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

<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#V3">Abelian</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="group_1.html#V4">associative</a> <a href="group_1.html#V7">commutative</a> <a href="vectsp_1.html#V6">right_unital</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_1.html#V8">left_unital</a> <a href="vectsp_1.html#V9">Field-like</a> non <a href="realset2.html#V3">trivial</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">p1</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>, <font color="Maroon">p2</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/>







<b>assume </b><a NAME="E1:67"/><i><font color="Green">E39</font></i>: 
(  <a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font>, <a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font> <a href="groeb_2.html#R1">are_disjoint</a>  &amp;  <a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font> is <a href="polynom7.html#V1">non-zero</a> &amp;  <a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font> is <a href="polynom7.html#V1">non-zero</a> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">red1</font> =  <a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font>, <font color="Maroon">red2</font> =  <a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font> as  <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/>
<b>set </b><font color="Maroon">j</font> =  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font></span>)</span>;<br/>
<a NAME="E3:67"/>
<font color="Maroon">p2</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="E4:67"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</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="E5:67"/><b>then </b>
 <a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font>
 
<b>by </b><i><a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/>
<a NAME="E6:67"/><b>then </b>
for <font color="Olive">t</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span> holds <br/><font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:67"/><b>then </b><i><font color="Green">E40</font></i>: 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<i><font color="Green">E41</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font></span>)</span> = 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T36">TERMORD:36</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="groeb_3.html#T9" target="_self">Th9</a>, <a class="ref" href="card_2.html#T63">CARD_2:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="ref" href="card_2.html#T60">CARD_2:60</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_2"/>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E2:67_2"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font>,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="E3:67_2"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font> <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/><a NAME="E4:67_2"/><b>then </b>
<font color="Maroon">p2</font> <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/><b>hence </b><a NAME="E5:67_2"/>
contradiction
 <b>by </b><i><a class="ref" href="polynom7.html#D2">POLYNOM7:def 2</a></i>;<br/></div><b>end;</b></div>
<a NAME="E10:67"/><b>then </b><i><font color="Green">E45</font></i>: 
1 <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">p2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/>
<a NAME="E11:67"/><b>then </b>
1 <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">j'</font> = <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>for <font color="Olive">m</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">m</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">p2</font></span>)</span> &amp;  <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#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Olive">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> holds <br/> <a href="polyred.html#K3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1">{</a><span class="default"><font color="Maroon">p1</font></span><a href="groeb_1.html#K1">}</a></span>,<font color="Maroon">T</font> <a href="rewrite1.html#R1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Olive">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Olive">m</font></span>)</span></span>)</span>;<br/>
<a NAME="E13:67"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:67_3"/>
( <font color="Maroon">m</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">p2</font></span>)</span> &amp;  <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#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<a NAME="E2:67_3"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></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="E3:67_3"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></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/>
<a NAME="E4:67_3"/><b>then </b>
 <a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font> <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/>
<b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T4">POLYRED:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <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>
<b>by </b><i><a class="ref" href="polyred.html#T5">POLYRED:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T2">POLYRED:2</a></i>
;<br/>
<b>hence </b><a NAME="E6:67_3"/>
 <a href="polyred.html#K3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1">{</a><span class="default"><font color="Maroon">p1</font></span><a href="groeb_1.html#K1">}</a></span>,<font color="Maroon">T</font> <a href="rewrite1.html#R1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rewrite1.html#T13">REWRITE1:13</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E14:67"/><i><font color="Green">E58</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j'</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font> <a href="nat_1.html#K1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:67_4"/><i><font color="Green">E70</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j'</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_4_1"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:67_4_1_1"/><i><font color="Green">E73</font></i>: 
( <font color="Maroon">m</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">p2</font></span>)</span> &amp;  <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#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><b>set </b><font color="Maroon">m'</font> = <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_4_1_1_1"/>
<font color="Maroon">m</font> <a href="hidden.html#R1">=</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">p2</font></span>)</span>
 ;<br/><a NAME="E2:67_4_1_1_1"/><b>then </b>
 <a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font> <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/>;<br/><b>hence </b><a NAME="E3:67_4_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="card_1.html#T47">CARD_1:47</a>, <a class="ref" href="polynom7.html#T1">POLYNOM7:1</a></i>;<br/></div><b>end;</b></div><a NAME="E3:67_4_1_1"/><b>then </b><i><font color="Green">E76</font></i>: 
<font color="Maroon">m</font> <a href="xxreal_0.html#NR3" target="_self">&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">p2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E4:67_4_1_1"/><b>then </b><i><font color="Green">E79</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 <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">p2</font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E5:67_4_1_1"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>
 <b>by </b><i><a class="ref" href="groeb_3.html#T5" target="_self">Th5</a>, </i>;<br/><a NAME="E6:67_4_1_1"/><b>then </b><i><font color="Green">E80</font></i>: 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="card_2.html#T63">CARD_2:63</a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="card_1.html#K4">card</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i>, , , </i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="card_1.html#T50">CARD_1:50</a></i>
;<br/><a NAME="E8:67_4_1_1"/><b>then </b><i><font color="Green">E81</font></i>: 
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E9:67_4_1_1"/><b>then </b><i><font color="Green">E82</font></i>: 
( <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 <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">p2</font></span>)</span> &amp;  <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#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> )
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E10:67_4_1_1"/><i><font color="Green">E83</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/><b>set </b><font color="Maroon">f</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>;<br/><a NAME="E11:67_4_1_1"/>
( <font color="Maroon">red1</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> &amp;  <a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</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="E12:67_4_1_1"/><b>then </b>
(  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <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="E13:67_4_1_1"/><b>then </b>
(  <a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red1</font> &amp;  <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<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#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> )
 <b>by </b><i><a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E14:67_4_1_1"/><b>then </b>
( <font color="Maroon">red1</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font> &amp; <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</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> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font> )
 <b>by </b><i><a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E15:67_4_1_1"/><b>then </b>
(  <a href="termord.html#K4">HC</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font> &amp;  <a href="termord.html#K4">HC</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font> )
 <b>by </b><i><a class="ref" href="termord.html#D7">TERMORD:def 7</a></i>;<br/><a NAME="E16:67_4_1_1"/><b>then </b><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><a href="termord.html#K4">HC</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="vectsp_2.html#D5">VECTSP_2:def 5</a></i>;<br/><a NAME="E17:67_4_1_1"/><i><font color="Green">E85</font></i>: 
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">red1</font></span>)</span>,<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span>
 <b>by </b><i><a class="ref" href="termord.html#T31">TERMORD:31</a></i>;<br/><a NAME="E18:67_4_1_1"/>
 <a href="termord.html#K4">HC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">red1</font></span>)</span>,<font color="Maroon">T</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E1:67_4_1_1"><i><font color="Green">E73</font></i></a>, <a class="ref" href="termord.html#T32">TERMORD:32</a></i>;<br/><a NAME="E19:67_4_1_1"/><b>then </b><i><font color="Green">E86</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">red1</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i>, <a class="ref" href="termord.html#D7">TERMORD:def 7</a></i>;<br/><a NAME="E20:67_4_1_1"/><i><font color="Green">E115</font></i>: 
<span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_4_1_1_3"/><i><font color="Green">E116</font></i>: 
<span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">red1</font> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:67_4_1_1_3"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">red1</font> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">s</font> <a href="polynom1.html#K9">+</a> <font color="Olive">t</font></span>)</span> where <font color="Olive">s</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Olive">t</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> : ( <font color="Olive">s</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red1</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="termord.html#T30">TERMORD:30</a></i>;<br/><a NAME="E3:67_4_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">s</font> <a href="polynom1.html#K9">+</a> <font color="Olive">t</font></span>)</span> where <font color="Olive">s</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Olive">t</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> : ( <font color="Olive">s</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red1</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) </span>}</span> 
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">s</font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Maroon">t</font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E5:67_4_1_1_3"/><i><font color="Green">E117</font></i>: 
( <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">t</font> &amp; <font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red1</font> &amp; <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="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 ;<br/><a NAME="E6:67_4_1_1_3"/><i><font color="Green">E118</font></i>: 
<font color="Maroon">t</font> <a href="termord.html#R2">&lt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_3_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_3_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_4_1_1_3_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_4_1_1_3_1_1_1"/>
( <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</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">p2</font></span>)</span> or <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</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">p2</font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_4_1_1_3_1_1_1_1"><b>case </b></a><a NAME="E1:67_4_1_1_3_1_1_1_1"/>
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</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">p2</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:67_4_1_1_3_1_1_1_1"/><b>then </b>
 <a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <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/>;<br/><b>hence </b><a NAME="E3:67_4_1_1_3_1_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="polynom7.html#T1">POLYNOM7:1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_4_1_1_3_1_1_1_2"><b>case </b></a><a NAME="E1:67_4_1_1_3_1_1_1_2"/>
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</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">p2</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:67_4_1_1_3_1_1_1_2"/><b>then </b>
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&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">p2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E3:67_4_1_1_3_1_1_1_2"/><b>then </b><i><font color="Green">E149</font></i>: 
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon">T</font> <a href="termord.html#R2">&lt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E8:67"><i><font color="Green">E41</font></i></a></i>;<br/><a NAME="E4:67_4_1_1_3_1_1_1_2"/>
<font color="Maroon">t</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><b>hence </b><a NAME="E5:67_4_1_1_3_1_1_1_2"/>
<font color="Maroon">t</font> <a href="termord.html#R2">&lt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E6:67_4_1_1"><i><font color="Green">E80</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="E2:67_4_1_1_3_1"/>
<font color="Maroon">t</font> <a href="termord.html#R2">&lt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 ;<br/>


