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

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1_1_1_1"/>
(  <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>  or ex <font color="Olive">b<sub>1</sub></font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font> st  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> )
 </span><b>by </b><i><a class="ref" href="polynom7.html#T6">POLYNOM7:6</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_1"><b>case </b></a><a NAME="E1:19_1_1_1_1_1"/><i><font color="Green">E9</font></i>: 
 <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 class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_1_1_1_1_1"/><i><font color="Green">E10</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="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/><a NAME="E3:19_1_1_1_1_1_1"/>
<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="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_1_1"><i><font color="Green">E10</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</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/><span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="polynom7.html#D10">POLYNOM7:def 10</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="binom.html#T2">BINOM:2</a></i>
;<br/><b>hence </b><a NAME="E6:19_1_1_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_1_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:19_1_1_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font> is <a href="polynom7.html#V3">monomial-like</a>
 <b>by </b><i><a class="ref" href="polynom7.html#T6">POLYNOM7:6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2"><b>case </b></a><a NAME="E1:19_1_1_1_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font> st  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:19_1_1_1_1_2"/><i><font color="Green">E9</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</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> <b>by </b><i><a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1_1_1_1_2_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:19_1_1_1_1_2_1_1_1"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_1_1_1_2_1_1_1_1"/><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="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/><a NAME="E3:19_1_1_1_1_2_1_1_1_1"/>
<font color="Maroon">c<sub>8</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="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_2_1_1_1_1"><i><font color="Green">E11</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>9</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/><span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="polynom7.html#D10">POLYNOM7:def 10</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_2_1_1_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="binom.html#T1">BINOM:1</a></i>
;<br/><b>hence </b><a NAME="E6:19_1_1_1_1_2_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_2_1_1_1_1"><i><font color="Green">E11</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:19_1_1_1_1_2_1_1_1"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:19_1_1_1_1_2_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><div><i><font color="Green">E10</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:19_1_1_1_1_2_1_1_2_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:19_1_1_1_1_2_1_1_2_1"/><b>then </b>
not <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>
 <b>by </b><i><a class="txt" href="groeb_2.html#E3:19_1_1_1_1_2"><i><font color="Green">E9</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:19_1_1_1_1_2_1_1_2_1"/><b>then </b><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E4:19_1_1_1_1_2_1_1_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom7.html#D10">POLYNOM7:def 10</a></i>;<br/><b>hence </b><a NAME="E5:19_1_1_1_1_2_1_1_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="groeb_2.html#E3:19_1_1_1_1_2_1_1_2_1"><i><font color="Green">E11</font></i></a>, <a class="ref" href="binom.html#T2">BINOM:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1_1_1_1_2_1_1_2_2_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2_1_1"><b>case </b></a><a NAME="E1:19_1_1_1_1_2_1_1_2_2_1_1"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_1_1_1_2_1_1_2_2_1_1_1"/><i><font color="Green">E12</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="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/><a NAME="E3:19_1_1_1_1_2_1_1_2_2_1_1_1"/>
<font color="Maroon">c<sub>8</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="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_2_1_1_2_2_1_1_1"><i><font color="Green">E12</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>9</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/><a NAME="E5:19_1_1_1_1_2_1_1_2_2_1_1_1"/><i><font color="Green">E13</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_2_1_1_2_2_1_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E6:19_1_1_1_1_2_1_1_2_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="groeb_2.html#E2:19_1_1_1_1_2_1_1_2"><i><font color="Green">E10</font></i></a></i>;<br/><b>hence </b><a NAME="E7:19_1_1_1_1_2_1_1_2_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_2_1_1_2_2_1_1"><i><font color="Green">E11</font></i></a>, <a class="txt" href="groeb_2.html#E5:19_1_1_1_1_2_1_1_2_2_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="polynom7.html#D10">POLYNOM7:def 10</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:19_1_1_1_1_2_1_1_2_2_1_1"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2_1_2"><b>case </b></a><a NAME="E1:19_1_1_1_1_2_1_1_2_2_1_2"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><div><i><font color="Green">E12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:19_1_1_1_1_2_1_1_2_2_1_2_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:19_1_1_1_1_2_1_1_2_2_1_2_1"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:19_1_1_1_1_2_1_1_2_2_1_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_2_1_1_2_2_1_2"><i><font color="Green">E11</font></i></a>, <a class="ref" href="polynom7.html#D10">POLYNOM7:def 10</a></i>;<br/><b>hence </b><a NAME="E4:19_1_1_1_1_2_1_1_2_2_1_2_1"/>
<font color="Maroon">c<sub>8</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="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_2.html#E2:19_1_1_1_1_2_1_1_2_2_1_2_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_1_2_1_1_2_2_1_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:19_1_1_1_1_2_1_1_2_2_1_2_2"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>8</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="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>9</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/><a NAME="E3:19_1_1_1_1_2_1_1_2_2_1_2_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:19_1_1_1_1_2_1_1_2_2_1_2_2"><i><font color="Green">E13</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E4:19_1_1_1_1_2_1_1_2_2_1_2_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="groeb_2.html#E2:19_1_1_1_1_2_1_1_2"><i><font color="Green">E10</font></i></a></i>;<br/><b>hence </b><a NAME="E5:19_1_1_1_1_2_1_1_2_2_1_2_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:19_1_1_1_1_2_1_1_2_2_1_2"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="groeb_2.html#E2:19_1_1_1_1_2_1_1_2_2_1_2"><i><font color="Green">E12</font></i></a>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:19_1_1_1_1_2_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font> is <a href="polynom7.html#V3">monomial-like</a>
 <b>by </b><i><a class="ref" href="polynom7.html#T6">POLYNOM7:6</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:19_1_1_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font> is <a href="polynom7.html#V3">monomial-like</a>
 <b>by </b><i><a class="ref" href="polynom7.html#T6">POLYNOM7:6</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:19_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="polynom7.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font> is <a href="polynom7.html#V3">monomial-like</a>
 ;<br/>


</div>
