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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>assume </b><a NAME="E1:37"/><i><font color="Green" title="E30">A1</font></i>: 
 <a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quofield.html#K13" title="QUOFIELD:func.13">q0.</a> <font color="Maroon" title="c1">I</font>
 ;<br/>

<a NAME="E2:37"/>
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D21" title="VECTSP_1:def.21">VECTSP_1:def 21</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c2">t</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">I</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="quofield.html#K1" title="QUOFIELD:func.1">Q.</a> <font color="Maroon" title="c1">I</font> <b>by </b><i><a class="ref" href="quofield.html#D1" target="_self" title="QUOFIELD:def.1">Def1</a></i>;<br/>
<a NAME="E4:37"/><i><font color="Green" title="E31">A2</font></i>: 
<font color="Maroon" title="c2">t</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></i>;<br/>
<a NAME="E5:37"/><b>then </b>
<font color="Maroon" title="c2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="quofield.html#K13" title="QUOFIELD:func.13">q0.</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="quofield.html#D8" target="_self" title="QUOFIELD:def.8">Def8</a></i>;<br/>
<a NAME="E6:37"/><b>then </b>
<font color="Maroon" title="c2">t</font> <a href="quofield.html#K2" title="QUOFIELD:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t</font> <a href="quofield.html#K3" title="QUOFIELD:func.3">`2</a> 
 
<b>by </b><i><a class="txt" href="quofield.html#E1:37"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="quofield.html#D9" target="_self" title="QUOFIELD:def.9">Def9</a></i>;<br/>
<a NAME="E7:37"/><b>then </b>
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="txt" href="quofield.html#E4:37"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E8:37"/>
contradiction
 <b>by </b><i><a class="ref" href="vectsp_1.html#D21" title="VECTSP_1:def.21">VECTSP_1:def 21</a></i>;<br/>


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