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<b>let </b><font color="Maroon">V</font> be   <a href="clvect_1.html#NM2">ComplexLinearSpace</a>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="clvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="clvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="clvect_1.html#M1" target="_self">Subspace</a> of <font color="Maroon">V</font>;<br/>







<a NAME="E1:97"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">u</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v</font>
 
;<br/>
<a NAME="E2:97"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">u</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> implies  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">u</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> )
 
<b>by </b><i><a class="txt" href="clvect_1.html#E2:97"><i><font color="Green">E31</font></i></a></i>;<br/>
<a NAME="E3:97"/>
(  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">u</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> implies  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">u</font></span>)</span> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> )
 
<b>by </b><i><a class="txt" href="clvect_1.html#E2:97"><i><font color="Green">E31</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:97"/>
( <font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">v</font> <a href="clvect_1.html#K4" target="_self">+</a> <font color="Maroon">W</font> iff <font color="Maroon">u</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> )
 <b>by </b><i>, , <a class="txt" href="clvect_1.html#E17"><i><font color="Green">Lemma61</font></i></a>, <a class="ref" href="rlvect_1.html#T30">RLVECT_1:30</a></i>;<br/>


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