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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">L</font> be  non <a href="struct_0.html#V3">empty</a> <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>  <a href="rlvect_1.html#L1">LoopStr</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/>







<b>set </b><font color="Maroon">u</font> =  <a href="groeb_3.html#K5" target="_self">Up</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>,0;<br/>
<b>set </b><font color="Maroon">l</font> =  <a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>,0;<br/>
<a NAME="E1:42"/><i><font color="Green">E39</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font></span>)</span>
 
;<br/>
<a NAME="E2:42"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" target="_self">Up</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>,0</span>)</span> <a href="hidden.html#R1">=</a>  <a href="groeb_3.html#K3" target="_self">Upper_Support</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>,0
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:42"/><b>then </b>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K5" target="_self">Up</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>,0</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:42"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" target="_self">Up</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>,0</span>)</span>,0 <a href="tarski.html#R2">are_equipotent</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#D5">CARD_1:def 5</a></i>;<br/>
<a NAME="E5:42"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" target="_self">Up</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>,0</span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#T46">CARD_1:46</a></i>;<br/>
<b>hence </b><a NAME="E6:42"/>
 <a href="groeb_3.html#K5" target="_self">Up</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>,0 <a href="funct_2.html#R2">=</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#T1">POLYNOM7:1</a></i>;<br/>

<a NAME="E7:42"/><b>then </b>
<span class="p1">(<span class="default"><a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span> <a href="polynom1.html#K22">+</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>,0</span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">p</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:42"/>
 <a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>,0 <a href="funct_2.html#R2">=</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="polyred.html#T2">POLYRED:2</a></i>;<br/>


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