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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="group_1.html#V7">commutative</a> non <a href="vectsp_1.html#V10">degenerated</a> <a href="vectsp_2.html#V2">domRing-like</a> <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:24"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="quofield.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E2:24"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </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>1</sub></font>
 
<b>by </b><i><a class="ref" href="vectsp_2.html#D5">VECTSP_2:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span></span><a href="domain_1.html#K1">]</a></span> as    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="quofield.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E4:24"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>;<br/>
<a NAME="E5:24"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>;<br/>
<a NAME="E6:24"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">c<sub>2</sub></font>,<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="quofield.html#K11" target="_self">qmult</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E1:24_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:24_1"/><b>then </b><i><font color="Green">E20</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="quofield.html#E4:24"><i><font color="Green">E17</font></i></a>, <a class="txt" href="quofield.html#E5:24"><i><font color="Green">E18</font></i></a>, <a class="ref" href="quofield.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E3:24_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="quofield.html#T6" target="_self">Th6</a></i>;<br/>
<b>hence </b><a NAME="E4:24_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K11" target="_self">qmult</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="quofield.html#E2:24_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="quofield.html#D7" target="_self">Def7</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:24"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K11" target="_self">qmult</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</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="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E1:24_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K11" target="_self">qmult</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:24_2"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="quofield.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E4:24_2"/><i><font color="Green">E21</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="quofield.html#E3:24_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="quofield.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E5:24_2"/><i><font color="Green">E22</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="quofield.html#E3:24_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="quofield.html#D4" target="_self">Def4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_2_1_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> or ( <font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_2_1_1_1"><b>case </b></a><a NAME="E1:24_2_1_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:24_2_1_1_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>;<br/><a NAME="E3:24_2_1_1_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="quofield.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E4:24_2_1_1_1"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="quofield.html#E4:24_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="quofield.html#E2:24_2_1_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="vectsp_2.html#D5">VECTSP_2:def 5</a></i>;<br/><a NAME="E5:24_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="quofield.html#E1:24_2_1_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>;<br/><a NAME="E6:24_2_1_1_1"/><b>then </b><i><font color="Green">E27</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>;<br/><a NAME="E7:24_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </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>1</sub></font>
 <b>by </b><i><a class="txt" href="quofield.html#E3:24_2_1_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="vectsp_2.html#D5">VECTSP_2:def 5</a></i>;<br/><a NAME="E8:24_2_1_1_1"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="quofield.html#E3:24_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="quofield.html#E6:24_2_1_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="vectsp_2.html#D5">VECTSP_2:def 5</a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E4:24_2_1_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E8:24_2_1_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
;<br/><b>hence </b><a NAME="E10:24_2_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="quofield.html#E4:24"><i><font color="Green">E17</font></i></a>, <a class="txt" href="quofield.html#E5:24"><i><font color="Green">E18</font></i></a>, <a class="ref" href="quofield.html#D4" target="_self">Def4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_2_1_1_2"><b>case </b></a><a NAME="E1:24_2_1_1_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:24_2_1_1_2"/><b>then </b><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>;<br/><a NAME="E3:24_2_1_1_2"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="quofield.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E4:24_2_1_1_2"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="quofield.html#E5:24_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="quofield.html#E2:24_2_1_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="vectsp_2.html#D5">VECTSP_2:def 5</a></i>;<br/><a NAME="E5:24_2_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="quofield.html#E1:24_2_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>;<br/><a NAME="E6:24_2_1_1_2"/><b>then </b><i><font color="Green">E27</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>;<br/><a NAME="E7:24_2_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </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>1</sub></font>
