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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>let </b><font color="Maroon" title="c2">T</font> be  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a> <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font>;<br/><b>let </b><font color="Maroon" title="c3">b1</font>, <font color="Maroon" title="c4">b2</font> be   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">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" title="c3">b1</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> or <font color="Maroon" title="c4">b2</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c2">T</font> )
 </span><b>by </b><i><a class="txt" href="termord.html#E15"><i><font color="Green" title="E13">Lm5</font></i></a></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" title="E19">A1</font></i>: 
<font color="Maroon" title="c3">b1</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font>
 ;<br/><div class="add"><a NAME="E2:27_1_1"/><b>then </b>
 <a href="termord.html#K1" title="TERMORD:func.1">min</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">b1</font>
 <b>by </b><i><a class="ref" href="termord.html#D4" target="_self" title="TERMORD:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E3:27_1_1"/>
(  <a href="termord.html#K1" title="TERMORD:func.1">min</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c2">T</font> &amp;  <a href="termord.html#K1" title="TERMORD:func.1">min</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> )
 <b>by </b><i><a class="txt" href="termord.html#E1:27_1_1"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="termord.html#E11"><i><font color="Green" title="E9">Lm2</font></i></a></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" title="E19">A2</font></i>: 
<font color="Maroon" title="c4">b2</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c2">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" title="c3">b1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">b2</font> or <font color="Maroon" title="c3">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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" title="E20">A3</font></i>: 
<font color="Maroon" title="c3">b1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">b2</font>
 ;<br/><div class="add"><a NAME="E2:27_1_2_1_1_1"/><b>then </b>
 <a href="termord.html#K1" title="TERMORD:func.1">min</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">b1</font>
 <b>by </b><i><a class="txt" href="termord.html#E23"><i><font color="Green" title="E18">Lm6</font></i></a></i>;<br/><b>hence </b><a NAME="E3:27_1_2_1_1_1"/>
(  <a href="termord.html#K1" title="TERMORD:func.1">min</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c2">T</font> &amp;  <a href="termord.html#K1" title="TERMORD:func.1">min</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> )
 <b>by </b><i><a class="txt" href="termord.html#E1:27_1_2_1_1_1"><i><font color="Green" title="E20">A3</font></i></a>, <a class="txt" href="termord.html#E11"><i><font color="Green" title="E9">Lm2</font></i></a></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" title="c3">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b2</font>
 ;<br/><div class="add"><a NAME="E2:27_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c4">b2</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="termord.html#E1:27_1_2"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="termord.html#D3" target="_self" title="TERMORD:def.3">Def3</a></i>;<br/><a NAME="E3:27_1_2_1_1_2"/><b>then </b>
not <font color="Maroon" title="c3">b1</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T5" target="_self" title="TERMORD:th.5">Th5</a></i>;<br/><a NAME="E4:27_1_2_1_1_2"/><b>then </b>
 <a href="termord.html#K1" title="TERMORD:func.1">min</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">b2</font>
 <b>by </b><i><a class="ref" href="termord.html#D4" target="_self" title="TERMORD:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E5:27_1_2_1_1_2"/>
(  <a href="termord.html#K1" title="TERMORD:func.1">min</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c2">T</font> &amp;  <a href="termord.html#K1" title="TERMORD:func.1">min</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> )
 <b>by </b><i><a class="txt" href="termord.html#E1:27_1_2"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="termord.html#E11"><i><font color="Green" title="E9">Lm2</font></i></a></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" title="TERMORD:func.1">min</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c2">T</font> &amp;  <a href="termord.html#K1" title="TERMORD:func.1">min</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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