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

<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/><b>let </b><font color="Maroon" title="c2">T</font> be  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a> <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font>;<br/><b>let </b><font color="Maroon" title="c3">L</font> be  non <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a> <a href="group_1.html#V6" title="GROUP_1:attr.6">commutative</a> <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">well-unital</a> <a href="vectsp_1.html#V8" title="VECTSP_1:attr.8">distributive</a> <a href="vectsp_1.html#NV11" title="VECTSP_1:NV.11">Field-like</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c4">P</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30" title="POLYNOM1:func.30">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c5">f</font>, <font color="Maroon" title="c6">g</font>, <font color="Maroon" title="c7">h</font>, <font color="Maroon" title="c8">h1</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>;<br/>









<b>assume </b><a NAME="E1:84"/><i><font color="Green" title="E64">A1</font></i>: 
( <font color="Maroon" title="c5">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c6">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c7">h</font> &amp;  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c7">h</font>,<font color="Maroon" title="c8">h1</font> )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ] <b>means </b>for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font>, <font color="Olive" title="b3">h</font> being  <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  st <font color="Olive" title="b1">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Olive" title="b2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">h</font> holds <br/>for <font color="Olive" title="b4">h1</font> being  <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font><br/> for <font color="Olive" title="b5">p</font> being   <a href="rewrite1.html#M1" title="REWRITE1:mode.1">RedSequence</a> of  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>  st <font color="Olive" title="b5">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">h</font> &amp; <font color="Olive" title="b5">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">h1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 holds <br/> ex <font color="Olive" title="b6">f1</font>, <font color="Olive" title="b7">g1</font> being  <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> st <br/>( <font color="Olive" title="b6">f1</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Olive" title="b7">g1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b4">h1</font> &amp;  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b6">f1</font> &amp;  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Olive" title="b2">g</font>,<font color="Olive" title="b7">g1</font> );<br/>
<a NAME="E2:84"/><i><font color="Green" title="E65">A2</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">f</font>, <font color="Maroon" title="c10">g</font>, <font color="Maroon" title="c11">h</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>;<br/>

<b>assume </b><a NAME="E1:84_1"/><i><font color="Green" title="E66">A3</font></i>: 
<font color="Maroon" title="c9">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c10">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c11">h</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c12">h1</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>;<br/><b>let </b><font color="Maroon" title="c13">p</font> be    <a href="rewrite1.html#M1" title="REWRITE1:mode.1">RedSequence</a> of  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>;<br/>



<b>assume </b><a NAME="E2:84_1"/><i><font color="Green" title="E67">A4</font></i>: 
( <font color="Maroon" title="c13">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">h</font> &amp; <font color="Maroon" title="c13">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">h1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 ;<br/>

<b>take </b>
<font color="Maroon" title="c9">f</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c10">g</font>
;<br/>

<b>thus </b><a NAME="E3:84_1"/>
( <font color="Maroon" title="c9">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c10">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c12">h1</font> &amp;  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c9">f</font> &amp;  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c10">g</font>,<font color="Maroon" title="c10">g</font> )
 <b>by </b><i><a class="txt" href="polyred.html#E1:84_1"><i><font color="Green" title="E66">A3</font></i></a>, <a class="txt" href="polyred.html#E2:84_1"><i><font color="Green" title="E67">A4</font></i></a>, <a class="ref" href="rewrite1.html#T13" title="REWRITE1:th.13">REWRITE1:13</a></i>;<br/>


</div><b>end;</b></div>
<div><i><font color="Green" title="E66">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:84_2"/><i><font color="Green" title="E67">A6</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">k</font>
 ;<br/><b>assume </b><a NAME="E2:84_2"/><i><font color="Green" title="E68">A7</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">k</font>]
 ;<br/><b>thus </b><a NAME="E3:84_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">f</font>, <font color="Maroon" title="c11">g</font>, <font color="Maroon" title="c12">h</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>;<br/>

<b>assume </b><a NAME="E1:84_2_1"/><i><font color="Green" title="E69">A8</font></i>: 
<font color="Maroon" title="c10">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c11">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c12">h</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c13">h1</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>;<br/><b>let </b><font color="Maroon" title="c14">r</font> be    <a href="rewrite1.html#M1" title="REWRITE1:mode.1">RedSequence</a> of  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>;<br/>