</div><b>end;</b></div><a NAME="E7:67_4_1_1_3"/>
<font color="Maroon">s</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E8:67_4_1_1_3"/><b>then </b>
<font color="Maroon">s</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">t</font> <a href="termord.html#R2">&lt;</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="txt" href="groeb_3.html#E4:67_4_1_1"><i><font color="Green">E79</font></i></a></i>;<br/><a NAME="E9:67_4_1_1_3"/><b>then </b>
<font color="Maroon">s</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">t</font> <a href="termord.html#R2">&lt;</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T26">TERMORD:26</a></i>;<br/><b>hence </b><a NAME="E10:67_4_1_1_3"/>
contradiction
 <b>by </b><i>, <a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/></div><b>end;</b></div><a NAME="E22:67_4_1_1"/><b>then </b><i><font color="Green">E150</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">red1</font> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span></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="txt" href="groeb_3.html#E3:67_4_1_1"><i><font color="Green">E76</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_4_1_1_4"/><i><font color="Green">E151</font></i>: 
<span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:67_4_1_1_4"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">s</font> <a href="polynom1.html#K9">+</a> <font color="Olive">t</font></span>)</span> where <font color="Olive">s</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Olive">t</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> : ( <font color="Olive">s</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#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="termord.html#T30">TERMORD:30</a></i>;<br/><a NAME="E3:67_4_1_1_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">s</font> <a href="polynom1.html#K9">+</a> <font color="Olive">t</font></span>)</span> where <font color="Olive">s</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Olive">t</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> : ( <font color="Olive">s</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#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> ) </span>}</span> 
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">s</font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Maroon">t</font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E5:67_4_1_1_4"/><i><font color="Green">E152</font></i>: 
( <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">t</font> &amp; <font color="Maroon">s</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#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> &amp; <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"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> )
 ;<br/><a NAME="E6:67_4_1_1_4"/><i><font color="Green">E154</font></i>: 
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font> <a href="hidden.html#R1">=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T26">TERMORD:26</a></i>;<br/><a NAME="E7:67_4_1_1_4"/>
<font color="Maroon">red1</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="E8:67_4_1_1_4"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">red1</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="E9:67_4_1_1_4"/><b>then </b><i><font color="Green">E155</font></i>: 
 <a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red1</font>
 <b>by </b><i><a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E10:67_4_1_1_4"/>
 <a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</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="E11:67_4_1_1_4"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <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="E12:67_4_1_1_4"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="termord.html#T21">TERMORD:21</a></i>;<br/><a NAME="E13:67_4_1_1_4"/><b>then </b><i><font color="Green">E156</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E4:67_4_1_1"><i><font color="Green">E79</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E14:67_4_1_1_4"/><i><font color="Green">E157</font></i>: 
<font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">red2</font> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>;<br/><a NAME="E15:67_4_1_1_4"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="groeb_1.html#T5">GROEB_1:5</a></i>;<br/><a NAME="E16:67_4_1_1_4"/><b>then </b><i><font color="Green">E158</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font></span>)</span> <a href="xboole_0.html#K2">\/</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#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_3.html#E10:67_4_1_1"><i><font color="Green">E83</font></i></a>, <a class="ref" href="polynom1.html#T79">POLYNOM1:79</a></i>;<br/><a NAME="E17:67_4_1_1_4"/><i><font color="Green">E159</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E18:67_4_1_1_4"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_4_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_4_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_4_1_1_4_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_4_1_1_4_1_1_1"/>
( <font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font> or <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="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 </span><b>by </b><i><a class="txt" href="groeb_3.html#E16:67_4_1_1"><i><font color="Green">E84</font></i></a>, <a class="txt" href="groeb_3.html#E4:67_4_1_1"><i><font color="Green">E79</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_4_1_1_4_1_1_1_1"><b>case </b></a><a NAME="E1:67_4_1_1_4_1_1_1_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:67_4_1_1_4_1_1_1_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_4_1_1_4_1_1_1_2"><b>case </b></a><a NAME="E1:67_4_1_1_4_1_1_1_2"/>
<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="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:67_4_1_1_4_1_1_1_2"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E17:67_4_1_1"><i><font color="Green">E85</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="E2:67_4_1_1_4_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font>
 ;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E19:67_4_1_1_4"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_3.html#E6:67_4_1_1"><i><font color="Green">E80</font></i></a>, <a class="txt" href="groeb_3.html#E8:67_4_1_1"><i><font color="Green">E81</font></i></a>, <a class="txt" href="groeb_3.html#E9:67_4_1_1"><i><font color="Green">E82</font></i></a>, <a class="txt" href="groeb_3.html#E4:67_4_1_1"><i><font color="Green">E79</font></i></a>, <a class="txt" href="groeb_3.html#E14:67"><i><font color="Green">E58</font></i></a>, </i>;<br/></div><b>end;</b></div><a NAME="E24:67_4_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span></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="txt" href="groeb_3.html#E3:67_4_1_1"><i><font color="Green">E76</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E25:67_4_1_1"/><b>then </b><i><font color="Green">E160</font></i>: 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></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="rlvect_1.html#T25">RLVECT_1:25</a></i>;<br/><a NAME="E26:67_4_1_1"/><i><font color="Green">E161</font></i>: 
<span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">red1</font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><font color="Maroon">red1</font> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">red1</font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span>
<b>by </b><i>, <a class="ref" href="polynom1.html#D21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">red1</font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">red1</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">red1</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span>
<b>by </b><i>, <a class="ref" href="polynom1.html#D22">POLYNOM1:def 22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">red1</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a></i>
;<br/><a NAME="E28:67_4_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">red1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="txt" href="groeb_3.html#E4:67_4_1_1"><i><font color="Green">E79</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E29:67_4_1_1"/><b>then </b><i><font color="Green">E162</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <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#T1">POLYNOM7:1</a></i>;<br/><a NAME="E30:67_4_1_1"/>
<font color="Maroon">red2</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="E31:67_4_1_1"/><b>then </b><i><font color="Green">E163</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</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="E32:67_4_1_1"/><i><font color="Green">E164</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="groeb_3.html#K4" target="_self">Lower_Support</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_6"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_4_1_1_6"/><i><font color="Green">E165</font></i>: 
 <a href="termord.html#K3">HT</a> <font color="Maroon">red2</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="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 ;<br/><a NAME="E2:67_4_1_1_6"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E3:67_4_1_1_6"/><b>then </b><i><font color="Green">E166</font></i>: 
for <font color="Olive">t</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> holds <br/><font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">t</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:67_4_1_1_6_1"/><i><font color="Green">E167</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font>
 ;<br/><b>then reconsider </b><font color="Maroon">t'</font> = <font color="Maroon">t</font> as   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/><a NAME="E3:67_4_1_1_6_1"/><i><font color="Green">E168</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font>
