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<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>, <font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K9" target="_self">Quot.</a> <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>consider </b><font color="Maroon">c<sub>5</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="E2:31"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="quofield.html#D5" target="_self">Def5</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</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="E4:31"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="quofield.html#D5" target="_self">Def5</a></i>;<br/>
<i><font color="Green">E26</font></i>:  <a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> = 
 <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>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E2:31"><i><font color="Green">E24</font></i></a>, <a class="txt" href="quofield.html#E4:31"><i><font color="Green">E25</font></i></a>, <a class="ref" href="quofield.html#T12" target="_self">Th12</a></i>
<br/>.= 
 <a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="quofield.html#E2:31"><i><font color="Green">E24</font></i></a>, <a class="txt" href="quofield.html#E4:31"><i><font color="Green">E25</font></i></a>, <a class="ref" href="quofield.html#T12" target="_self">Th12</a></i>
;<br/>
<b>consider </b><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="E7:31"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="quofield.html#D5" target="_self">Def5</a></i>;<br/>
 <a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> = 
 <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>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <span class="p2">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E2:31"><i><font color="Green">E24</font></i></a>, <a class="txt" href="quofield.html#E4:31"><i><font color="Green">E25</font></i></a>, <a class="txt" href="quofield.html#E7:31"><i><font color="Green">E27</font></i></a>, <a class="ref" href="quofield.html#T12" target="_self">Th12</a></i>
<br/>.= 
 <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>5</sub></font>,<span class="p2">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#T12" target="_self">Th12</a></i>
<br/>.= 
 <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <span class="p2">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#T5" target="_self">Th5</a></i>
<br/>.= 
 <a href="quofield.html#K11" target="_self">qmult</a> <span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <span class="p2">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#T12" target="_self">Th12</a></i>
<br/>.= 
 <a href="quofield.html#K11" target="_self">qmult</a> <span class="p1">(<span class="default"><a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="quofield.html#E2:31"><i><font color="Green">E24</font></i></a>, <a class="txt" href="quofield.html#E4:31"><i><font color="Green">E25</font></i></a>, <a class="txt" href="quofield.html#E7:31"><i><font color="Green">E27</font></i></a>, <a class="ref" href="quofield.html#T12" target="_self">Th12</a></i>
;<br/>
<b>hence </b><a NAME="E9:31"/>
(  <a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K11" target="_self">qmult</a> <span class="p1">(<span class="default"><a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="quofield.html#E5:31"><i><font color="Green">E26</font></i></a></i>;<br/>


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