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

<b>let </b><font color="Maroon">n</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="group_1.html#V2">unital</a> <a href="vectsp_1.html#V7">distributive</a> non <a href="realset2.html#V3">trivial</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">P</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="ideal_1.html#M2">LeftLinearCombination</a> of <font color="Maroon">P</font>;<br/>









<b>assume </b><a NAME="E1:47"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">A</font> <a href="groeb_2.html#R2" target="_self">is_MonomialRepresentation_of</a> <font color="Maroon">f</font>
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>for <font color="Olive">f</font> being  <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font><br/> for <font color="Olive">A</font> being   <a href="ideal_1.html#M2">LeftLinearCombination</a> of <font color="Maroon">P</font>  st <font color="Olive">A</font> <a href="groeb_2.html#R2" target="_self">is_MonomialRepresentation_of</a> <font color="Olive">f</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> holds <br/> <a href="polynom1.html#K12">Support</a> <font color="Olive">f</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font></span>)</span></span>)</span> where <font color="Olive">m</font> is   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> :  ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Olive">A</font> &amp; <font color="Olive">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> ) </span>}</span> ;<br/>
<a NAME="E2:47"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">f</font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="ideal_1.html#M2">LeftLinearCombination</a> of <font color="Maroon">P</font>;<br/>



<b>assume </b><a NAME="E1:47_1"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">A</font> <a href="groeb_2.html#R2" target="_self">is_MonomialRepresentation_of</a> <font color="Maroon">f</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<a NAME="E2:47_1"/><b>then </b>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K6">&lt;*&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T32">FINSEQ_1:32</a></i>;<br/>
<a NAME="E3:47_1"/><b>then </b>
 <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T60">RLVECT_1:60</a></i>;<br/>
<a NAME="E4:47_1"/><b>then </b>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:47_1"/><b>then </b>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/>
<a NAME="E6:47_1"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="polynom7.html#T1">POLYNOM7:1</a></i>;<br/>
<b>hence </b><a NAME="E7:47_1"/>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font></span>)</span></span>)</span> where <font color="Olive">m</font> is   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> :  ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E35</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="47_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:47_2"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font>]
 ;<br/><a NAME="E2:47_2"/>
for <font color="Olive">f</font> being  <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font><br/> for <font color="Olive">A</font> being   <a href="ideal_1.html#M2">LeftLinearCombination</a> of <font color="Maroon">P</font>  st <font color="Olive">A</font> <a href="groeb_2.html#R2" target="_self">is_MonomialRepresentation_of</a> <font color="Olive">f</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 holds <br/> <a href="polynom1.html#K12">Support</a> <font color="Olive">f</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font></span>)</span></span>)</span> where <font color="Olive">m</font> is   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> :  ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Olive">A</font> &amp; <font color="Olive">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> ) </span>}</span> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">f</font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="ideal_1.html#M2">LeftLinearCombination</a> of <font color="Maroon">P</font>;<br/>



<b>assume </b><a NAME="E1:47_2_1"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">A</font> <a href="groeb_2.html#R2" target="_self">is_MonomialRepresentation_of</a> <font color="Maroon">f</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/>

<a NAME="E2:47_2_1"/><b>then </b><i><font color="Green">E40</font></i>: 
(  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> holds <br/> ex <font color="Olive">m</font> being  <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> ex <font color="Olive">p</font> being  <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> st <br/>( <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> ) ) )
 
