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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="clvect_1.html#M1" target="_self">Subspace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="clvect_1.html#M2" target="_self">Coset</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>







<b>thus </b><a NAME="E1:113"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> implies <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="clvect_1.html#K4" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:113_1"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:113_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="clvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="clvect_1.html#K4" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="clvect_1.html#D8" target="_self">Def8</a></i>;<br/>
<b>hence </b><a NAME="E3:113_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="clvect_1.html#K4" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="clvect_1.html#E1:113_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="clvect_1.html#T74" target="_self">Th74</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:113"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="clvect_1.html#K4" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="clvect_1.html#T63" target="_self">Th63</a></i>;<br/>


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