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<b>let </b><font color="Maroon">R</font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="vectsp_2.html#NM7">RightMod</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="vectsp_2.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="vectsp_2.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="rmod_2.html#M1" target="_self">Submodule</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">C</font> be    <a href="rmod_2.html#M2" target="_self">Coset</a> of <font color="Maroon">W</font>;<br/>











<b>assume </b><a NAME="E1:79"/>
( <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 ;<br/>

<a NAME="E2:79"/><b>then </b>
( <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="rmod_2.html#K3" target="_self">+</a> <font color="Maroon">W</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="rmod_2.html#K3" target="_self">+</a> <font color="Maroon">W</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:79"/>
 ex <font color="Olive">v1</font> being  <a href="vectsp_2.html#NM5">Vector</a> of <font color="Maroon">V</font> st <br/>( <font color="Olive">v1</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> &amp; <font color="Maroon">u</font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">v1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> )
 <b>by </b><i/>;<br/>


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