<b>by </b><i/>;<br/>
<a NAME="E3:47_2_1"/>
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K6">&lt;*&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T32">FINSEQ_1:32</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">A</font> = <font color="Maroon">A</font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="ideal_1.html#M2">LeftLinearCombination</a> of <font color="Maroon">P</font> ;<br/>
<b>consider </b><font color="Maroon">A'</font> being    <a href="ideal_1.html#M2">LeftLinearCombination</a> of <font color="Maroon">P</font>, <font color="Maroon">e</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span><b> such that </b><br/><a NAME="E6:47_2_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A'</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="binarith.html#K11">*&gt;</a></span> &amp; <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="binarith.html#K11">*&gt;</a></span> is    <a href="ideal_1.html#M2">LeftLinearCombination</a> of <font color="Maroon">P</font> )
 <b>by </b><i><a class="ref" href="ideal_1.html#T33">IDEAL_1:33</a></i>;<br/>
<i><font color="Green">E42</font></i>:  <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">A'</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">A'</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>
;<br/>
<a NAME="E8:47_2_1"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">A'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 
<b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">g</font> =  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">A'</font> as   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> <b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/>
<a NAME="E10:47_2_1"/><i><font color="Green">E47</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E11:47_2_1"/><i><font color="Green">E48</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A'</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">k</font>
 
<b>by </b><i><a class="txt" href="groeb_2.html#E1:47"><i><font color="Green">E31</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E12:47_2_1"/>
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E13:47_2_1"/><b>then </b><i><font color="Green">E49</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A'</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="txt" href="groeb_2.html#E2:47"><i><font color="Green">E33</font></i></a>, <a class="ref" href="finseq_1.html#T7">FINSEQ_1:7</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_2_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:47_2_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A'</font>
 ;<br/><b>then </b><font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> = 
<font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">A'</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="txt" href="groeb_2.html#E3:47"><i><font color="Green">E35</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">A'</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="txt" href="groeb_2.html#E3:47"><i><font color="Green">E35</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>hence </b><a NAME="E3:47_2_1_2"/>
 ex <font color="Olive">m</font> being  <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> ex <font color="Olive">p</font> being  <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> st <br/>( <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">A'</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> )
 <b>by </b><i>, , <a class="txt" href="groeb_2.html#E3:47"><i><font color="Green">E35</font></i></a>, </i>;<br/></div><b>end;</b></div>
<a NAME="E15:47_2_1"/><b>then </b>
<font color="Maroon">A'</font> <a href="groeb_2.html#R2" target="_self">is_MonomialRepresentation_of</a> <font color="Maroon">g</font>
 
<b>by </b><i/>;<br/>
<a NAME="E16:47_2_1"/><b>then </b><i><font color="Green">E51</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">g</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font></span>)</span></span>)</span> where <font color="Olive">m</font> is   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> :  ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A'</font> &amp; <font color="Maroon">A'</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="groeb_2.html#T2" target="_self">Th2</a>, <a class="txt" href="groeb_2.html#E1:47"><i><font color="Green">E31</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">ep</font> =  <a href="rlvect_1.html#K9">Sum</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="binarith.html#K11">*&gt;</a></span> as   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> <b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/>
<font color="Maroon">f</font> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">A'</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
<b>by </b><i>, , <a class="ref" href="rlvect_1.html#T58">RLVECT_1:58</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="polynom1.html#K22">+</a> <font color="Maroon">ep</font>
<b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>
;<br/>
<a NAME="E19:47_2_1"/><b>then </b><i><font color="Green">E52</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">g</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">ep</font></span>)</span>
 
