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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> 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/>



<i><font color="Green">E43</font></i>: <span class="p1">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K19" target="_self">quotaddinv</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="quofield.html#K15" target="_self">qaddinv</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D14" target="_self">Def14</a></i>
<br/>.= 
 <a href="quofield.html#K10" target="_self">qadd</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="quofield.html#K15" target="_self">qaddinv</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D12" target="_self">Def12</a></i>
<br/>.= 
 <a href="quofield.html#K13" target="_self">q0.</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="quofield.html#T19" target="_self">Th19</a></i>
;<br/>
<span class="p1">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K19" target="_self">quotaddinv</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="quofield.html#K15" target="_self">qaddinv</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="quofield.html#D14" target="_self">Def14</a></i>
<br/>.= 
 <a href="quofield.html#K10" target="_self">qadd</a> <span class="p1">(<span class="default"><a href="quofield.html#K15" target="_self">qaddinv</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="quofield.html#D12" target="_self">Def12</a></i>
<br/>.= 
 <a href="quofield.html#K13" target="_self">q0.</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="quofield.html#T19" target="_self">Th19</a></i>
;<br/>
<b>hence </b><a NAME="E3:50"/>
( <span class="p1">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K19" target="_self">quotaddinv</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K13" target="_self">q0.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K19" target="_self">quotaddinv</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K13" target="_self">q0.</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="quofield.html#E1:50"><i><font color="Green">E43</font></i></a></i>;<br/>


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