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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">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a>  <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">LoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c4">p</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>;<br/>







<b>set </b><font color="Maroon" title="c5">u</font> =  <a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<b>set </b><font color="Maroon" title="c6">l</font> =  <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<a NAME="E1:42"/><i><font color="Green" title="E35">A1</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">p</font></span>)</span>
 
;<br/>
<a NAME="E2:42"/><b>then </b>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="groeb_3.html#K3" title="GROEB_3:func.3">Upper_Support</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="groeb_3.html#E32"><i><font color="Green" title="E25">Lm3</font></i></a></i>;<br/>
<a NAME="E3:42"/><b>then </b>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="groeb_3.html#E1:42"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="groeb_3.html#D2" target="_self" title="GROEB_3:def.2">Def2</a></i>;<br/>
<a NAME="E4:42"/><b>then </b>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>, <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">are_equipotent</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#D5" title="CARD_1:def.5">CARD_1:def 5</a></i>;<br/>
<a NAME="E5:42"/><b>then </b>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#T46" title="CARD_1:th.46">CARD_1:46</a></i>;<br/>
<b>hence </b><a NAME="E6:42"/>
 <a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></i>;<br/>

<a NAME="E7:42"/><b>then </b>
<span class="p1">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span> <a href="polynom1.html#K22" title="POLYNOM1:func.22">+</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="txt" href="groeb_3.html#E1:42"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="groeb_3.html#T33" target="_self" title="GROEB_3:th.33">Th33</a></i>;<br/>
<b>hence </b><a NAME="E8:42"/>
 <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">p</font>
 <b>by </b><i><a class="ref" href="polyred.html#T2" title="POLYRED:th.2">POLYRED:2</a></i>;<br/>


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