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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="relat_2.html#V6">connected</a> <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>;<br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:27_1"/>
( <font color="Maroon">b1</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b2</font>,<font color="Maroon">T</font> or <font color="Maroon">b2</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b1</font>,<font color="Maroon">T</font> )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_1"><b>suppose </b></a><a NAME="E1:27_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">b1</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b2</font>,<font color="Maroon">T</font>
 ;<br/><div class="add"><a NAME="E2:27_1_1"/><b>then </b>
 <a href="termord.html#K1" target="_self">min</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">T</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b1</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:27_1_1"/>
(  <a href="termord.html#K1" target="_self">min</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">T</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b1</font>,<font color="Maroon">T</font> &amp;  <a href="termord.html#K1" target="_self">min</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">T</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b2</font>,<font color="Maroon">T</font> )
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_2"><b>suppose </b></a><a NAME="E1:27_1_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">b2</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b1</font>,<font color="Maroon">T</font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:27_1_2_1_1"/>
( <font color="Maroon">b1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b2</font> or <font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_2_1_1_1"><b>case </b></a><a NAME="E1:27_1_2_1_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">b1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b2</font>
 ;<br/><div class="add"><a NAME="E2:27_1_2_1_1_1"/><b>then </b>
 <a href="termord.html#K1" target="_self">min</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">T</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b1</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:27_1_2_1_1_1"/>
(  <a href="termord.html#K1" target="_self">min</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">T</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b1</font>,<font color="Maroon">T</font> &amp;  <a href="termord.html#K1" target="_self">min</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">T</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b2</font>,<font color="Maroon">T</font> )
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_2_1_1_2"><b>case </b></a><a NAME="E1:27_1_2_1_1_2"/>
<font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2</font>
 ;<br/><div class="add"><a NAME="E2:27_1_2_1_1_2"/><b>then </b>
<font color="Maroon">b2</font> <a href="termord.html#R2" target="_self">&lt;</a> <font color="Maroon">b1</font>,<font color="Maroon">T</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:27_1_2_1_1_2"/><b>then </b>
not <font color="Maroon">b1</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b2</font>,<font color="Maroon">T</font>
 <b>by </b><i/>;<br/><a NAME="E4:27_1_2_1_1_2"/><b>then </b>
 <a href="termord.html#K1" target="_self">min</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">T</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b2</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E5:27_1_2_1_1_2"/>
(  <a href="termord.html#K1" target="_self">min</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">T</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b1</font>,<font color="Maroon">T</font> &amp;  <a href="termord.html#K1" target="_self">min</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">T</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b2</font>,<font color="Maroon">T</font> )
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:27_1_2"/>
(  <a href="termord.html#K1" target="_self">min</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">T</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b1</font>,<font color="Maroon">T</font> &amp;  <a href="termord.html#K1" target="_self">min</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">T</font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">b2</font>,<font color="Maroon">T</font> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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