<b>by </b><i><a class="ref" href="polynom1.html#T79">POLYNOM1:79</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_2_1_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:47_2_1_4"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font>
 ;<br/><b>then reconsider </b><font color="Maroon">u</font> = <font color="Maroon">x</font> as    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_2_1_4_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_2_1_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:47_2_1_4_1_1"/>
( <font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">g</font> or <font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">ep</font> )
 </span><b>by </b><i>, <a class="txt" href="groeb_2.html#E1:47_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_2_1_4_1_1_1"><b>case </b></a><a NAME="E1:47_2_1_4_1_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">g</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">Y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:47_2_1_4_1_1_1"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font></span>)</span></span>)</span> where <font color="Olive">m</font> is   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> :  ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A'</font> &amp; <font color="Maroon">A'</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> ) </span>}</span>  )
 <b>by </b><i><a class="txt" href="groeb_2.html#E3:47"><i><font color="Green">E35</font></i></a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/><b>consider </b><font color="Maroon">m'</font> being   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Maroon">p'</font> being   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font><b> such that </b><br/><a NAME="E5:47_2_1_4_1_1_1"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">m'</font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">p'</font></span>)</span> &amp;  ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A'</font> &amp; <font color="Maroon">A'</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m'</font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">p'</font> ) )
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E7:47_2_1_4_1_1_1"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A'</font> &amp; <font color="Maroon">A'</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m'</font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">p'</font> )
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:47_2_1"><i><font color="Green">E39</font></i></a></i>;<br/><font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> = 
<font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="txt" href="groeb_2.html#E2:47_2_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">A'</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="txt" href="groeb_2.html#E2:47_2_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">A'</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="txt" href="groeb_2.html#E2:47_2_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><a NAME="E9:47_2_1_4_1_1_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font></span>)</span></span>)</span> where <font color="Olive">m</font> is   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> :  ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> ) </span>}</span> 
 <b>by </b><i>, <a class="txt" href="groeb_2.html#E1:47_2_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="groeb_2.html#E2:47_2_1"><i><font color="Green">E40</font></i></a></i>;<br/><b>hence </b><a NAME="E10:47_2_1_4_1_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font></span>)</span></span>)</span> where <font color="Olive">m</font> is   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> :  ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> ) </span>}</span> 
 <b>by </b><i>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_2_1_4_1_1_2"><b>case </b></a><a NAME="E1:47_2_1_4_1_1_2"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">ep</font>
 ;<br/><div class="add"><a NAME="E2:47_2_1_4_1_1_2"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>;<br/><a NAME="E3:47_2_1_4_1_1_2"/><i><font color="Green">E61</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E4:47_2_1_4_1_1_2"/>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E5:47_2_1_4_1_1_2"/><b>then </b><i><font color="Green">E62</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E6:47_2_1_4_1_1_2"/><b>then </b><i><font color="Green">E63</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E7:47_2_1_4_1_1_2"/><i><font color="Green">E64</font></i>: 
 ex <font color="Olive">m'</font> being  <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> ex <font color="Olive">p'</font> being  <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> st <br/>( <font color="Olive">p'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">m'</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p'</font> )
 <b>by </b><i>, <a class="txt" href="groeb_2.html#E2:47_2_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="groeb_2.html#E6:47_2_1"><i><font color="Green">E41</font></i></a>, </i>;<br/><a NAME="E8:47_2_1_4_1_1_2"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_2.html#E7:47_2_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><a NAME="E9:47_2_1_4_1_1_2"/>
<font color="Maroon">e</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="binarith.html#K11">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T61">RLVECT_1:61</a></i>;<br/><a NAME="E10:47_2_1_4_1_1_2"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">ep</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font></span>)</span></span>)</span> where <font color="Olive">m</font> is   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> :  ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:47_2_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="groeb_2.html#E7:47_2_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="groeb_2.html#E8:47_2_1"><i><font color="Green">E43</font></i></a>, </i>;<br/><b>hence </b><a NAME="E11:47_2_1_4_1_1_2"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font></span>)</span></span>)</span> where <font color="Olive">m</font> is   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> :  ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> ) </span>}</span> 
 <b>by </b><i>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:47_2_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font></span>)</span></span>)</span> where <font color="Olive">m</font> is   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> :  ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> ) </span>}</span> 
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E21:47_2_1"/>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font></span>)</span></span>)</span> where <font color="Olive">m</font> is   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> :  ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:47_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div>
<a NAME="E4:47"/><i><font color="Green">E117</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(, );<br/></i>
<b>consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E6:47"/><i><font color="Green">E118</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 ;<br/>
<b>thus </b><a NAME="E7:47"/>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font></span>)</span></span>)</span> where <font color="Olive">m</font> is   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Olive">p</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> :  ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="polynom1.html#K28">*'</a> <font color="Olive">p</font> ) </span>}</span> 
 <b>by </b><i>, <a class="ref" href="groeb_2.html#T2" target="_self">Th2</a>, </i>;<br/>


</div>