<b>assume </b><a NAME="E2:84_2_1"/><i><font color="Green" title="E70">A9</font></i>: 
( <font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">h</font> &amp; <font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">h1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 ;<br/>

<a NAME="E3:84_2_1"/><b>then </b><i><font color="Green" title="E71">A10</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c14">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<b>set </b><font color="Maroon" title="c15">h2</font> = <font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font>;<br/>
<a NAME="E4:84_2_1"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E5:84_2_1"/><b>then </b><i><font color="Green" title="E72">A11</font></i>: 
<font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c14">r</font>
 
<b>by </b><i><a class="txt" href="polyred.html#E3:84_2_1"><i><font color="Green" title="E71">A10</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E6:84_2_1"/>
<font color="Maroon" title="c9">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E7:84_2_1"/><b>then </b>
<font color="Maroon" title="c9">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c14">r</font>
 
<b>by </b><i><a class="txt" href="polyred.html#E1:84_2"><i><font color="Green" title="E67">A6</font></i></a>, <a class="txt" href="polyred.html#E3:84_2_1"><i><font color="Green" title="E71">A10</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E8:84_2_1"/><b>then </b><i><font color="Green" title="E73">A12</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 
<b>by </b><i><a class="txt" href="polyred.html#E5:84_2_1"><i><font color="Green" title="E72">A11</font></i></a>, <a class="ref" href="rewrite1.html#D2" title="REWRITE1:def.2">REWRITE1:def 2</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c16">x</font>, <font color="Maroon" title="c17">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E10:84_2_1"/><i><font color="Green" title="E74">A13</font></i>: 
( <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30" title="POLYNOM1:func.30">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30" title="POLYNOM1:func.30">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">x</font>,<font color="Maroon" title="c17">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<i><font color="Green" title="E75">A14</font></i>: <font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">x</font>,<font color="Maroon" title="c17">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<b>by </b><i><a class="txt" href="polyred.html#E10:84_2_1"><i><font color="Green" title="E74">A13</font></i></a>, <a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></i>
<br/>.= 
<font color="Maroon" title="c16">x</font>
<b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon" title="c18">h2</font> = <font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font> as   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> <b>by </b><i><a class="txt" href="polyred.html#E10:84_2_1"><i><font color="Green" title="E74">A13</font></i></a>, <a class="ref" href="polynom1.html#D27" title="POLYNOM1:def.27">POLYNOM1:def 27</a></i>;<br/>
<a NAME="E13:84_2_1"/>
not <font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</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"><span class="p2">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="polyred.html#E10:84_2_1"><i><font color="Green" title="E74">A13</font></i></a>, <a class="txt" href="polyred.html#E11:84_2_1"><i><font color="Green" title="E75">A14</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E14:84_2_1"/><b>then </b>
<font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c19">h2</font> = <font color="Maroon" title="c18">h2</font> as  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> <b>by </b><i><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></i>;<br/>
<b>set </b><font color="Maroon" title="c20">q</font> = <font color="Maroon" title="c14">r</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c9">k</font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c21">q</font> = <font color="Maroon" title="c14">r</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c9">k</font></span>)</span> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> <b>by </b><i><a class="ref" href="finseq_1.html#T19" title="FINSEQ_1:th.19">FINSEQ_1:19</a></i>;<br/>
<a NAME="E17:84_2_1"/><i><font color="Green" title="E76">A15</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c14">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="polyred.html#E2:84_2_1"><i><font color="Green" title="E70">A9</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E18:84_2_1"/><i><font color="Green" title="E77">A16</font></i>: 
<font color="Maroon" title="c9">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E19:84_2_1"/><b>then </b><i><font color="Green" title="E78">A17</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c21">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">k</font>
 
<b>by </b><i><a class="txt" href="polyred.html#E2:84_2_1"><i><font color="Green" title="E70">A9</font></i></a>, <a class="ref" href="finseq_1.html#T21" title="FINSEQ_1:th.21">FINSEQ_1:21</a></i>;<br/>
<a NAME="E20:84_2_1"/><i><font color="Green" title="E79">A18</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c21">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c9">k</font>
 