 <b>by </b><i><a class="ref" href="termord.html#T35">TERMORD:35</a></i>;<br/><a NAME="E4:67_4_1_1_6_1"/>
<font color="Maroon">t'</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">red2</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E17:67_4_1_1"><i><font color="Green">E85</font></i></a>, <a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><b>hence </b><a NAME="E5:67_4_1_1_6_1"/>
<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="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_3.html#E10:67_4_1_1"><i><font color="Green">E83</font></i></a>, <a class="txt" href="groeb_3.html#E19:67_4_1_1"><i><font color="Green">E86</font></i></a>, <a class="txt" href="groeb_3.html#E9:67_4_1_1"><i><font color="Green">E82</font></i></a>, <a class="txt" href="groeb_3.html#E17:67_4_1_1"><i><font color="Green">E85</font></i></a>, , </i>;<br/></div><b>end;</b></div><a NAME="E5:67_4_1_1_6"/><b>then </b>
<font color="Maroon">j'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 <b>by </b><i>, <a class="txt" href="groeb_3.html#E16:67_4_1_1"><i><font color="Green">E84</font></i></a>, <a class="ref" href="tarski.html#T2">TARSKI:2</a>, <a class="txt" href="groeb_3.html#E1:67_4"><i><font color="Green">E70</font></i></a></i>;<br/><b>hence </b><a NAME="E6:67_4_1_1_6"/>
contradiction
 <b>by </b><i><a class="ref" href="groeb_3.html#T10" target="_self">Th10</a></i>;<br/></div><b>end;</b></div><a NAME="E34:67_4_1_1"/><b>then </b>
 <a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">red2</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E8:67_4_1_1"><i><font color="Green">E81</font></i></a>, <a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E35:67_4_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <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/>;<br/><b>then reconsider </b><font color="Maroon">z1</font> = <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> as  <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> <b>by </b><i><a class="ref" href="polynom7.html#D2">POLYNOM7:def 2</a></i>;<br/><a NAME="E37:67_4_1_1"/>
<font color="Maroon">z1</font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>;<br/><a NAME="E38:67_4_1_1"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">z1</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T79">POLYNOM1:79</a></i>;<br/><a NAME="E39:67_4_1_1"/><b>then </b><i><font color="Green">E169</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">z1</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</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#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="groeb_1.html#T5">GROEB_1:5</a></i>;<br/><a NAME="E40:67_4_1_1"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>
 <b>by </b><i>, , </i>;<br/><a NAME="E41:67_4_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</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#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T9">XBOOLE_1:9</a></i>;<br/><a NAME="E42:67_4_1_1"/><b>then </b><i><font color="Green">E170</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">z1</font> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E10:67_4_1_1"><i><font color="Green">E83</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><b>reconsider </b><font color="Maroon">z</font> = <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">z1</font> as  <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="E44:67_4_1_1"/>
<font color="Maroon">z</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="E45:67_4_1_1"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">z</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="E46:67_4_1_1"/><b>then </b>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="ref" href="card_2.html#T59">CARD_2:59</a></i>;<br/><a NAME="E47:67_4_1_1"/><b>then </b>
1 <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">z</font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/><b>then reconsider </b><font color="Maroon">w</font> = <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T18">INT_1:18</a></i>;<br/><b>reconsider </b><font color="Maroon">lowzw</font> =  <a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">z</font>,<font color="Maroon">T</font>,<font color="Maroon">w</font> as  <a href="polynom7.html#V1">non-zero</a> <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> <b>by </b><i><a class="txt" href="groeb_3.html#E1:67"><i><font color="Green">E39</font></i></a></i>;<br/><a NAME="E50:67_4_1_1"/><i><font color="Green">E171</font></i>: 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</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">z1</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E51:67_4_1_1"/>
<font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">z1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i/>;<br/><b>then reconsider </b><font color="Maroon">lowz1w</font> =  <a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">z1</font>,<font color="Maroon">T</font>,<font color="Maroon">w</font> as  <a href="polynom7.html#V1">non-zero</a> <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> <b>by </b><i><a class="txt" href="groeb_3.html#E1:67"><i><font color="Green">E39</font></i></a></i>;<br/><b>set </b><font color="Maroon">b</font> =  <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font>;<br/><a NAME="E53:67_4_1_1"/><i><font color="Green">E172</font></i>: 
 <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/><b>set </b><font color="Maroon">s</font> = <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span>;<br/><a NAME="E54:67_4_1_1"/><i><font color="Green">E173</font></i>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/><b>set </b><font color="Maroon">g</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span></span>)</span>;<br/><a NAME="E55:67_4_1_1"/><i><font color="Green">E174</font></i>: 
<font color="Maroon">p1</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="E56:67_4_1_1"/>
<font color="Maroon">lowzw</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="E57:67_4_1_1"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">lowzw</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="E58:67_4_1_1"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">lowzw</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="polynom7.html#T7">POLYNOM7:7</a></i>;<br/><a NAME="E59:67_4_1_1"/><b>then </b><i><font color="Green">E211</font></i>: 
 <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">lowzw</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E60:67_4_1_1"/>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">w</font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E61:67_4_1_1"/><b>then </b><i><font color="Green">E212</font></i>: 
<font color="Maroon">w</font> <a href="xxreal_0.html#NR3" target="_self">&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">z</font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T41">NAT_1:41</a></i>;<br/><a NAME="E62:67_4_1_1"/><b>then </b><i><font color="Green">E213</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">lowzw</font> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">z</font>
 <b>by </b><i/>;<br/><a NAME="E63:67_4_1_1"/><b>then </b><i><font color="Green">E214</font></i>: 
 <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">z1</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E64:67_4_1_1"/><i><font color="Green">E215</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">z1</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i>, , <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E65:67_4_1_1"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">z1</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">t'</font> <a href="polynom1.html#K9">+</a> <font color="Olive">t</font></span>)</span> where <font color="Olive">t'</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Olive">t</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> : ( <font color="Olive">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#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">z1</font> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="termord.html#T30">TERMORD:30</a></i>;<br/><a NAME="E66:67_4_1_1"/><b>then </b>
 <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">t'</font> <a href="polynom1.html#K9">+</a> <font color="Olive">t</font></span>)</span> where <font color="Olive">t'</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Olive">t</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> : ( <font color="Olive">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#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">z1</font> ) </span>}</span> 
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">t'</font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Maroon">t</font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E68:67_4_1_1"/><i><font color="Green">E216</font></i>: 
(  <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t'</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">t</font> &amp; <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#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> &amp; <font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">z1</font> )
 ;<br/><a NAME="E69:67_4_1_1"/>
 <a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</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="E70:67_4_1_1"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <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/><b>then </b> <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> = 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="polynom7.html#T7">POLYNOM7:7</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="termord.html#T22">TERMORD:22</a></i>
