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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="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> <a href="vectsp_2.html#V2">domRing-like</a> non <a href="realset2.html#V3">trivial</a> <a href="algstr_1.html#V1">left_zeroed</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="polynom7.html#V1">non-zero</a> <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>







<a NAME="E1:10"/><i><font color="Green">E11</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="polynom1.html#K9">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span> where B is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font>, B is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="termord.html#T30">TERMORD:30</a></i>;<br/>
<a NAME="E2:10"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="polynom7.html#D2">POLYNOM7:def 2</a></i>;<br/>
<a NAME="E3:10"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="polynom7.html#T1">POLYNOM7:1</a></i>;<br/>
<a NAME="E4:10"/><b>then </b><i><font color="Green">E12</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="polynom7.html#T7">POLYNOM7:7</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] means <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_7.html#K1">In</a> <font color="Maroon">a<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="polynom2.html#K4">@</a> </span>)</span>;<br/>
<a NAME="E5:10"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:10_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font> ;<br/>
<i><font color="Green">E15</font></i>: <font color="Maroon">c<sub>6</sub></font> = 
 <a href="funct_7.html#K1">In</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_7.html#D1">FUNCT_7:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="funct_7.html#K1">In</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="polynom2.html#K4">@</a> 
<b>by </b><i><a class="ref" href="polynom2.html#D3">POLYNOM2:def 3</a></i>
;<br/>
<a NAME="E4:10_1"/>
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="groeb_3.html#E1:10_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="groeb_3.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E5:10_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font>] )
 <b>by </b><i><a class="txt" href="groeb_3.html#E3:10_1"><i><font color="Green">E15</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being  <a href="relat_2.html#V6">connected</a> <a href="bagorder.html#V2">admissible</a> <a href="bagorder.html#NM1">TermOrder</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font>, <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span><b> such that </b><br/><a NAME="E8:10"/><i><font color="Green">E14</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>]
 <b>from </b><i><a class="ref" href="funct_2.html#S1">FUNCT_2:sch 1</a>(<a class="txt" href="groeb_3.html#E5:10"><i><font color="Green">E13</font></i></a>);<br/></i>
<div><i><font color="Green">E15</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:10_2"/><i><font color="Green">E16</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:10_2_1"/>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:10_2_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="polynom7.html#T1">POLYNOM7:1</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>3</sub></font> as  <a href="polynom7.html#V1">non-zero</a> <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="polynom7.html#D2">POLYNOM7:def 2</a></i>;<br/><a NAME="E4:10_2_1"/>
<span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="termord.html#T29">TERMORD:29</a></i>;<br/><b>hence </b><a NAME="E5:10_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_3.html#E1:10_2"><i><font color="Green">E16</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:10_2"/>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/></div><b>end;</b></div>
<a NAME="E10:10"/><b>then </b><i><font color="Green">E16</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:10_3"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>8</sub></font> as    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font> ;<br/><i><font color="Green">E18</font></i>: <font color="Maroon">c<sub>10</sub></font> = 
 <a href="funct_7.html#K1">In</a> <font color="Maroon">c<sub>10</sub></font>,<span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_7.html#D1">FUNCT_7:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="funct_7.html#K1">In</a> <font color="Maroon">c<sub>10</sub></font>,<span class="p2">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="polynom2.html#K4">@</a> 
<b>by </b><i><a class="ref" href="polynom2.html#D3">POLYNOM2:def 3</a></i>
;<br/><font color="Maroon">c<sub>9</sub></font> = 
 <a href="funct_7.html#K1">In</a> <font color="Maroon">c<sub>9</sub></font>,<span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_7.html#D1">FUNCT_7:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="funct_7.html#K1">In</a> <font color="Maroon">c<sub>9</sub></font>,<span class="p2">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="polynom2.html#K4">@</a> 
<b>by </b><i><a class="ref" href="polynom2.html#D3">POLYNOM2:def 3</a></i>
;<br/><b>then </b><i><font color="Green">E19</font></i>: <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>9</sub></font> = 
<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="groeb_3.html#E1:10_3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="groeb_3.html#E8:10"><i><font color="Green">E14</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="groeb_3.html#E3:10_3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="groeb_3.html#E1:10_3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="groeb_3.html#E8:10"><i><font color="Green">E14</font></i></a></i>
;<br/><b>thus </b><font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="polynom1.html#K9">+</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="polynom1.html#K10">-'</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="groeb_3.html#E5:10_3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="polynom1.html#T52">POLYNOM1:52</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="polynom1.html#T52">POLYNOM1:52</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E12:10"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="groeb_3.html#E9:10"><i><font color="Green">E15</font></i></a>, <a class="ref" href="funct_2.html#T25">FUNCT_2:25</a></i>;<br/>
<a NAME="E13:10"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R2">are_equipotent</a> 
 
<b>by </b><i><a class="txt" href="groeb_3.html#E10:10"><i><font color="Green">E16</font></i></a>, <a class="ref" href="card_1.html#T60">CARD_1:60</a></i>;<br/>
<a NAME="E14:10"/><i><font color="Green">E18</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:10_4"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font> ;<br/><a NAME="E3:10_4"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="polynom1.html#K9">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span> where B is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font>, B is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="groeb_3.html#E1:10_4"><i><font color="Green">E19</font></i></a>, <a class="txt" href="groeb_3.html#E1:10"><i><font color="Green">E11</font></i></a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:10_4"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/><i><font color="Green">E21</font></i>: <font color="Maroon">c<sub>10</sub></font> = 
 <a href="funct_7.html#K1">In</a> <font color="Maroon">c<sub>10</sub></font>,<span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_7.html#D1">FUNCT_7:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="funct_7.html#K1">In</a> <font color="Maroon">c<sub>10</sub></font>,<span class="p2">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="polynom2.html#K4">@</a> 
<b>by </b><i><a class="ref" href="polynom2.html#D3">POLYNOM2:def 3</a></i>
;<br/><a NAME="E7:10_4"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2">term</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E5:10_4"><i><font color="Green">E20</font></i></a>, <a class="txt" href="groeb_3.html#E4:10"><i><font color="Green">E12</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E8:10_4"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E5:10_4"><i><font color="Green">E20</font></i></a>, <a class="txt" href="groeb_3.html#E8:10"><i><font color="Green">E14</font></i></a>, <a class="txt" href="groeb_3.html#E6:10_4"><i><font color="Green">E21</font></i></a></i>;<br/><a NAME="E9:10_4"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E5:10_4"><i><font color="Green">E20</font></i></a>, <a class="txt" href="groeb_3.html#E9:10"><i><font color="Green">E15</font></i></a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>hence </b><a NAME="E10:10_4"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_3.html#E8:10_4"><i><font color="Green">E22</font></i></a>, <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/></div><b>end;</b></div>
<a NAME="E16:10"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="groeb_3.html#E14:10"><i><font color="Green">E18</font></i></a>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<b>hence </b><a NAME="E17:10"/>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K28">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_3.html#E13:10"><i><font color="Green">E17</font></i></a>, <a class="ref" href="card_1.html#T21">CARD_1:21</a></i>;<br/>


</div>
