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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#V2">admissible</a> <a href="bagorder.html#NM1">TermOrder</a> of <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">L</font> be  <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> non <a href="realset2.html#V3">trivial</a>  <a href="rlvect_1.html#L1">LoopStr</a> ;<br/><b>let </b><font color="Maroon">p</font> be  <a href="polynom7.html#V1">non-zero</a> <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/>







<a NAME="E1:57"/>
 <a href="termord.html#K6">Red</a> <font color="Maroon">p</font>,<font color="Maroon">T</font> <a href="polyred.html#R2" target="_self">&lt;</a>  <a href="termord.html#K5">HM</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:57"/><b>then </b><i><font color="Green">E23</font></i>: 
 <a href="termord.html#K6">Red</a> <font color="Maroon">p</font>,<font color="Maroon">T</font> <a href="polyred.html#R1" target="_self">&lt;=</a>  <a href="termord.html#K5">HM</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 
<b>by </b><i><a class="txt" href="polyred.html#E2"><i><font color="Green">Lemma32</font></i></a></i>;<br/>
<a NAME="E3:57"/>
 <a href="termord.html#K5">HM</a> <font color="Maroon">p</font>,<font color="Maroon">T</font> <a href="polyred.html#R1" target="_self">&lt;=</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:57"/><b>then </b><i><font color="Green">E24</font></i>: 
 <a href="termord.html#K6">Red</a> <font color="Maroon">p</font>,<font color="Maroon">T</font> <a href="polyred.html#R1" target="_self">&lt;=</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:57"/>
<font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="polynom7.html#D2">POLYNOM7:def 2</a></i>;<br/>
<a NAME="E6:57"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="polynom7.html#T1">POLYNOM7:1</a></i>;<br/>
<a NAME="E7:57"/><b>then </b><i><font color="Green">E26</font></i>: 
 <a href="termord.html#K3">HT</a> <font color="Maroon">p</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/>
<a NAME="E8:57"/>
<span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="termord.html#T39">TERMORD:39</a></i>;<br/>
<a NAME="E9:57"/><b>then </b>
not  <a href="termord.html#K3">HT</a> <font color="Maroon">p</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p</font>,<font color="Maroon">T</font></span>)</span>
 
<b>by </b><i><a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/>
<b>hence </b><a NAME="E10:57"/>
 <a href="termord.html#K6">Red</a> <font color="Maroon">p</font>,<font color="Maroon">T</font> <a href="polyred.html#R2" target="_self">&lt;</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>
 <b>by </b><i>, , <a class="txt" href="polyred.html#E2"><i><font color="Green">Lemma32</font></i></a></i>;<br/>


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