;<br/><a NAME="E72:67_4_1_1"/><b>then </b><i><font color="Green">E217</font></i>: 
<font color="Maroon">t'</font> <a href="hidden.html#R1">=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="groeb_3.html#T11" target="_self">Th11</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E73:67_4_1_1"/><b>then </b><i><font color="Green">E218</font></i>: 
 <a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font> <a href="polynom1.html#R3">divides</a>  <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font>
 <b>by </b><i><a class="ref" href="groeb_3.html#T11" target="_self">Th11</a>, <a class="ref" href="polynom1.html#T54">POLYNOM1:54</a></i>;<br/><a NAME="E74:67_4_1_1"/><b>then </b><i><font color="Green">E219</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font>
 <b>by </b><i><a class="ref" href="groeb_2.html#D1">GROEB_2:def 1</a></i>;<br/><i><font color="Green">E220</font></i>: <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K10">-'</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T52">POLYNOM1:52</a></i>
<br/>.= 
<font color="Maroon">t</font>
<b>by </b><i>, <a class="ref" href="groeb_3.html#T11" target="_self">Th11</a>, , <a class="ref" href="polynom1.html#T52">POLYNOM1:52</a></i>
;<br/><a NAME="E76:67_4_1_1"/><b>then </b><i><font color="Green">E221</font></i>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <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">p2</font>,<font color="Maroon">T</font></span>)</span>
 <b>by </b><i><a class="ref" href="groeb_3.html#T11" target="_self">Th11</a>, <a class="txt" href="groeb_3.html#E16:67_4_1_1"><i><font color="Green">E84</font></i></a></i>;<br/><a NAME="E77:67_4_1_1"/><i><font color="Green">E222</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font>
 <b>by </b><i><a class="ref" href="termord.html#T35">TERMORD:35</a></i>;<br/><a NAME="E78:67_4_1_1"/>
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="termord.html#T36">TERMORD:36</a></i>;<br/><a NAME="E79:67_4_1_1"/><b>then </b>
not <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E80:67_4_1_1"/><b>then </b><i><font color="Green">E223</font></i>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E81:67_4_1_1"/><b>then </b><i><font color="Green">E224</font></i>: 
<span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="groeb_3.html#T14" target="_self">Th14</a>, <a class="ref" href="termord.html#T40">TERMORD:40</a></i>;<br/><div><i><font color="Green">E225</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_9"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_4_1_1_9"/>
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 ;<br/><a NAME="E2:67_4_1_1_9"/><b>then </b><i><font color="Green">E226</font></i>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="groeb_3.html#K4" target="_self">Lower_Support</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E3:67_4_1_1_9"/>
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">p2</font> <a href="groeb_3.html#K2" target="_self">|</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K4" target="_self">Lower_Support</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_3.html#E1:67_4_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="groeb_3.html#E18"><i><font color="Green">Lemma104</font></i></a>, </i>;<br/><a NAME="E4:67_4_1_1_9"/><b>then </b><i><font color="Green">E227</font></i>: 
<font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D22">POLYNOM1:def 22</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
<b>by </b><i><a class="ref" href="groeb_3.html#T16" target="_self">Th16</a>, , <a class="ref" href="rlvect_1.html#T16">RLVECT_1:16</a></i>
;<br/><b>hence </b><a NAME="E6:67_4_1_1_9"/>
contradiction
 <b>by </b><i><a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a>, <a class="ref" href="groeb_3.html#T11" target="_self">Th11</a>, <a class="ref" href="groeb_3.html#T13" target="_self">Th13</a></i>;<br/></div><b>end;</b></div><a NAME="E83:67_4_1_1"/><b>then </b><i><font color="Green">E228</font></i>: 
<span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></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="txt" href="groeb_3.html#E11"><i><font color="Green">Lemma87</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><div><i><font color="Green">E229</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_10"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_4_1_1_10"/><i><font color="Green">E230</font></i>: 
 <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><a NAME="E2:67_4_1_1_10"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">u</font> <a href="polynom1.html#K9">+</a> <font color="Olive">v</font></span>)</span> where <font color="Olive">u</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Olive">v</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> : ( <font color="Olive">u</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#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> &amp; <font color="Olive">v</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">p1</font>,<font color="Maroon">T</font></span>)</span> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="termord.html#T30">TERMORD:30</a></i>;<br/><a NAME="E3:67_4_1_1_10"/><b>then </b>
 <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">u</font> <a href="polynom1.html#K9">+</a> <font color="Olive">v</font></span>)</span> where <font color="Olive">u</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Olive">v</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> : ( <font color="Olive">u</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#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> &amp; <font color="Olive">v</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">p1</font>,<font color="Maroon">T</font></span>)</span> ) </span>}</span> 
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">t'</font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Maroon">t</font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E5:67_4_1_1_10"/><i><font color="Green">E232</font></i>: 
(  <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t'</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">t</font> &amp; <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#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> &amp; <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">p1</font>,<font color="Maroon">T</font></span>)</span> )
 ;<br/><a NAME="E6:67_4_1_1_10"/>
 <a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</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="E7:67_4_1_1_10"/><b>then </b><i><font color="Green">E233</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <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="E8:67_4_1_1_10"/><b>then </b>
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>,<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#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>
 <b>by </b><i><a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E9:67_4_1_1_10"/><b>then </b><i><font color="Green">E234</font></i>: 
 <a href="termord.html#K3">HT</a> <font color="Maroon">p2</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#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span>
 <b>by </b><i><a class="ref" href="termord.html#T26">TERMORD:26</a></i>;<br/><b>consider </b><font color="Maroon">x</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E11:67_4_1_1_10"/><i><font color="Green">E235</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="polynom7.html#T6">POLYNOM7:6</a></i>;<br/><a NAME="E12:67_4_1_1_10"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E13:67_4_1_1_10"/><b>then </b>
<font color="Maroon">t'</font> <a href="hidden.html#R1">=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="groeb_3.html#D2" target="_self">Def2</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E14:67_4_1_1_10"/>
contradiction
 <b>by </b><i><a class="ref" href="groeb_3.html#D2" target="_self">Def2</a>, , <a class="ref" href="groeb_3.html#T13" target="_self">Th13</a>, <a class="ref" href="groeb_3.html#T11" target="_self">Th11</a>, <a class="txt" href="groeb_3.html#E16:67_4_1_1"><i><font color="Green">E84</font></i></a>, <a class="txt" href="groeb_3.html#E14:67"><i><font color="Green">E58</font></i></a>, </i>;<br/></div><b>end;</b></div><div><i><font color="Green">E236</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_11"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_4_1_1_11"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 ;<br/><a NAME="E2:67_4_1_1_11"/><b>then </b><i><font color="Green">E237</font></i>: 
 <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_3.html#E19:67_4_1_1"><i><font color="Green">E86</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E3:67_4_1_1_11"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">u</font> <a href="polynom1.html#K9">+</a> <font color="Olive">v</font></span>)</span> where <font color="Olive">u</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Olive">v</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> : ( <font color="Olive">u</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">p1</font>,<font color="Maroon">T</font></span>)</span> &amp; <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="termord.html#T30">TERMORD:30</a></i>;<br/><a NAME="E4:67_4_1_1_11"/><b>then </b>
 <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">u</font> <a href="polynom1.html#K9">+</a> <font color="Olive">v</font></span>)</span> where <font color="Olive">u</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Olive">v</font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> : ( <font color="Olive">u</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">p1</font>,<font color="Maroon">T</font></span>)</span> &amp; <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="groeb_3.html#D2" target="_self">Def2</a></i>;<br/><b>then consider </b><font color="Maroon">t'</font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Maroon">t</font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E6:67_4_1_1_11"/><i><font color="Green">E238</font></i>: 
