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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="rlvect_2.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="rlvect_2.html#K1" target="_self">vector</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="rlvect_2.html#K1" target="_self">vector</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E1:79"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="rlvect_2.html#D16" target="_self">Def16</a></i>;<br/>
<a NAME="E2:79"/><b>then </b><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#R1">in</a>  <a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="rlvect_1.html#R1">in</a>  <a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E3:79"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_2.html#R1" target="_self">=</a>  <a href="rlvect_2.html#K12" target="_self">@</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K13" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="rlvect_2.html#R1" target="_self">=</a>  <a href="rlvect_2.html#K12" target="_self">@</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K13" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 
;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="rlvect_2.html#K1" target="_self">vector</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" target="_self">vector</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> = 
the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_2.html#K1" target="_self">vector</a> <span class="p3">(<span class="default"><a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="rlvect_2.html#K1" target="_self">vector</a> <span class="p3">(<span class="default"><a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D3">RLVECT_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" target="_self">LCAdd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_2.html#K1" target="_self">vector</a> <span class="p3">(<span class="default"><a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="rlvect_2.html#K1" target="_self">vector</a> <span class="p3">(<span class="default"><a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" target="_self">LCAdd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="rlvect_2.html#K1" target="_self">vector</a> <span class="p3">(<span class="default"><a href="rlvect_2.html#K16" target="_self">LC_RLSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="rlvect_2.html#E2:79"><i><font color="Green">E50</font></i></a>, <a class="ref" href="rlvect_2.html#D1" target="_self">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" target="_self">LCAdd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="rlvect_2.html#E2:79"><i><font color="Green">E50</font></i></a>, <a class="ref" href="rlvect_2.html#D1" target="_self">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" target="_self">LCAdd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_2.html#K13" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" target="_self">LCAdd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_2.html#K13" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="rlvect_2.html#K13" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" target="_self">LCAdd</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K13" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_2.html#K7" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E3:79"><i><font color="Green">E51</font></i></a>, <a class="ref" href="rlvect_2.html#D19" target="_self">Def19</a></i>
;<br/>


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