<b>by </b><i><a class="txt" href="polyred.html#E2:84_2_1"><i><font color="Green" title="E70">A9</font></i></a>, <a class="txt" href="polyred.html#E18:84_2_1"><i><font color="Green" title="E77">A16</font></i></a>, <a class="ref" href="finseq_1.html#T21" title="FINSEQ_1:th.21">FINSEQ_1:21</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c22">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:84_2_1_2"/><i><font color="Green" title="E80">A19</font></i>: 
( <font color="Maroon" title="c22">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c21">q</font> &amp; <font color="Maroon" title="c22">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c21">q</font> )
 ;<br/><a NAME="E2:84_2_1_2"/><b>then </b><i><font color="Green" title="E81">A20</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c22">i</font> &amp; <font color="Maroon" title="c22">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">k</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c22">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c22">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">k</font> )
 <b>by </b><i><a class="txt" href="polyred.html#E20:84_2_1"><i><font color="Green" title="E79">A18</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E3:84_2_1_2"/><b>then </b><i><font color="Green" title="E82">A21</font></i>: 
( <font color="Maroon" title="c22">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c22">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 <b>by </b><i><a class="txt" href="polyred.html#E18:84_2_1"><i><font color="Green" title="E77">A16</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E4:84_2_1_2"/><b>then </b><i><font color="Green" title="E83">A22</font></i>: 
<font color="Maroon" title="c22">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c14">r</font>
 <b>by </b><i><a class="txt" href="polyred.html#E17:84_2_1"><i><font color="Green" title="E76">A15</font></i></a>, <a class="txt" href="polyred.html#E2:84_2_1_2"><i><font color="Green" title="E81">A20</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E5:84_2_1_2"/>
<font color="Maroon" title="c22">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c14">r</font>
 <b>by </b><i><a class="txt" href="polyred.html#E17:84_2_1"><i><font color="Green" title="E76">A15</font></i></a>, <a class="txt" href="polyred.html#E2:84_2_1_2"><i><font color="Green" title="E81">A20</font></i></a>, <a class="txt" href="polyred.html#E3:84_2_1_2"><i><font color="Green" title="E82">A21</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E6:84_2_1_2"/><b>then </b><i><font color="Green" title="E84">A23</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E4:84_2_1_2"><i><font color="Green" title="E83">A22</font></i></a>, <a class="ref" href="rewrite1.html#D2" title="REWRITE1:def.2">REWRITE1:def 2</a></i>;<br/><a NAME="E7:84_2_1_2"/>
<font color="Maroon" title="c14">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">i</font>
 <b>by </b><i><a class="txt" href="polyred.html#E1:84_2_1_2"><i><font color="Green" title="E80">A19</font></i></a>, <a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>;<br/><b>hence </b><a NAME="E8:84_2_1_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c21">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c21">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E1:84_2_1_2"><i><font color="Green" title="E80">A19</font></i></a>, <a class="txt" href="polyred.html#E6:84_2_1_2"><i><font color="Green" title="E84">A23</font></i></a>, <a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c22">q</font> = <font color="Maroon" title="c21">q</font> as    <a href="rewrite1.html#M1" title="REWRITE1:mode.1">RedSequence</a> of  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <b>by </b><i><a class="txt" href="polyred.html#E1:84_2"><i><font color="Green" title="E67">A6</font></i></a>, <a class="txt" href="polyred.html#E19:84_2_1"><i><font color="Green" title="E78">A17</font></i></a>, <a class="ref" href="rewrite1.html#D2" title="REWRITE1:def.2">REWRITE1:def 2</a></i>;<br/>
<a NAME="E23:84_2_1"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c22">q</font>
 
<b>by </b><i><a class="txt" href="polyred.html#E1:84_2"><i><font color="Green" title="E67">A6</font></i></a>, <a class="txt" href="polyred.html#E20:84_2_1"><i><font color="Green" title="E79">A18</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E24:84_2_1"/><b>then </b><i><font color="Green" title="E80">A24</font></i>: 
<font color="Maroon" title="c22">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">h</font>
 
<b>by </b><i><a class="txt" href="polyred.html#E2:84_2_1"><i><font color="Green" title="E70">A9</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/>
<a NAME="E25:84_2_1"/><i><font color="Green" title="E81">A25</font></i>: 
<font color="Maroon" title="c9">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c22">q</font>
 