(  <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t'</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">t</font> &amp; <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">p1</font>,<font color="Maroon">T</font></span>)</span> &amp; <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="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 ;<br/><a NAME="E7:67_4_1_1_11"/><i><font color="Green">E239</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t'</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">t</font>
 <b>by </b><i><a class="ref" href="groeb_3.html#T12" target="_self">Th12</a>, , <a class="ref" href="groeb_2.html#D1">GROEB_2:def 1</a></i>;<br/><a NAME="E8:67_4_1_1_11"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p1</font>
 <b>by </b><i><a class="ref" href="termord.html#T35">TERMORD:35</a></i>;<br/><a NAME="E9:67_4_1_1_11"/><b>then </b><i><font color="Green">E240</font></i>: 
<font color="Maroon">t'</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E10:67_4_1_1_11"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p1</font></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="termord.html#T36">TERMORD:36</a></i>;<br/><a NAME="E11:67_4_1_1_11"/><b>then </b>
not <font color="Maroon">t'</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E12:67_4_1_1_11"/><b>then </b>
<font color="Maroon">t'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E13:67_4_1_1_11"/><b>then </b><i><font color="Green">E241</font></i>: 
<font color="Maroon">t'</font> <a href="termord.html#R2">&lt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_11_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_4_1_1_11_1"/>
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="termord.html#R2">&lt;</a> <font color="Maroon">t</font>,<font color="Maroon">T</font>
 ;<br/><a NAME="E2:67_4_1_1_11_1"/><b>then </b><i><font color="Green">E242</font></i>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">t</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/><a NAME="E3:67_4_1_1_11_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="groeb_3.html#K4" target="_self">Lower_Support</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, , </i>;<br/><a NAME="E4:67_4_1_1_11_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="groeb_3.html#K4" target="_self">Lower_Support</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, , , <a class="ref" href="groeb_3.html#T14" target="_self">Th14</a>, </i>;<br/><b>hence </b><a NAME="E5:67_4_1_1_11_1"/>
contradiction
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><a NAME="E15:67_4_1_1_11"/><b>then </b>
<font color="Maroon">t</font> <a href="termord.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T5">TERMORD:5</a></i>;<br/><a NAME="E16:67_4_1_1_11"/><b>then </b>
<font color="Maroon">t</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">t'</font> <a href="termord.html#R2">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E17:67_4_1_1_11"/>
contradiction
 <b>by </b><i>, <a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/></div><b>end;</b></div><i><font color="Green">E243</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">red1</font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><font color="Maroon">red1</font> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">red1</font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span>
<b>by </b><i>, <a class="ref" href="polynom1.html#D21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">red1</font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">red1</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="groeb_3.html#T16" target="_self">Th16</a>, <a class="txt" href="groeb_3.html#E19:67_4_1_1"><i><font color="Green">E86</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a></i>
<br/>.= 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D22">POLYNOM1:def 22</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_13"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_4_1_1_13"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 ;<br/><a NAME="E2:67_4_1_1_13"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">z1</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span>
 <b>by </b><i><a class="ref" href="groeb_3.html#D2" target="_self">Def2</a>, <a class="ref" href="rlvect_1.html#T30">RLVECT_1:30</a></i>;<br/><b>hence </b><a NAME="E3:67_4_1_1_13"/>
contradiction
 <b>by </b><i>, <a class="ref" href="rlvect_1.html#T25">RLVECT_1:25</a></i>;<br/></div><b>end;</b></div><a NAME="E88:67_4_1_1"/><b>then </b>
 <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_3.html#E19:67_4_1_1"><i><font color="Green">E86</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E89:67_4_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polyred.html#R3">reduces_to</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span></span>)</span>,<font color="Maroon">p1</font>, <a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E6:67_4_1_1"><i><font color="Green">E80</font></i></a>, , , <a class="ref" href="polyred.html#D5">POLYRED:def 5</a></i>;<br/><a NAME="E90:67_4_1_1"/><b>then </b><i><font color="Green">E244</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polyred.html#R4">reduces_to</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span></span>)</span>,<font color="Maroon">p1</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#D6">POLYRED:def 6</a></i>;<br/><a NAME="E91:67_4_1_1"/>
<font color="Maroon">p1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="groeb_1.html#K1">{</a><span class="default"><font color="Maroon">p1</font></span><a href="groeb_1.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E92:67_4_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polyred.html#R5">reduces_to</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span></span>)</span>,<span class="p1"><a href="groeb_1.html#K1">{</a><span class="default"><font color="Maroon">p1</font></span><a href="groeb_1.html#K1">}</a></span>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="polyred.html#D7">POLYRED:def 7</a></i>;<br/><a NAME="E93:67_4_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="polyred.html#K3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1">{</a><span class="default"><font color="Maroon">p1</font></span><a href="groeb_1.html#K1">}</a></span>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#D13">POLYRED:def 13</a></i>;<br/><a NAME="E94:67_4_1_1"/><b>then </b><i><font color="Green">E245</font></i>: 
 <a href="polyred.html#K3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1">{</a><span class="default"><font color="Maroon">p1</font></span><a href="groeb_1.html#K1">}</a></span>,<font color="Maroon">T</font> <a href="rewrite1.html#R1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rewrite1.html#T16">REWRITE1:16</a></i>;<br/><a NAME="E95:67_4_1_1"/>
<font color="Maroon">p1</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="E96:67_4_1_1"/><b>then </b><i><font color="Green">E246</font></i>: 
 <a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="termord.html#T17">TERMORD:17</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> = 
 <a href="polynom7.html#K2">term</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">lowz1w</font></span>)</span>
<b>by </b><i><a class="txt" href="groeb_3.html#E13:67"><i><font color="Green">E46</font></i></a>, , , <a class="txt" href="groeb_3.html#E17:67_4_1_1"><i><font color="Green">E85</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowz1w</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowz1w</font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T22">TERMORD:22</a></i>
;<br/><b>then </b><i><font color="Green">E247</font></i>: <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowz1w</font></span>)</span></span>)</span> <a href="polynom1.html#K10">-'</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T52">POLYNOM1:52</a></i>
<br/>.= 
 <a href="polynom7.html#K2">term</a> <font color="Maroon">lowz1w</font>
<b>by </b><i><a class="ref" href="polynom1.html#T52">POLYNOM1:52</a></i>
;<br/><a NAME="E99:67_4_1_1"/>
<font color="Maroon">w</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">z1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i/>;<br/><a NAME="E100:67_4_1_1"/><b>then </b><i><font color="Green">E248</font></i>: 
<font color="Maroon">w</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">z1</font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E101:67_4_1_1"/>
<font color="Maroon">lowz1w</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="E102:67_4_1_1"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">lowz1w</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="E103:67_4_1_1"/><b>then </b><i><font color="Green">E249</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">lowz1w</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowz1w</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="polynom7.html#T7">POLYNOM7:7</a></i>;<br/><a NAME="E104:67_4_1_1"/><b>then </b><i><font color="Green">E250</font></i>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">lowz1w</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E105:67_4_1_1"/><i><font color="Green">E251</font></i>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="groeb_3.html#K4" target="_self">Lower_Support</a> <font color="Maroon">z1</font>,<font color="Maroon">T</font>,<font color="Maroon">w</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E106:67_4_1_1"/><i><font color="Green">E252</font></i>: 
 <a href="polynom7.html#K1">Monom</a> <span class="p1">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="termord.html#K5">HM</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_16"><b>proof </b></a><div class="add">

