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

<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">T</font> being  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>  <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font><br/> for <font color="Olive" title="b2">L</font> being non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/> for <font color="Olive" title="b3">p</font> being  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">L</font> holds <br/> (  <a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">T</font>,1 <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">T</font> &amp;  <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">T</font>,1 <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">T</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">T</font> be   <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>  <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">L</font> being non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/> for <font color="Olive" title="b2">p</font> being  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font> holds <br/> (  <a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">T</font>,1 <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">T</font> &amp;  <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">T</font>,1 <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">T</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">L</font> be  non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> holds <br/> (  <a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font>,1 <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font> &amp;  <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font>,1 <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font> be   <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1 <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font> &amp;  <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1 <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font> )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">u</font> =  <a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">l</font> =  <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1;<br/>
<div><span class="lab"><font color="Green" title="E37">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:44_1"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c4">p</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:44_1"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T14" title="NAT_1:th.14">NAT_1:14</a></span>;<br/><a NAME="E3:44_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:44_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E2:44"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="groeb_3.html#K3" title="GROEB_3:func.3">Upper_Support</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="groeb_3.html#E32"><span class="lab"><font color="Green" title="E25">Lm3</font></span></a></span>;<br/>
<a NAME="E3:44"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="groeb_3.html#D2" target="_self" title="GROEB_3:def.2">Def2</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E5:44"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T60" title="CARD_2:th.60">CARD_2:60</a></span>;<br/>
<a NAME="E6:44"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="txt" href="#E5:44"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="ref" href="groeb_3.html#T30" target="_self" title="GROEB_3:th.30">Th30</a></span>;<br/>
<a NAME="E7:44"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A3</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:44"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E8:44"/>
 <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></span>;<br/>
<a NAME="E9:44"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/>
<a NAME="E10:44"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A4</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:44"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="ref" href="termord.html#T21" title="TERMORD:th.21">TERMORD:21</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E41">A5</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="44_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> implies <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:44_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">x9</font> = <font color="Maroon" title="c8">x</font> as    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font> ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:44_2_1_1"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> or  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_2_1_1_1"><span class="kw">case </span></a><a NAME="E1:44_2_1_1_1"/><span class="lab"><font color="Green" title="E42">A6</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c9">x9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c9">x9</font></span><br/><div class="add"><a NAME="E2:44_2_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">x9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:44"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="txt" href="#E10:44"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c9">x9</font> = 
<font color="Maroon" title="c4">p</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c9">x9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T18" title="TERMORD:th.18">TERMORD:18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c9">x9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:44"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="txt" href="#E1:44_2_1_1_1"><span class="lab"><font color="Green" title="E42">A6</font></span></a>, <a class="ref" href="groeb_3.html#T16" target="_self" title="GROEB_3:th.16">Th16</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_2_1_1_2"><span class="kw">case </span></a><a NAME="E1:44_2_1_1_2"/><span class="lab"><font color="Green" title="E42">A7</font></span>: 
not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c9">x9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c9">x9</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c9">x9</font> = 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c9">x9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:44"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="txt" href="#E1:44_2_1_1_2"><span class="lab"><font color="Green" title="E42">A7</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:44_2"/>
<span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> = 
 <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
<br/>.= 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E13:44"/>
 <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="groeb_3.html#K5" title="GROEB_3:func.5">Up</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:44"><span class="lab"><font color="Green" title="E41">A5</font></span></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1 <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span><br/>

<a NAME="E14:44"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A8</font></span>: 
<span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="groeb_3.html#T33" target="_self" title="GROEB_3:th.33">Th33</a></span>;<br/>
<span class="kw">thus </span> <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font> = 
<font color="Maroon" title="c4">p</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D9" title="TERMORD:def.9">TERMORD:def 9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:44"><span class="lab"><font color="Green" title="E42">A8</font></span></a>, <a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T80" title="POLYNOM1:th.80">POLYNOM1:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T3" title="POLYRED:th.3">POLYRED:3</a></span>
<br/>.= 
 <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,1
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T2" title="POLYRED:th.2">POLYRED:2</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
