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<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">V</font>;<br/>







<b>assume </b><a NAME="E1:9"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">v</font> <a href="rlsub_1.html#K3">+</a> <font color="Maroon">W</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">C</font> = <font color="Maroon">v</font> <a href="rlsub_1.html#K3">+</a> <font color="Maroon">W</font> as    <a href="rlsub_1.html#M2">Coset</a> of <font color="Maroon">W</font> <b>by </b><i><a class="ref" href="rlsub_1.html#D6">RLSUB_1:def 6</a></i>;<br/>
<a NAME="E3:9"/>
<font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="rlsub_1.html#K3">+</a> <font color="Maroon">W</font>
 
<b>by </b><i>, <a class="ref" href="rlsub_1.html#T94">RLSUB_1:94</a></i>;<br/>
<b>hence </b><a NAME="E4:9"/>
<font color="Maroon">v</font> <a href="rlsub_1.html#K3">+</a> <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="rlsub_1.html#K3">+</a> <font color="Maroon">W</font>
 ;<br/>


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