<b>by </b><i><a class="txt" href="polyred.html#E1:84_2"><i><font color="Green" title="E67">A6</font></i></a>, <a class="txt" href="polyred.html#E20:84_2_1"><i><font color="Green" title="E79">A18</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<font color="Maroon" title="c22">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c22">q</font></span>)</span> = 
<font color="Maroon" title="c22">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font>
<b>by </b><i><a class="txt" href="polyred.html#E2:84_2_1"><i><font color="Green" title="E70">A9</font></i></a>, <a class="txt" href="polyred.html#E18:84_2_1"><i><font color="Green" title="E77">A16</font></i></a>, <a class="ref" href="finseq_1.html#T21" title="FINSEQ_1:th.21">FINSEQ_1:21</a></i>
<br/>.= 
<font color="Maroon" title="c19">h2</font>
<b>by </b><i><a class="txt" href="polyred.html#E25:84_2_1"><i><font color="Green" title="E81">A25</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
;<br/>
<b>then consider </b><font color="Maroon" title="c23">f2</font>, <font color="Maroon" title="c24">g2</font> being   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font><b> such that </b><br/><a NAME="E28:84_2_1"/><i><font color="Green" title="E82">A26</font></i>: 
( <font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c24">g2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c19">h2</font> &amp;  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c23">f2</font> &amp;  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c11">g</font>,<font color="Maroon" title="c24">g2</font> )
 <b>by </b><i><a class="txt" href="polyred.html#E2:84_2"><i><font color="Green" title="E68">A7</font></i></a>, <a class="txt" href="polyred.html#E1:84_2_1"><i><font color="Green" title="E69">A8</font></i></a>, <a class="txt" href="polyred.html#E19:84_2_1"><i><font color="Green" title="E78">A17</font></i></a>, <a class="txt" href="polyred.html#E24:84_2_1"><i><font color="Green" title="E80">A24</font></i></a></i>;<br/>
<a NAME="E29:84_2_1"/>
<font color="Maroon" title="c19">h2</font> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a> <font color="Maroon" title="c13">h1</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 
<b>by </b><i><a class="txt" href="polyred.html#E2:84_2_1"><i><font color="Green" title="E70">A9</font></i></a>, <a class="txt" href="polyred.html#E8:84_2_1"><i><font color="Green" title="E73">A12</font></i></a>, <a class="ref" href="polyred.html#D13" target="_self" title="POLYRED:def.13">Def13</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c25">p</font> being   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font><b> such that </b><br/><a NAME="E31:84_2_1"/><i><font color="Green" title="E83">A27</font></i>: 
( <font color="Maroon" title="c25">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c19">h2</font> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a> <font color="Maroon" title="c13">h1</font>,<font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font> )
 <b>by </b><i><a class="ref" href="polyred.html#D7" target="_self" title="POLYRED:def.7">Def7</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c26">b</font> being   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E33:84_2_1"/><i><font color="Green" title="E84">A28</font></i>: 
<font color="Maroon" title="c19">h2</font> <a href="polyred.html#R3" title="POLYRED:pred.3">reduces_to</a> <font color="Maroon" title="c13">h1</font>,<font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c26">b</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E31:84_2_1"><i><font color="Green" title="E83">A27</font></i></a>, <a class="ref" href="polyred.html#D6" target="_self" title="POLYRED:def.6">Def6</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c27">s</font> being   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E35:84_2_1"/><i><font color="Green" title="E85">A29</font></i>: 
( <font color="Maroon" title="c27">s</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">b</font> &amp; <font color="Maroon" title="c13">h1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c19">h2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c19">h2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="polyred.html#E33:84_2_1"><i><font color="Green" title="E84">A28</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self" title="POLYRED:def.5">Def5</a></i>;<br/>
<b>set </b><font color="Maroon" title="c28">f1</font> = <font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c29">g1</font> = <font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>;<br/>
<i><font color="Green" title="E86">A30</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D23" title="VECTSP_1:def.23">VECTSP_1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D23" title="VECTSP_1:def.23">VECTSP_1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T41" title="VECTSP_1:th.41">VECTSP_1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D18" title="VECTSP_1:def.18">VECTSP_1:def 18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c24">g2</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D22" title="POLYNOM1:def.22">POLYNOM1:def 22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c24">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D21" title="POLYNOM1:def.21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c24">g2</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c24">g2</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D23" title="VECTSP_1:def.23">VECTSP_1:def 23</a></i>
;<br/>
