<?xml version="1.0"?>
<div class="add">

<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>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:12"/><i><font color="Green">E3</font></i>: 
( not <font color="Maroon">c<sub>1</sub></font> is <a href="realset2.html#V3">trivial</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="lmod_5.html#V1">linearly-independent</a> )
 ;<br/>

<a NAME="E2:12"/><b>then </b>
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="lmod_6.html#D2">LMOD_6:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:12"/>
not  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="lmod_7.html#E1:12"><i><font color="Green">E3</font></i></a>, <a class="ref" href="lmod_5.html#T3">LMOD_5:3</a></i>;<br/>


</div>
