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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="clvect_1.html#NM2">ComplexLinearSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="clvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="cfunct_1.html#NM1">Complex</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="clvect_1.html#M1" target="_self">Subspace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:93"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="complex1.html#K6">1r</a> 
 <b>and </b><br/><a NAME="E2:93"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="clvect_1.html#K4" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E3:93"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="complex1.html#K11">-</a> <a href="complex1.html#K6">1r</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="clvect_1.html#E1:93"><i><font color="Green">E60</font></i></a></i>;<br/>
<a NAME="E4:93"/>
<font color="Maroon">c<sub>3</sub></font> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="clvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>4</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="clvect_1.html#E2:93"><i><font color="Green">E61</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="clvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:93"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E7:93"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>
<font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T28">RLVECT_1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="clvect_1.html#E6:93"><i><font color="Green">E63</font></i></a>, <a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</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">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="clvect_1.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="clvect_1.html#T11" target="_self">Th11</a></i>
;<br/>
<a NAME="E9:93"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="complex1.html#K11">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="complex1.html#K12">"</a> </span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="complex1.html#K11">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="complex1.html#K12">"</a> </span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="complex1.html#K11">-</a> <a href="complex1.html#K6">1r</a> </span>)</span></span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="complex1.html#K11">-</a> <a href="complex1.html#K6">1r</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 
<b>by </b><i><a class="txt" href="clvect_1.html#E3:93"><i><font color="Green">E62</font></i></a>, <a class="ref" href="clvect_1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E10:93"/><b>then </b>
<a href="complex1.html#K6">1r</a>  <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="complex1.html#K11">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="complex1.html#K12">"</a> </span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>;<br/>
<a NAME="E11:93"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="complex1.html#K11">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="complex1.html#K12">"</a> </span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="clvect_1.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E12:93"/>
<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="clvect_1.html#E7:93"><i><font color="Green">E64</font></i></a>, <a class="ref" href="clvect_1.html#T41" target="_self">Th41</a></i>;<br/>


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