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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">u</font>, <font color="Maroon" title="c3">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="c4">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/><b>let </b><font color="Maroon" title="c5">C</font> be    <a href="clvect_1.html#M2" title="CLVECT_1:mode.2">Coset</a> of <font color="Maroon" title="c4">W</font>;<br/>









<b>assume </b><a NAME="E1:114"/>
( <font color="Maroon" title="c2">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">C</font> &amp; <font color="Maroon" title="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">C</font> )
 ;<br/>

<a NAME="E2:114"/><b>then </b>
( <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">u</font> <a href="clvect_1.html#K4" title="CLVECT_1:func.4">+</a> <font color="Maroon" title="c4">W</font> &amp; <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="clvect_1.html#K4" title="CLVECT_1:func.4">+</a> <font color="Maroon" title="c4">W</font> )
 
<b>by </b><i><a class="ref" href="clvect_1.html#T98" target="_self" title="CLVECT_1:th.98">Th98</a></i>;<br/>
<b>hence </b><a NAME="E3:114"/>
 ex <font color="Olive" title="b1">v1</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">v1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c4">W</font> &amp; <font color="Maroon" title="c2">u</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b1">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> )
 <b>by </b><i><a class="ref" href="clvect_1.html#T86" target="_self" title="CLVECT_1:th.86">Th86</a></i>;<br/>


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