<div><i><font color="Green">E253</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_16_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">t</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>;<br/><b>assume </b><a NAME="E1:67_4_1_1_16_1"/><i><font color="Green">E254</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">z1</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_16_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_4_1_1_16_1_1"/><i><font color="Green">E255</font></i>: 
<font color="Maroon">t</font> <a href="termord.html#R2">&lt;</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font>
 ;<br/><a NAME="E2:67_4_1_1_16_1_1"/><b>then </b>
<font color="Maroon">t</font> <a href="termord.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/><a NAME="E3:67_4_1_1_16_1_1"/><b>then </b>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="groeb_3.html#K4" target="_self">Lower_Support</a> <font color="Maroon">z1</font>,<font color="Maroon">T</font>,<font color="Maroon">w</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E20:67_4_1_1"><i><font color="Green">E115</font></i></a>, , , </i>;<br/><a NAME="E4:67_4_1_1_16_1_1"/><b>then </b>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">lowz1w</font>
 <b>by </b><i>, </i>;<br/><a NAME="E5:67_4_1_1_16_1_1"/><b>then </b>
<font color="Maroon">t</font> <a href="hidden.html#R1">=</a>  <a href="polynom7.html#K2">term</a> <font color="Maroon">lowz1w</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:67_4_1_1_16_1_1"/>
contradiction
 <b>by </b><i>, <a class="txt" href="groeb_3.html#E24"><i><font color="Green">Lemma119</font></i></a>, <a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:67_4_1_1_16_1"/>
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">t</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T5">TERMORD:5</a></i>;<br/></div><b>end;</b></div>
<b>set </b><font color="Maroon">r</font> =  <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font>;<br/>
<a NAME="E2:67_4_1_1_16"/>
<span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span> <a href="xboole_0.html#K4">\</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#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:67_4_1_1_16"/><b>then </b><i><font color="Green">E256</font></i>: 
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</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#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span> <a href="xboole_0.html#K4">\</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#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:67_4_1_1_16"/><b>then </b><i><font color="Green">E257</font></i>: 
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<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="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E5:67_4_1_1_16"/><b>then </b><i><font color="Green">E258</font></i>: 
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="groeb_3.html#K4" target="_self">Lower_Support</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:67_4_1_1_16"/><i><font color="Green">E259</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:67_4_1_1_16"/><i><font color="Green">E260</font></i>: 
not  <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<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="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_16_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_4_1_1_16_2"/><i><font color="Green">E261</font></i>: 
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font> <a href="hidden.html#R1">=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>
 ;<br/><div><i><font color="Green">E262</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_16_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:67_4_1_1_16_2_1"/><i><font color="Green">E263</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font>
 ;<br/><b>then reconsider </b><font color="Maroon">u'</font> = <font color="Maroon">u</font> as    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> ;<br/><a NAME="E3:67_4_1_1_16_2_1"/>
<font color="Maroon">u'</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="groeb_3.html#T23" target="_self">Th23</a>, <a class="txt" href="groeb_3.html#E33"><i><font color="Green">Lemma125</font></i></a>, <a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E4:67_4_1_1_16_2_1"/><b>then </b>
<font color="Maroon">u'</font> <a href="hidden.html#R2">in</a>  <a href="groeb_3.html#K4" target="_self">Lower_Support</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="groeb_3.html#T19" target="_self">Th19</a>, <a class="txt" href="groeb_3.html#E33"><i><font color="Green">Lemma125</font></i></a>, , </i>;<br/><b>hence </b><a NAME="E5:67_4_1_1_16_2_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><a NAME="E3:67_4_1_1_16_2"/>
for <font color="Olive">u</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">u</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span> holds <br/><font color="Olive">u</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font>
 <b>by </b><i><a class="ref" href="groeb_3.html#T20" target="_self">Th20</a></i>;<br/><a NAME="E4:67_4_1_1_16_2"/><b>then </b><i><font color="Green">E264</font></i>: 
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</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">p2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="groeb_3.html#T24" target="_self">Th24</a>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><b>thus </b><a NAME="E5:67_4_1_1_16_2"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_3.html#E33"><i><font color="Green">Lemma125</font></i></a>, <a class="ref" href="groeb_3.html#T10" target="_self">Th10</a></i>;<br/></div><b>end;</b></div>
<a NAME="E9:67_4_1_1_16"/><b>then </b><i><font color="Green">E265</font></i>: 
not  <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E10:67_4_1_1_16"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="termord.html#T36">TERMORD:36</a></i>;<br/>
<a NAME="E11:67_4_1_1_16"/><b>then </b><i><font color="Green">E266</font></i>: 
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font>
 
