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<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>, <font color="Maroon" title="c5">z</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#D8" title="RELAT_2:def.8">RELAT_2:def 8</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:129"/><i><font color="Green" title="E70">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; <font color="Maroon" title="c5">z</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> )
 <b>and </b><br/><a NAME="E2:129"/><i><font color="Green" title="E71">A2</font></i>: 
( <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="c5">z</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>reconsider </b><font color="Maroon" title="c6">b1</font> = <font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c7">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="txt" href="polynom1.html#E1:129"><i><font color="Green" title="E70">A1</font></i></a>, <a class="ref" href="polynom1.html#D14" target="_self" title="POLYNOM1:def.14">Def14</a></i>;<br/>
<a NAME="E4:129"/><i><font color="Green" title="E72">A3</font></i>: 
<font color="Maroon" title="c6">b1</font> <a href="polynom1.html#R2" title="POLYNOM1:pred.2">&lt;='</a> <font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E2:129"><i><font color="Green" title="E71">A2</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="c8">b1'</font> = <font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c9">b2'</font> = <font color="Maroon" title="c5">z</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#E1:129"><i><font color="Green" title="E70">A1</font></i></a>, <a class="ref" href="polynom1.html#D14" target="_self" title="POLYNOM1:def.14">Def14</a></i>;<br/>
<a NAME="E6:129"/><i><font color="Green" title="E73">A4</font></i>: 
<font color="Maroon" title="c8">b1'</font> <a href="polynom1.html#R2" title="POLYNOM1:pred.2">&lt;='</a> <font color="Maroon" title="c9">b2'</font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E2:129"><i><font color="Green" title="E71">A2</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="c10">B1</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c11">B2'</font> = <font color="Maroon" title="c9">b2'</font> as   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font> ;<br/>
<a NAME="E8:129"/>
<font color="Maroon" title="c10">B1</font> <a href="polynom1.html#R2" title="POLYNOM1:pred.2">&lt;='</a> <font color="Maroon" title="c11">B2'</font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E4:129"><i><font color="Green" title="E72">A3</font></i></a>, <a class="txt" href="polynom1.html#E6:129"><i><font color="Green" title="E73">A4</font></i></a>, <a class="ref" href="polynom1.html#T46" target="_self" title="POLYNOM1:th.46">Th46</a></i>;<br/>
<b>hence </b><a NAME="E9:129"/>
<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="c5">z</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>
 <b>by </b><i><a class="ref" href="polynom1.html#D16" target="_self" title="POLYNOM1:def.16">Def16</a></i>;<br/>


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