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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">z</font> be   <a href="cfunct_1.html#NM1">Complex</a>;<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/>







<b>assume </b><a NAME="E1:94"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font>
 ;<br/>

<i><font color="Green">E31</font></i>: <font color="Maroon">z</font> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="complex1.html#K11">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="complex1.html#K8">+</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</font>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="complex1.html#K11">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K6">1r</a>  <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">v</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="complex1.html#K11">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</font></span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E3:94"/>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="complex1.html#K11">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</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>, </i>;<br/>
<a NAME="E4:94"/><b>then </b>
<font color="Maroon">z</font> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">u</font></span>)</span> where <font color="Olive">u</font> is   <a href="clvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font> : <font color="Olive">u</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:94"/>
<font color="Maroon">z</font> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">v</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>
 ;<br/>


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