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<b>take </b>
 <a href="vectsp_2.html#K4" target="_self">LeftModule</a> <font color="Maroon">R</font>
;<br/>

<b>thus </b><a NAME="E1:62_1_1"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">R</font><br/> for <font color="Olive">v</font>, <font color="Olive">w</font> being  <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp_2.html#K4" target="_self">LeftModule</a> <font color="Maroon">R</font></span>)</span> holds <br/> ( <font color="Olive">x</font> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Olive">v</font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">w</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">w</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">y</font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">y</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="group_1.html#K1">*</a> <font color="Olive">y</font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Olive">y</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Olive">v</font> <a href="hidden.html#R1">=</a> <font color="Olive">v</font> )
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_1.html#D26">VECTSP_1:def 26</a><br/>

<b>thus </b><a NAME="E2:62_1_1"/>
(  <a href="vectsp_2.html#K4" target="_self">LeftModule</a> <font color="Maroon">R</font> is <a href="rlvect_1.html#V3">Abelian</a> &amp;  <a href="vectsp_2.html#K4" target="_self">LeftModule</a> <font color="Maroon">R</font> is <a href="rlvect_1.html#V4">add-associative</a> &amp;  <a href="vectsp_2.html#K4" target="_self">LeftModule</a> <font color="Maroon">R</font> is <a href="rlvect_1.html#V5">right_zeroed</a> &amp;  <a href="vectsp_2.html#K4" target="_self">LeftModule</a> <font color="Maroon">R</font> is <a href="rlvect_1.html#V6">right_complementable</a> &amp;  <a href="vectsp_2.html#K4" target="_self">LeftModule</a> <font color="Maroon">R</font> is <a href="vectsp_1.html#V11">strict</a> )
 ;<br/>


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