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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="clvect_1.html#NM2" title="CLVECT_1:NM.2">ComplexLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">v</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>;<br/><b>let </b><font color="Maroon" title="c3">W</font> be    <a href="clvect_1.html#M1" title="CLVECT_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">V</font>;<br/>





<a NAME="E1:95"/><i><font color="Green" title="E61">A1</font></i>: 
( ( <font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c3">W</font> implies <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">v</font> <a href="clvect_1.html#K4" title="CLVECT_1:func.4">+</a> <font color="Maroon" title="c3">W</font> ) &amp; <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">v</font> )
 
<b>by </b><i><a class="ref" href="clvect_1.html#T4" target="_self" title="CLVECT_1:th.4">Th4</a>, <a class="ref" href="clvect_1.html#T79" target="_self" title="CLVECT_1:th.79">Th79</a></i>;<br/>
<a NAME="E2:95"/><i><font color="Green" title="E62">A2</font></i>: 
(  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> &amp;  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="complex1.html#T34" title="COMPLEX1:th.34">COMPLEX1:34</a></i>;<br/>
<a NAME="E3:95"/>
(  <a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a>  &amp; <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">v</font> <a href="clvect_1.html#K4" title="CLVECT_1:func.4">+</a> <font color="Maroon" title="c3">W</font> implies <font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c3">W</font> )
 
<b>by </b><i><a class="ref" href="clvect_1.html#T78" target="_self" title="CLVECT_1:th.78">Th78</a></i>;<br/>
<b>hence </b><a NAME="E4:95"/>
(  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">v</font> <a href="clvect_1.html#K4" title="CLVECT_1:func.4">+</a> <font color="Maroon" title="c3">W</font> iff <font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c3">W</font> )
 <b>by </b><i><a class="txt" href="clvect_1.html#E1:95"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="clvect_1.html#E2:95"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="complex1.html#T15" title="COMPLEX1:th.15">COMPLEX1:15</a></i>;<br/>


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