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<b>let </b><font color="Maroon">GF</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</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> <a href="group_1.html#V4">associative</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_1.html#V8">left_unital</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">V</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</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> <a href="vectsp_1.html#V12">VectSp-like</a>  <a href="vectsp_1.html#L4">VectSpStr</a> of <font color="Maroon">GF</font>;<br/>



<b>consider </b><font color="Maroon">F</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E2:18"/>
<font color="Maroon">F</font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>and </b><br/><a NAME="E3:18"/><i><font color="Green">E47</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_6.html#K1" target="_self">Carrier</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K2" target="_self">ZeroLC</a> <font color="Maroon">V</font></span>)</span>
 <b>and </b><br/><a NAME="E4:18"/><i><font color="Green">E55</font></i>: 
 <a href="vectsp_6.html#K4" target="_self">Sum</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K2" target="_self">ZeroLC</a> <font color="Maroon">V</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_6.html#K2" target="_self">ZeroLC</a> <font color="Maroon">V</font></span>)</span> <a href="vectsp_6.html#K3" target="_self">(#)</a> <font color="Maroon">F</font></span>)</span>
 <b>by </b><i/>;<br/>
<a NAME="E5:18"/>
 <a href="vectsp_6.html#K1" target="_self">Carrier</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K2" target="_self">ZeroLC</a> <font color="Maroon">V</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E6:18"/><b>then </b>
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T27">FINSEQ_1:27</a></i>;<br/>
<a NAME="E7:18"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<a NAME="E8:18"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_6.html#K2" target="_self">ZeroLC</a> <font color="Maroon">V</font></span>)</span> <a href="vectsp_6.html#K3" target="_self">(#)</a> <font color="Maroon">F</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E9:18"/>
 <a href="vectsp_6.html#K4" target="_self">Sum</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K2" target="_self">ZeroLC</a> <font color="Maroon">V</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font>
 <b>by </b><i>, <a class="ref" href="rlvect_1.html#T94">RLVECT_1:94</a></i>;<br/>


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