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

<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/>

<b>set </b><font color="Maroon" title="c2">BO</font> =  <a href="polynom1.html#K17" title="POLYNOM1:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font>;<br/>
<b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_2.html#D4" title="RELAT_2:def.4">RELAT_2:def 4</a><br/>

<b>assume </b><a NAME="E1:128"/><i><font color="Green" title="E69">A1</font></i>: 
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K17" title="POLYNOM1:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K17" title="POLYNOM1:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">b1</font> = <font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c6">b2</font> = <font color="Maroon" title="c4">y</font> as   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font> <b>by </b><i><a class="ref" href="polynom1.html#D14" target="_self" title="POLYNOM1:def.14">Def14</a></i>;<br/>
<a NAME="E3:128"/><i><font color="Green" title="E70">A2</font></i>: 
<font color="Maroon" title="c5">b1</font> <a href="polynom1.html#R2" title="POLYNOM1:pred.2">&lt;='</a> <font color="Maroon" title="c6">b2</font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E1:128"><i><font color="Green" title="E69">A1</font></i></a>, <a class="ref" href="polynom1.html#D16" target="_self" title="POLYNOM1:def.16">Def16</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">b1'</font> = <font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c8">b2'</font> = <font color="Maroon" title="c3">x</font> as   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font> <b>by </b><i><a class="txt" href="polynom1.html#E1:128"><i><font color="Green" title="E69">A1</font></i></a>, <a class="ref" href="polynom1.html#D14" target="_self" title="POLYNOM1:def.14">Def14</a></i>;<br/>
<a NAME="E5:128"/>
<font color="Maroon" title="c7">b1'</font> <a href="polynom1.html#R2" title="POLYNOM1:pred.2">&lt;='</a> <font color="Maroon" title="c8">b2'</font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E1:128"><i><font color="Green" title="E69">A1</font></i></a>, <a class="ref" href="polynom1.html#D16" target="_self" title="POLYNOM1:def.16">Def16</a></i>;<br/>
<a NAME="E6:128"/><b>then </b>
( ( <font color="Maroon" title="c5">b1</font> <a href="polynom1.html#R1" title="POLYNOM1:pred.1">&lt;</a> <font color="Maroon" title="c6">b2</font> or <font color="Maroon" title="c5">b1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c6">b2</font> ) &amp; ( <font color="Maroon" title="c7">b1'</font> <a href="polynom1.html#R1" title="POLYNOM1:pred.1">&lt;</a> <font color="Maroon" title="c8">b2'</font> or <font color="Maroon" title="c7">b1'</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c8">b2'</font> ) )
 
<b>by </b><i><a class="txt" href="polynom1.html#E3:128"><i><font color="Green" title="E70">A2</font></i></a>, <a class="ref" href="polynom1.html#D12" target="_self" title="POLYNOM1:def.12">Def12</a></i>;<br/>
<b>hence </b><a NAME="E7:128"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font>
 ;<br/>


</div>
