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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>assume </b><a NAME="E1:37"/><i><font color="Green">E20</font></i>: 
 <a href="quofield.html#K14" target="_self">q1.</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K13" target="_self">q0.</a> <font color="Maroon">I</font>
 ;<br/>

<a NAME="E2:37"/>
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">I</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D21">VECTSP_1:def 21</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">t</font> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">I</font></span>)</span></span><a href="domain_1.html#K1">]</a></span> as    <a href="subset_1.html#M2">Element</a> of  <a href="quofield.html#K1" target="_self">Q.</a> <font color="Maroon">I</font> <b>by </b><i/>;<br/>
<a NAME="E4:37"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">t</font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>;<br/>
<a NAME="E5:37"/><b>then </b>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="quofield.html#K13" target="_self">q0.</a> <font color="Maroon">I</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:37"/><b>then </b>
<font color="Maroon">t</font> <a href="quofield.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="quofield.html#K3" target="_self">`2</a> 
 
<b>by </b><i><a class="ref" href="quofield.html#T4" target="_self">Th4</a>, </i>;<br/>
<a NAME="E7:37"/><b>then </b>
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">I</font>
 
<b>by </b><i>, <a class="ref" href="mcart_1.html#D2">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">VECTSP_1:def 21</a></i>;<br/>


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