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<b>let </b><font color="Maroon" title="c1">I</font> be  <a href="group_1.html#V7" title="GROUP_1:attr.7">commutative</a> non <a href="vectsp_1.html#V10" title="VECTSP_1:attr.10">degenerated</a> <a href="vectsp_2.html#V2" title="VECTSP_2:attr.2">domRing-like</a> <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c2">u</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" title="QUOFIELD:func.21">the_Field_of_Quotients</a> <font color="Maroon" title="c1">I</font></span>)</span>;<br/>



<b>assume </b><a NAME="E1:70"/>
<font color="Maroon" title="c2">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <span class="p1">(<span class="default"><a href="quofield.html#K21" title="QUOFIELD:func.21">the_Field_of_Quotients</a> <font color="Maroon" title="c1">I</font></span>)</span>
 ;<br/>

<a NAME="E2:70"/><b>then </b><i><font color="Green" title="E59">A1</font></i>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="quofield.html#K13" title="QUOFIELD:func.13">q0.</a> <font color="Maroon" title="c1">I</font>
 
;<br/>
<b>reconsider </b><font color="Maroon" title="c3">u</font> = <font color="Maroon" title="c2">u</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="quofield.html#K9" title="QUOFIELD:func.9">Quot.</a> <font color="Maroon" title="c1">I</font> ;<br/>
<a NAME="E4:70"/><i><font color="Green" title="E60">A2</font></i>: 
<span class="p1">(<span class="default"><a href="quofield.html#K18" title="QUOFIELD:func.18">quotmult</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">u</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quofield.html#K20" title="QUOFIELD:func.20">quotmultinv</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="txt" href="quofield.html#E2:70"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="quofield.html#T31" target="_self" title="QUOFIELD:th.31">Th31</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">v</font> = <span class="p1">(<span class="default"><a href="quofield.html#K20" title="QUOFIELD:func.20">quotmultinv</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">u</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" title="QUOFIELD:func.21">the_Field_of_Quotients</a> <font color="Maroon" title="c1">I</font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">u</font> = <font color="Maroon" title="c3">u</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" title="QUOFIELD:func.21">the_Field_of_Quotients</a> <font color="Maroon" title="c1">I</font></span>)</span> ;<br/>
<a NAME="E7:70"/>
<font color="Maroon" title="c5">u</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <span class="p1">(<span class="default"><a href="quofield.html#K21" title="QUOFIELD:func.21">the_Field_of_Quotients</a> <font color="Maroon" title="c1">I</font></span>)</span>
 
<b>by </b><i><a class="txt" href="quofield.html#E4:70"><i><font color="Green" title="E60">A2</font></i></a>, <a class="txt" href="quofield.html#E65"><i><font color="Green" title="E55">Lm10</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:70"/>
 ex <font color="Olive" title="b1">v</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" title="QUOFIELD:func.21">the_Field_of_Quotients</a> <font color="Maroon" title="c1">I</font></span>)</span> st <font color="Maroon" title="c2">u</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <span class="p1">(<span class="default"><a href="quofield.html#K21" title="QUOFIELD:func.21">the_Field_of_Quotients</a> <font color="Maroon" title="c1">I</font></span>)</span>
 ;<br/>


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