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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="vectsp_2.html#NM6">LeftMod</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:8"/><i><font color="Green">E5</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="realset2.html#V3">trivial</a> &amp; not <font color="Maroon">c<sub>2</sub></font> is <a href="realset2.html#V3">trivial</a> )
 ;<br/>

<a NAME="E2:8"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="anproj_1.html#D8">ANPROJ_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E3:8"/>
contradiction
 <b>by </b><i><a class="txt" href="lmod_6.html#E1:8"><i><font color="Green">E5</font></i></a>, <a class="ref" href="lmod_6.html#T5" target="_self">Th5</a></i>;<br/>


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