<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="relat_2.html#V6">connected</a> <a href="bagorder.html#NM1">TermOrder</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></font> be  <a href="polynom7.html#V1">non-zero</a> <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>









<b>assume </b><a NAME="E1:30"/><i><font color="Green">E25</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <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">c<sub>4</sub></font></span>)</span> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="groeb_3.html#K3" target="_self">Upper_Support</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<a NAME="E2:30"/><i><font color="Green">E26</font></i>: 
(  <a href="groeb_3.html#K3" target="_self">Upper_Support</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K3" target="_self">Upper_Support</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="groeb_3.html#K3" target="_self">Upper_Support</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="termord.html#R1">&lt;=</a> <font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="groeb_3.html#K3" target="_self">Upper_Support</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) )
 
<b>by </b><i><a class="txt" href="groeb_3.html#E1:30"><i><font color="Green">E25</font></i></a>, <a class="ref" href="groeb_3.html#D2" target="_self">Def2</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="groeb_3.html#K3" target="_self">Upper_Support</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<a NAME="E4:30"/><i><font color="Green">E27</font></i>: 
 <a href="groeb_3.html#K3" target="_self">Upper_Support</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="groeb_3.html#E1:30"><i><font color="Green">E25</font></i></a>, <a class="ref" href="groeb_3.html#D2" target="_self">Def2</a>, <a class="ref" href="card_1.html#T78">CARD_1:78</a></i>;<br/>
<a NAME="E5:30"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="groeb_3.html#K3" target="_self">Upper_Support</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E7:30"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="polynom7.html#D2">POLYNOM7:def 2</a></i>;<br/>
<a NAME="E8:30"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></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="E9:30"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/>
<a NAME="E10:30"/>
<font color="Maroon">c<sub>8</sub></font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="groeb_3.html#E2:30"><i><font color="Green">E26</font></i></a>, <a class="txt" href="groeb_3.html#E5:30"><i><font color="Green">E28</font></i></a>, <a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/>
<b>hence </b><a NAME="E11:30"/>
 <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="groeb_3.html#K3" target="_self">Upper_Support</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E1:30"><i><font color="Green">E25</font></i></a>, <a class="txt" href="groeb_3.html#E4:30"><i><font color="Green">E27</font></i></a>, <a class="txt" href="groeb_3.html#E9:30"><i><font color="Green">E29</font></i></a>, <a class="ref" href="groeb_3.html#D2" target="_self">Def2</a></i>;<br/>


</div>
