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<b>consider </b><font color="Maroon">a1</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E2:50_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font>
 <b>by </b><i/>;<br/>
<div><i><font color="Green">E33</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/><b>assume </b><a NAME="E1:50_1_1_1"/>
<font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font>
 ;<br/><a NAME="E2:50_1_1_1"/><b>then </b>
<font color="Maroon">a</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">a1</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:50_1_1_1"/><b>then </b>
<font color="Maroon">r</font> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">a1</font></span>)</span> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font>
 <b>by </b><i><a class="ref" href="vectsp_4.html#T29">VECTSP_4:29</a></i>;<br/><a NAME="E4:50_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a1</font></span>)</span> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T70">VECTSP_1:70</a></i>;<br/><b>hence </b><a NAME="E5:50_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a1</font></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>take </b>
<span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a1</font></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font>
;<br/>

<b>thus </b><a NAME="E4:50_1_1"/>
for <font color="Olive">a</font> being  <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font>  st <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a1</font></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">a</font></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font>
 <b>by </b><i/>;<br/>


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