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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>, <font color="Maroon">c<sub>3</sub></font> be   <a href="vectsp_2.html#NM6">LeftMod</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:27"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lmod_6.html#R1" target="_self">c=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:27"/><b>then </b><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is    <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="lmod_6.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E3:27"/>
<font color="Maroon">c<sub>3</sub></font> is    <a href="vectsp_4.html#M1">Subspace</a> of  <a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="lmod_6.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E4:27"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is    <a href="vectsp_4.html#M1">Subspace</a> of  <a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="lmod_6.html#E2:27"><i><font color="Green">E11</font></i></a>, <a class="ref" href="vectsp_4.html#T34">VECTSP_4:34</a></i>;<br/>
<b>hence </b><a NAME="E5:27"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lmod_6.html#R1" target="_self">c=</a>  <a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="lmod_6.html#D7" target="_self">Def7</a></i>;<br/>


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