 <b>by </b><i><a class="txt" href="quofield.html#E3:24_2_1_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="vectsp_2.html#D5">VECTSP_2:def 5</a></i>;<br/><a NAME="E8:24_2_1_1_2"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="quofield.html#E3:24_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="quofield.html#E6:24_2_1_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="vectsp_2.html#D5">VECTSP_2:def 5</a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E4:24_2_1_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E8:24_2_1_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
;<br/><b>hence </b><a NAME="E10:24_2_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="quofield.html#E4:24"><i><font color="Green">E17</font></i></a>, <a class="txt" href="quofield.html#E5:24"><i><font color="Green">E18</font></i></a>, <a class="ref" href="quofield.html#D4" target="_self">Def4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_2_1_1_3"><b>case </b></a><a NAME="E1:24_2_1_1_3"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/><div class="add"><a NAME="E2:24_2_1_1_3"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="gcd_1.html#R2">divides</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span>
 <b>by </b><i><a class="txt" href="quofield.html#E4:24_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="gcd_1.html#D1">GCD_1:def 1</a></i>;<br/><a NAME="E3:24_2_1_1_3"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="gcd_1.html#K1">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span>
 <b>by </b><i><a class="txt" href="quofield.html#E4:24_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="quofield.html#E1:24_2_1_1_3"><i><font color="Green">E23</font></i></a>, <a class="ref" href="gcd_1.html#D4">GCD_1:def 4</a></i>;<br/><a NAME="E4:24_2_1_1_3"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="gcd_1.html#R2">divides</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span>
 <b>by </b><i><a class="txt" href="quofield.html#E5:24_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="gcd_1.html#D1">GCD_1:def 1</a></i>;<br/><a NAME="E5:24_2_1_1_3"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K3" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="gcd_1.html#K1">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span>
 <b>by </b><i><a class="txt" href="quofield.html#E5:24_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="quofield.html#E1:24_2_1_1_3"><i><font color="Green">E23</font></i></a>, <a class="ref" href="gcd_1.html#D4">GCD_1:def 4</a></i>;<br/><a NAME="E6:24_2_1_1_3"/><i><font color="Green">E28</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </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>1</sub></font>
 <b>by </b><i><a class="txt" href="quofield.html#E1:24_2_1_1_3"><i><font color="Green">E23</font></i></a>, <a class="ref" href="vectsp_2.html#D5">VECTSP_2:def 5</a></i>;<br/><a NAME="E7:24_2_1_1_3"/><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="gcd_1.html#R2">divides</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="quofield.html#E2:24_2_1_1_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="quofield.html#E4:24_2_1_1_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="gcd_1.html#T3">GCD_1:3</a></i>;<br/><a NAME="E8:24_2_1_1_3"/><b>then </b><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="gcd_1.html#R2">divides</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7">GCD_1:7</a></i>;<br/><a NAME="E9:24_2_1_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="gcd_1.html#R2">divides</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span>
 ;<br/><a NAME="E10:24_2_1_1_3"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="gcd_1.html#R2">divides</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7">GCD_1:7</a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="gcd_1.html#K1">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E1:24_2_1_1_3"><i><font color="Green">E23</font></i></a>, <a class="txt" href="quofield.html#E2:24_2_1_1_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="quofield.html#E3:24_2_1_1_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="quofield.html#E4:24_2_1_1_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="quofield.html#E5:24_2_1_1_3"><i><font color="Green">E27</font></i></a>, <a class="ref" href="gcd_1.html#T14">GCD_1:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="gcd_1.html#K1">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E6:24_2_1_1_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="quofield.html#E7:24_2_1_1_3"><i><font color="Green">E29</font></i></a>, <a class="txt" href="quofield.html#E8:24_2_1_1_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="gcd_1.html#T11">GCD_1:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="gcd_1.html#K1">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="gcd_1.html#K1">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="gcd_1.html#K1">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="gcd_1.html#K1">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E3:24_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="gcd_1.html#K1">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="gcd_1.html#K1">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="gcd_1.html#K1">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E6:24_2_1_1_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="quofield.html#E10:24_2_1_1_3"><i><font color="Green">E31</font></i></a>, <a class="ref" href="gcd_1.html#T11">GCD_1:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E6:24_2_1_1_3"><i><font color="Green">E28</font></i></a>, <a class="ref" href="gcd_1.html#T9">GCD_1:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="quofield.html#K3" target="_self">`2</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="quofield.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
;<br/><b>hence </b><a NAME="E12:24_2_1_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="quofield.html#E4:24"><i><font color="Green">E17</font></i></a>, <a class="txt" href="quofield.html#E5:24"><i><font color="Green">E18</font></i></a>, <a class="ref" href="quofield.html#D4" target="_self">Def4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E7:24_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:24"/>
 <a href="quofield.html#K11" target="_self">qmult</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="quofield.html#E6:24"><i><font color="Green">E19</font></i></a>, <a class="ref" href="subset_1.html#T8">SUBSET_1:8</a></i>;<br/>


</div>
