th9</a>, <a class="ref" href="polynom1.html#T8" target="_self">Th8</a></i>;<br/>
<b>reconsider </b><font color="Maroon">B1</font> = <font color="Maroon">b1</font>, <font color="Maroon">B2'</font> = <font color="Maroon">b2'</font> as   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> ;<br/>
<a NAME="E8:132"/>
<font color="Maroon">B1</font> <a href="polynom1.html#R2" target="_self">&lt;='</a> <font color="Maroon">B2'</font>
 
<b>by </b><i>, <a class="ref" href="polynom1.html#T10" target="_self">Th10</a>, <a class="ref" href="polynom1.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E9:132"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K17" target="_self">BagOrder</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T8" target="_self">Th8</a></i>;<br/>


</div>
