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<div class="add">

<b>set </b><font color="Maroon">G</font> = <font color="Maroon">V</font> <a href="lmod_7.html#K13" target="_self">.</a> <font color="Maroon">W</font>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D5">RLVECT_1:def 5</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">V</font> <a href="lmod_7.html#K13" target="_self">.</a> <font color="Maroon">W</font></span>)</span>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">V</font> <a href="lmod_7.html#K13" target="_self">.</a> <font color="Maroon">W</font></span>)</span>;<br/><b>consider </b><font color="Maroon">a</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E2:49_1_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">x</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>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">b</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E4:49_1_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font>
 <b>by </b><i/>;<br/><a NAME="E5:49_1_1_1"/>
( <font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font> &amp; <font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">a</font></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font> )
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E6:49_1_1_1"/>
<font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">x</font>
 ;<br/></div>
<b>end;</b></div>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">V</font> <a href="lmod_7.html#K13" target="_self">.</a> <font color="Maroon">W</font></span>)</span>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">V</font> <a href="lmod_7.html#K13" target="_self">.</a> <font color="Maroon">W</font></span>)</span>, <font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">V</font> <a href="lmod_7.html#K13" target="_self">.</a> <font color="Maroon">W</font></span>)</span>;<br/><b>consider </b><font color="Maroon">a</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E2:49_1_1_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">x</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>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">b</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E4:49_1_1_2"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">c</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E6:49_1_1_2"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font>
 <b>by </b><i/>;<br/><a NAME="E7:49_1_1_2"/><i><font color="Green">E77</font></i>: 
( <font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font> &amp; <font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">a</font></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font> &amp; <font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font> )
 <b>by </b><i>, , , </i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">y</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
<font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i>, , </i>
;<br/><br/></div>
<b>end;</b></div>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">V</font> <a href="lmod_7.html#K13" target="_self">.</a> <font color="Maroon">W</font></span>)</span>;<br/><b>consider </b><font color="Maroon">a</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E2:49_1_1_3"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">x</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>
 <b>by </b><i/>;<br/><a NAME="E3:49_1_1_3"/>
 <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><font color="Maroon">V</font> <a href="lmod_7.html#K13" target="_self">.</a> <font color="Maroon">W</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font>
 ;<br/><b>hence </b><font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <span class="p2">(<span class="default"><font color="Maroon">V</font> <a href="lmod_7.html#K13" target="_self">.</a> <font color="Maroon">W</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>
;<br/><br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">V</font> <a href="lmod_7.html#K13" target="_self">.</a> <font color="Maroon">W</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D8">RLVECT_1:def 8</a><br/>

<b>consider </b><font color="Maroon">a</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E5:49_1_1"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">x</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>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">b</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E7:49_1_1"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font> <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#D8">RLVECT_1:def 8</a></i>;<br/>
<b>reconsider </b><font color="Maroon">b'</font> = <font color="Maroon">b</font> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">V</font> <a href="lmod_7.html#K13" target="_self">.</a> <font color="Maroon">W</font></span>)</span> ;<br/>
<b>take </b>
<font color="Maroon">b'</font>
;<br/>

<b>thus </b><font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">b'</font> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span> <a href="lmod_7.html#K14" target="_self">.</a> <font color="Maroon">W</font>
<b>by </b><i>, , </i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><font color="Maroon">V</font> <a href="lmod_7.html#K13" target="_self">.</a> <font color="Maroon">W</font></span>)</span>

;<br/>


</div>