<i><font color="Green" title="E87">A31</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p0">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c24">g2</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p0">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T1" target="_self" title="POLYRED:th.1">Th1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p0">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c24">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80" title="POLYNOM1:th.80">POLYNOM1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c24">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80" title="POLYNOM1:th.80">POLYNOM1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c24">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80" title="POLYNOM1:th.80">POLYNOM1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c24">g2</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c24">g2</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T9" target="_self" title="POLYRED:th.9">Th9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c24">g2</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p0">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T10" target="_self" title="POLYRED:th.10">Th10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c24">g2</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p0">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T9" target="_self" title="POLYRED:th.9">Th9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c24">g2</font></span>)</span> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p0">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c24">g2</font></span>)</span> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p0">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T45" title="RLVECT_1:th.45">RLVECT_1:45</a></i>
<br/>.= 
<font color="Maroon" title="c13">h1</font>
<b>by </b><i><a class="txt" href="polyred.html#E28:84_2_1"><i><font color="Green" title="E82">A26</font></i></a>, <a class="txt" href="polyred.html#E35:84_2_1"><i><font color="Green" title="E85">A29</font></i></a>, <a class="txt" href="polyred.html#E36:84_2_1"><i><font color="Green" title="E86">A30</font></i></a>, <a class="ref" href="rlvect_1.html#T30" title="RLVECT_1:th.30">RLVECT_1:30</a></i>
;<br/>
<div><i><font color="Green" title="E88">A32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2_1_6"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_2_1_6_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:84_2_1_6_1"/>
(  not <font color="Maroon" title="c26">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c23">f2</font> or <font color="Maroon" title="c26">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c23">f2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_2_1_6_1_1"><b>case </b></a><a NAME="E1:84_2_1_6_1_1"/><i><font color="Green" title="E89">A33</font></i>: 
not <font color="Maroon" title="c26">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c23">f2</font>
 ;<br/><div class="add"><a NAME="E2:84_2_1_6_1_1"/>
<font color="Maroon" title="c26">b</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D14" title="POLYNOM1:def.14">POLYNOM1:def 14</a></i>;<br/><a NAME="E3:84_2_1_6_1_1"/><b>then </b>
<font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="txt" href="polyred.html#E1:84_2_1_6_1_1"><i><font color="Green" title="E89">A33</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><b>then </b><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D23" title="VECTSP_1:def.23">VECTSP_1:def 23</a></i>
<br/>.= 
<font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binom.html#T1" title="BINOM:th.1">BINOM:1</a></i>
<br/>.= 
<font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T8" target="_self" title="POLYRED:th.8">Th8</a></i>
<br/>.= 
<font color="Maroon" title="c23">f2</font>
<b>by </b><i><a class="ref" href="polyred.html#T4" target="_self" title="POLYRED:th.4">Th4</a></i>
;<br/><b>hence </b><a NAME="E5:84_2_1_6_1_1"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E28:84_2_1"><i><font color="Green" title="E82">A26</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_2_1_6_1_2"><b>case </b></a><a NAME="E1:84_2_1_6_1_2"/><i><font color="Green" title="E89">A34</font></i>: 
<font color="Maroon" title="c26">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c23">f2</font>
 ;<br/><div class="add"><a NAME="E2:84_2_1_6_1_2"/><b>then </b>
<font color="Maroon" title="c23">f2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c30">f2</font> = <font color="Maroon" title="c23">f2</font> as  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> <b>by </b><i><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></i>;<br/><a NAME="E4:84_2_1_6_1_2"/>
( <font color="Maroon" title="c30">f2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c25">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> )
 <b>by </b><i><a class="txt" href="polyred.html#E31:84_2_1"><i><font color="Green" title="E83">A27</font></i></a>, <a class="txt" href="polyred.html#E74"><i><font color="Green" title="E59">Lm18</font></i></a>, <a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></i>;<br/><a NAME="E5:84_2_1_6_1_2"/><b>then </b>
<font color="Maroon" title="c30">f2</font> <a href="polyred.html#R3" title="POLYRED:pred.3">reduces_to</a> <font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c26">b</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E35:84_2_1"><i><font color="Green" title="E85">A29</font></i></a>, <a class="txt" href="polyred.html#E1:84_2_1_6_1_2"><i><font color="Green" title="E89">A34</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self" title="POLYRED:def.5">Def5</a></i>;<br/><a NAME="E6:84_2_1_6_1_2"/><b>then </b>
<font color="Maroon" title="c30">f2</font> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a> <font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#D6" target="_self" title="POLYRED:def.6">Def6</a></i>;<br/><a NAME="E7:84_2_1_6_1_2"/><b>then </b>
<font color="Maroon" title="c30">f2</font> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a> <font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E31:84_2_1"><i><font color="Green" title="E83">A27</font></i></a>, <a class="ref" href="polyred.html#D7" target="_self" title="POLYRED:def.7">Def7</a></i>;<br/><a NAME="E8:84_2_1_6_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c30">f2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#D13" target="_self" title="POLYRED:def.13">Def13</a></i>;<br/><a NAME="E9:84_2_1_6_1_2"/><b>then </b>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c30">f2</font>,<font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rewrite1.html#T16" title="REWRITE1:th.16">REWRITE1:16</a></i>;<br/><b>hence </b><a NAME="E10:84_2_1_6_1_2"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c23">f2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E28:84_2_1"><i><font color="Green" title="E82">A26</font></i></a>, <a class="ref" href="rewrite1.html#T17" title="REWRITE1:th.17">REWRITE1:17</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2_1_7"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_2_1_7_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:84_2_1_7_1"/>
