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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/>

<a NAME="E1:67"/><i><font color="Green">E56</font></i>: 
 <a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">c<sub>1</sub></font> is <a href="group_1.html#V2">unital</a>
 
<b>by </b><i><a class="txt" href="quofield.html#E64"><i><font color="Green">Lemma54</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> =  <a href="quofield.html#K14" target="_self">q1.</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span> ;<br/>
<a NAME="E3:67"/>
for <font color="Olive">b<sub>1</sub></font> being  <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">c<sub>1</sub></font></span>)</span> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K10">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="quofield.html#E63"><i><font color="Green">Lemma53</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:67"/>
 <a href="group_1.html#K2">1.</a> <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K14" target="_self">q1.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="quofield.html#E1:67"><i><font color="Green">E56</font></i></a>, <a class="ref" href="group_1.html#D5">GROUP_1:def 5</a></i>;<br/>


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