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<b>let </b><font color="Maroon">n</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">T</font> be   <a href="bagorder.html#NM1">TermOrder</a> of <font color="Maroon">n</font>;<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="E1:21"/>
( <font color="Maroon">b1</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b2</font>,<font color="Maroon">T</font> &amp; <font color="Maroon">b2</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b3</font>,<font color="Maroon">T</font> )
 ;<br/>

<a NAME="E2:21"/><b>then </b><i><font color="Green">E32</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b2</font>,<font color="Maroon">b3</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E3:21"/>
 <a href="relat_1.html#K3">field</a> <font color="Maroon">T</font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="orders_1.html#T97">ORDERS_1:97</a></i>;<br/>
<a NAME="E4:21"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">T</font> <a href="relat_2.html#R8">is_transitive_in</a>  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="relat_2.html#D16">RELAT_2:def 16</a></i>;<br/>
<a NAME="E5:21"/>
( <font color="Maroon">b1</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> &amp; <font color="Maroon">b2</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> &amp; <font color="Maroon">b3</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> )
 
<b>by </b><i><a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/>
<a NAME="E6:21"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b3</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 
<b>by </b><i>, , <a class="ref" href="relat_2.html#D8">RELAT_2:def 8</a></i>;<br/>
<b>hence </b><a NAME="E7:21"/>
<font color="Maroon">b1</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b3</font>,<font color="Maroon">T</font>
 <b>by </b><i/>;<br/>


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