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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="vectsp_2.html#NM7">RightMod</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be  <a href="vectsp_2.html#V3">strict</a>  <a href="rmod_2.html#M1" target="_self">Submodule</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="rmod_2.html#M2" target="_self">Coset</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="rmod_2.html#M2" target="_self">Coset</a> of <font color="Maroon">c<sub>4</sub></font>;<br/>









<a NAME="E1:71"/><i><font color="Green">E48</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="vectsp_2.html#NM5">Vector</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="rmod_2.html#K3" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="rmod_2.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E2:71"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="vectsp_2.html#NM5">Vector</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="rmod_2.html#K3" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="rmod_2.html#D6" target="_self">Def6</a></i>;<br/>
<b>hence </b><a NAME="E3:71"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="rmod_2.html#E1:71"><i><font color="Green">E48</font></i></a>, <a class="ref" href="rmod_2.html#T80" target="_self">Th80</a></i>;<br/>


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