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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="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">I</font></span>)</span>, <font color="Maroon">v</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">I</font></span>)</span>, <font color="Maroon">w</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">I</font></span>)</span>;<br/>



<b>reconsider </b><font color="Maroon">s</font> = <span class="p1">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">v</font>,<font color="Maroon">w</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">I</font></span>)</span> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">t</font> = <span class="p1">(<span class="default"><a href="quofield.html#K18" target="_self">quotmult</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">u</font>,<font color="Maroon">v</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">I</font></span>)</span> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">r</font> = <span class="p1">(<span class="default"><a href="quofield.html#K18" target="_self">quotmult</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">u</font>,<font color="Maroon">w</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">I</font></span>)</span> <b>by </b><i/>;<br/>
<i><font color="Green">E20</font></i>: <font color="Maroon">u</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">w</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="quofield.html#K18" target="_self">quotmult</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">u</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">v</font>,<font color="Maroon">w</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">t</font>,<font color="Maroon">r</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="group_1.html#K10">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="group_1.html#K10">*</a> <font color="Maroon">w</font></span>)</span>

;<br/>
<b>reconsider </b><font color="Maroon">s</font> = <span class="p1">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">u</font>,<font color="Maroon">v</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">I</font></span>)</span> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">t</font> = <span class="p1">(<span class="default"><a href="quofield.html#K18" target="_self">quotmult</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">u</font>,<font color="Maroon">w</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">I</font></span>)</span> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">r</font> = <span class="p1">(<span class="default"><a href="quofield.html#K18" target="_self">quotmult</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">v</font>,<font color="Maroon">w</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">I</font></span>)</span> <b>by </b><i/>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">v</font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">w</font> = 
<span class="p1">(<span class="default"><a href="quofield.html#K18" target="_self">quotmult</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">u</font>,<font color="Maroon">v</font></span>)</span>,<font color="Maroon">w</font>

<br/>.= 
<span class="p1">(<span class="default"><a href="quofield.html#K17" target="_self">quotadd</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K18" target="_self">quotmult</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">u</font>,<font color="Maroon">w</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K18" target="_self">quotmult</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">v</font>,<font color="Maroon">w</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="group_1.html#K10">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="group_1.html#K10">*</a> <font color="Maroon">w</font></span>)</span>

;<br/>
<b>hence </b><a NAME="E9:71"/>
( <font color="Maroon">u</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">w</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="group_1.html#K10">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="group_1.html#K10">*</a> <font color="Maroon">w</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">v</font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="group_1.html#K10">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="group_1.html#K10">*</a> <font color="Maroon">w</font></span>)</span> )
 <b>by </b><i/>;<br/>


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