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<b>let </b><font color="Maroon">I</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">u</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K9" target="_self">Quot.</a> <font color="Maroon">I</font>, <font color="Maroon">v</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K9" target="_self">Quot.</a> <font color="Maroon">I</font>, <font color="Maroon">w</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K9" target="_self">Quot.</a> <font color="Maroon">I</font>;<br/>



<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">I</font><b> such that </b><br/><a NAME="E2:31"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">x</font>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">y</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">I</font><b> such that </b><br/><a NAME="E4:31"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">y</font>
 <b>by </b><i/>;<br/>
<i><font color="Green">E24</font></i>:  <a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">u</font>,<font color="Maroon">v</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">x</font>,<font color="Maroon">y</font></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E5:31"><i><font color="Green">E24</font></i></a>, <a class="txt" href="quofield.html#E7:31"><i><font color="Green">E25</font></i></a>, </i>
<br/>.= 
 <a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">v</font>,<font color="Maroon">u</font>
<b>by </b><i><a class="txt" href="quofield.html#E5:31"><i><font color="Green">E24</font></i></a>, <a class="txt" href="quofield.html#E7:31"><i><font color="Green">E25</font></i></a>, </i>
;<br/>
<b>consider </b><font color="Maroon">z</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">I</font><b> such that </b><br/><a NAME="E7:31"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">w</font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">z</font>
 <b>by </b><i/>;<br/>
 <a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">u</font>,<span class="p1">(<span class="default"><a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">v</font>,<font color="Maroon">w</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">x</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">y</font>,<font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="quofield.html#E5:31"><i><font color="Green">E24</font></i></a>, <a class="txt" href="quofield.html#E7:31"><i><font color="Green">E25</font></i></a>, <a class="ref" href="quofield.html#T2" target="_self">Th2</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">x</font>,<span class="p2">(<span class="default"><a href="quofield.html#K7" target="_self">pmult</a> <font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><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">x</font>,<font color="Maroon">y</font></span>)</span>,<font color="Maroon">z</font></span>)</span>
<b>by </b><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">x</font>,<font color="Maroon">y</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="quofield.html#K12" target="_self">QClass.</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><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">u</font>,<font color="Maroon">v</font></span>)</span>,<font color="Maroon">w</font>
<b>by </b><i><a class="txt" href="quofield.html#E5:31"><i><font color="Green">E24</font></i></a>, <a class="txt" href="quofield.html#E7:31"><i><font color="Green">E25</font></i></a>, <a class="ref" href="quofield.html#T2" target="_self">Th2</a>, </i>
;<br/>
<b>hence </b><a NAME="E9:31"/>
(  <a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">u</font>,<span class="p1">(<span class="default"><a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">v</font>,<font color="Maroon">w</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">u</font>,<font color="Maroon">v</font></span>)</span>,<font color="Maroon">w</font> &amp;  <a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K11" target="_self">qmult</a> <font color="Maroon">v</font>,<font color="Maroon">u</font> )
 <b>by </b><i><a class="ref" href="quofield.html#T1" target="_self">Th1</a></i>;<br/>


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