<b>by </b><i><a class="ref" href="groeb_3.html#T23" target="_self">Th23</a>, <a class="txt" href="groeb_3.html#E24"><i><font color="Green">Lemma119</font></i></a>, <a class="ref" href="groeb_3.html#T20" target="_self">Th20</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D22">POLYNOM1:def 22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="groeb_3.html#T22" target="_self">Th22</a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T25">RLVECT_1:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</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> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a></i>
;<br/>
<a NAME="E13:67_4_1_1_16"/><b>then </b>
<font color="Maroon">z1</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="groeb_3.html#T24" target="_self">Th24</a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/>
<a NAME="E14:67_4_1_1_16"/><b>then </b>
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">z1</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/>
<a NAME="E15:67_4_1_1_16"/><b>then </b><i><font color="Green">E267</font></i>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 
<b>by </b><i/>;<br/>
<a NAME="E16:67_4_1_1_16"/>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">red2</font> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p2</font>
 
<b>by </b><i><a class="ref" href="termord.html#T35">TERMORD:35</a></i>;<br/>
<a NAME="E17:67_4_1_1_16"/><b>then </b>
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="groeb_3.html#K4" target="_self">Lower_Support</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font>
 
<b>by </b><i>, , <a class="ref" href="groeb_3.html#T19" target="_self">Th19</a>, <a class="txt" href="groeb_3.html#E33"><i><font color="Green">Lemma125</font></i></a>, </i>;<br/>
<a NAME="E18:67_4_1_1_16"/><b>then </b><i><font color="Green">E268</font></i>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E19:67_4_1_1_16"/><b>then </b>
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</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#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span> <a href="xboole_0.html#K4">\</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#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E20:67_4_1_1_16"/><b>then </b>
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E21:67_4_1_1_16"/><b>then </b><i><font color="Green">E269</font></i>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then </b><i><font color="Green">E270</font></i>: <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<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> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T18">TERMORD:18</a></i>
<br/>.= 
<font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i>, , </i>
;<br/>
 <a href="termord.html#K4">HC</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font> = 
<span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#D7">TERMORD:def 7</a></i>
<br/>.= 
<font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="groeb_3.html#T25" target="_self">Th25</a>, <a class="ref" href="termord.html#T18">TERMORD:18</a></i>
;<br/>
<b>hence </b><a NAME="E24:67_4_1_1_16"/>
 <a href="polynom7.html#K1">Monom</a> <span class="p1">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="termord.html#K5">HM</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="termord.html#D8">TERMORD:def 8</a></i>;<br/>