(  not <font color="Maroon" title="c26">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c24">g2</font> or <font color="Maroon" title="c26">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c24">g2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_2_1_7_1_1"><b>case </b></a><a NAME="E1:84_2_1_7_1_1"/><i><font color="Green" title="E89">A35</font></i>: 
not <font color="Maroon" title="c26">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c24">g2</font>
 ;<br/><div class="add"><a NAME="E2:84_2_1_7_1_1"/>
<font color="Maroon" title="c26">b</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D14" title="POLYNOM1:def.14">POLYNOM1:def 14</a></i>;<br/><a NAME="E3:84_2_1_7_1_1"/><b>then </b>
<font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="txt" href="polyred.html#E1:84_2_1_7_1_1"><i><font color="Green" title="E89">A35</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><b>then </b><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D23" title="VECTSP_1:def.23">VECTSP_1:def 23</a></i>
<br/>.= 
<font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binom.html#T1" title="BINOM:th.1">BINOM:1</a></i>
<br/>.= 
<font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T8" target="_self" title="POLYRED:th.8">Th8</a></i>
<br/>.= 
<font color="Maroon" title="c24">g2</font>
<b>by </b><i><a class="ref" href="polyred.html#T4" target="_self" title="POLYRED:th.4">Th4</a></i>
;<br/><b>hence </b><a NAME="E5:84_2_1_7_1_1"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c11">g</font>,<font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E28:84_2_1"><i><font color="Green" title="E82">A26</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_2_1_7_1_2"><b>case </b></a><a NAME="E1:84_2_1_7_1_2"/><i><font color="Green" title="E89">A36</font></i>: 
<font color="Maroon" title="c26">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c24">g2</font>
 ;<br/><div class="add"><a NAME="E2:84_2_1_7_1_2"/><b>then </b>
<font color="Maroon" title="c24">g2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c30">g2</font> = <font color="Maroon" title="c24">g2</font> as  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> <b>by </b><i><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></i>;<br/><a NAME="E4:84_2_1_7_1_2"/>
( <font color="Maroon" title="c30">g2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c25">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> )
 <b>by </b><i><a class="txt" href="polyred.html#E31:84_2_1"><i><font color="Green" title="E83">A27</font></i></a>, <a class="txt" href="polyred.html#E74"><i><font color="Green" title="E59">Lm18</font></i></a>, <a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></i>;<br/><a NAME="E5:84_2_1_7_1_2"/><b>then </b>
<font color="Maroon" title="c30">g2</font> <a href="polyred.html#R3" title="POLYRED:pred.3">reduces_to</a> <font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c26">b</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E35:84_2_1"><i><font color="Green" title="E85">A29</font></i></a>, <a class="txt" href="polyred.html#E1:84_2_1_7_1_2"><i><font color="Green" title="E89">A36</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self" title="POLYRED:def.5">Def5</a></i>;<br/><a NAME="E6:84_2_1_7_1_2"/><b>then </b>
<font color="Maroon" title="c30">g2</font> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a> <font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#D6" target="_self" title="POLYRED:def.6">Def6</a></i>;<br/><a NAME="E7:84_2_1_7_1_2"/><b>then </b>
<font color="Maroon" title="c30">g2</font> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a> <font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E31:84_2_1"><i><font color="Green" title="E83">A27</font></i></a>, <a class="ref" href="polyred.html#D7" target="_self" title="POLYRED:def.7">Def7</a></i>;<br/><a NAME="E8:84_2_1_7_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c30">g2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#D13" target="_self" title="POLYRED:def.13">Def13</a></i>;<br/><a NAME="E9:84_2_1_7_1_2"/><b>then </b>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c30">g2</font>,<font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rewrite1.html#T16" title="REWRITE1:th.16">REWRITE1:16</a></i>;<br/><b>hence </b><a NAME="E10:84_2_1_7_1_2"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c11">g</font>,<font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c24">g2</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c26">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c25">p</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E28:84_2_1"><i><font color="Green" title="E82">A26</font></i></a>, <a class="ref" href="rewrite1.html#T17" title="REWRITE1:th.17">REWRITE1:17</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E40:84_2_1"/>
 ex <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">g1</font> being  <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> st <br/>( <font color="Olive" title="b1">f1</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Olive" title="b2">g1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c13">h1</font> &amp;  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c10">f</font>,<font color="Olive" title="b1">f1</font> &amp;  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c11">g</font>,<font color="Olive" title="b2">g1</font> )
 <b>by </b><i><a class="txt" href="polyred.html#E37:84_2_1"><i><font color="Green" title="E87">A31</font></i></a>, <a class="txt" href="polyred.html#E38:84_2_1"><i><font color="Green" title="E88">A32</font></i></a></i>;<br/>


