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<b>let </b><font color="Maroon">R</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> non <a href="vectsp_1.html#V10">degenerated</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/>

<b>assume </b><a NAME="E1:2"/>
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span>
 ;<br/>

<b>then </b> <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> = 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T25">RLVECT_1:25</a></i>
<br/>.= 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30">RLVECT_1:30</a></i>
;<br/>
<b>hence </b><a NAME="E3:2"/>
contradiction
 <b>by </b><i><a class="ref" href="vectsp_1.html#D21">VECTSP_1:def 21</a></i>;<br/>


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