</div><b>end;</b></div><i><font color="Green">E271</font></i>:  <a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font> = 
<span class="p1">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i>, <a class="ref" href="termord.html#T38">TERMORD:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="groeb_3.html#E10:67"><i><font color="Green">E45</font></i></a></i>
;<br/><i><font color="Green">E272</font></i>:  <a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font> = 
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font>
<b>by </b><i><a class="ref" href="termord.html#T26">TERMORD:26</a></i>
<br/>.= 
 <a href="polynom7.html#K2">term</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T23">TERMORD:23</a></i>
;<br/><a NAME="E109:67_4_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_19"><b>proof </b></a><div class="add">

<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="groeb_3.html#T12" target="_self">Th12</a>, <a class="ref" href="groeb_2.html#D1">GROEB_2:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="polyred.html#T7">POLYRED:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T18">TERMORD:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#D7">TERMORD:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">red2</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="groeb_3.html#T15" target="_self">Th15</a>, , <a class="ref" href="groeb_3.html#T14" target="_self">Th14</a>, <a class="ref" href="termord.html#T40">TERMORD:40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D22">POLYNOM1:def 22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="groeb_3.html#E18"><i><font color="Green">Lemma104</font></i></a>, <a class="ref" href="rlvect_1.html#T25">RLVECT_1:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a></i>
;<br/>
<b>hence </b><a NAME="E2:67_4_1_1_19"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="groeb_3.html#D2" target="_self">Def2</a></i>;<br/>


</div><b>end;</b></div><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p2">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p2">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T41">VECTSP_1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D23">VECTSP_1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="vectsp_1.html#D22">VECTSP_1:def 22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D5">GROUP_1:def 5</a></i>
;<br/><b>then </b><i><font color="Green">E273</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T9">POLYRED:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polyred.html#K1">*'</a> <font color="Maroon">p1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30">RLVECT_1:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p1</font></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T22">POLYRED:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T38">TERMORD:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p0">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p4">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p4">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T85">POLYNOM1:85</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p4">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p4">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p4">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p4">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80">POLYNOM1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p4">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p5">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80">POLYNOM1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p5">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T6">POLYRED:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p5">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80">POLYNOM1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p5">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T85">POLYNOM1:85</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p4">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p5">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p4">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80">POLYNOM1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p4">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p5">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="polynom1.html#T85">POLYNOM1:85</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p0">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p4">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p5">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p0">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p5">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p0">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p4">(<span class="default"><a href="polynom7.html#K1">Monom</a> <span class="p5">(<span class="default"><font color="Maroon">p2</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">lowzw</font></span>)</span> <a href="groeb_2.html#K1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T1">POLYRED:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p4">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p5">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="polynom1.html#T80">POLYNOM1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p5">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T1">POLYRED:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T6">POLYRED:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
;<br/><a NAME="E112:67_4_1_1"/>
 <a href="polyred.html#K3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1">{</a><span class="default"><font color="Maroon">p1</font></span><a href="groeb_1.html#K1">}</a></span>,<font color="Maroon">T</font> <a href="rewrite1.html#R1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p5">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="txt" href="groeb_3.html#E1:67_4_1"><i><font color="Green">E71</font></i></a></i>;<br/><b>hence </b><a NAME="E113:67_4_1_1"/>
 <a href="polyred.html#K3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1">{</a><span class="default"><font color="Maroon">p1</font></span><a href="groeb_1.html#K1">}</a></span>,<font color="Maroon">T</font> <a href="rewrite1.html#R1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,<font color="Maroon">m</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="rewrite1.html#T17">REWRITE1:17</a>, <a class="txt" href="groeb_3.html#E24"><i><font color="Green">Lemma119</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:67_4_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:67_4"/>
(  not <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font>] or <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1] )
 ;<br/>


</div><b>end;</b></div>
<a NAME="E15:67"/><i><font color="Green">E274</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j'</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">i</font>]
 
<b>from </b><i><a class="ref" href="polynom2.html#S4">POLYNOM2:sch 4</a>(, );<br/></i>
<a NAME="E16:67"/><i><font color="Green">E275</font></i>: 
 <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#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">j'</font>
 
<b>by </b><i>, <a class="ref" href="groeb_3.html#T3" target="_self">Th3</a></i>;<br/>
<i><font color="Green">E276</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p4">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="groeb_3.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T83">POLYNOM1:83</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T5">POLYRED:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" target="_self">Low</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font>,1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T4">POLYRED:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="groeb_3.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T85">POLYNOM1:85</a></i>
<br/>.= 
<font color="Maroon">p2</font> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T38">TERMORD:38</a></i>
;<br/>
<b>thus </b><a NAME="E18:67"/>
 <a href="polyred.html#K3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1">{</a><span class="default"><font color="Maroon">p1</font></span><a href="groeb_1.html#K1">}</a></span>,<font color="Maroon">T</font> <a href="rewrite1.html#R1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p2</font>,<font color="Maroon">T</font></span>)</span></span>)</span>,<font color="Maroon">p2</font> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">p1</font>,<font color="Maroon">T</font></span>)</span>
 <b>by </b><i><a class="ref" href="groeb_3.html#T10" target="_self">Th10</a>, , , </i>;<br/>


</div>