</div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E4:84"/><i><font color="Green" title="E67">A37</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S8" title="NAT_1:sch.8">NAT_1:sch 8</a>(<a class="txt" href="polyred.html#E2:84"><i><font color="Green" title="E65">A2</font></i></a>, <a class="txt" href="polyred.html#E3:84"><i><font color="Green" title="E66">A5</font></i></a>);<br/></i>
<b>consider </b><font color="Maroon" title="c9">p</font> being    <a href="rewrite1.html#M1" title="REWRITE1:mode.1">RedSequence</a> of  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font><b> such that </b><br/><a NAME="E6:84"/><i><font color="Green" title="E68">A38</font></i>: 
( <font color="Maroon" title="c9">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">h</font> &amp; <font color="Maroon" title="c9">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">h1</font> )
 <b>by </b><i><a class="txt" href="polyred.html#E1:84"><i><font color="Green" title="E64">A1</font></i></a>, <a class="ref" href="rewrite1.html#D3" title="REWRITE1:def.3">REWRITE1:def 3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E8:84"/><i><font color="Green" title="E69">A39</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">k</font>
 ;<br/>
<a NAME="E9:84"/>
<font color="Maroon" title="c10">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="polyred.html#E8:84"><i><font color="Green" title="E69">A39</font></i></a>, <a class="ref" href="rewrite1.html#D2" title="REWRITE1:def.2">REWRITE1:def 2</a></i>;<br/>
<a NAME="E10:84"/><b>then </b>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">k</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T14" title="NAT_1:th.14">NAT_1:14</a></i>;<br/>
<b>hence </b><a NAME="E11:84"/>
 ex <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">g1</font> being  <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> st <br/>( <font color="Olive" title="b1">f1</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Olive" title="b2">g1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">h1</font> &amp;  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c5">f</font>,<font color="Olive" title="b1">f1</font> &amp;  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c6">g</font>,<font color="Olive" title="b2">g1</font> )
 <b>by </b><i><a class="txt" href="polyred.html#E1:84"><i><font color="Green" title="E64">A1</font></i></a>, <a class="txt" href="polyred.html#E4:84"><i><font color="Green" title="E67">A37</font></i></a>, <a class="txt" href="polyred.html#E6:84"><i><font color="Green" title="E68">A38</font></i></a>, <a class="txt" href="polyred.html#E8:84"><i><font color="Green" title="E69">A39</font></i></a></i>;<br/>


</div>
