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<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="polynom1.html#NM3">Series</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:24_1_2"/><i><font color="Green">E21</font></i>: 
for <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 <font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#R3">divides</a> <font color="Olive">b<sub>1</sub></font> holds <br/>( <font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K15">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="polynom1.html#K10">-'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font> st not <font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#R3">divides</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K15">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>3</sub></font> ) )
 <b>and </b><br/><a NAME="E2:24_1_2"/><i><font color="Green">E22</font></i>: 
for <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 <font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#R3">divides</a> <font color="Olive">b<sub>1</sub></font> holds <br/>( <font color="Maroon">c<sub>6</sub></font> <a href="polynom1.html#K15">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="polynom1.html#K10">-'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font> st not <font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#R3">divides</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Maroon">c<sub>6</sub></font> <a href="polynom1.html#K15">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>3</sub></font> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</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/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_1_2_1_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">c<sub>7</sub></font> or  not <font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">c<sub>7</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_2_1_1_1_1"><b>case </b></a><a NAME="E1:24_1_2_1_1_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="polynom1.html#K10">-'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polyred.html#E1:24_1_2"><i><font color="Green">E21</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="polyred.html#E2:24_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="polyred.html#E1:24_1_2_1_1_1_1"><i><font color="Green">E23</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_2_1_1_1_2"><b>case </b></a><a NAME="E1:24_1_2_1_1_1_2"/><i><font color="Green">E23</font></i>: 
not <font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font> = 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="polyred.html#E1:24_1_2"><i><font color="Green">E21</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="polyred.html#E2:24_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="polyred.html#E1:24_1_2_1_1_1_2"><i><font color="Green">E23</font></i></a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E2:24_1_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K15">.</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="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:24_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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