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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#NM6">LeftMod</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="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:13"/><i><font color="Green">E11</font></i>: 
(  <a href="mod_3.html#K1" target="_self">Lin</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E2:13"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is    <a href="vectsp_4.html#M1">Subspace</a> of  <a href="mod_3.html#K1" target="_self">Lin</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="mod_3.html#T17" target="_self">Th17</a></i>;<br/>
<b>hence </b><a NAME="E3:13"/>
 <a href="mod_3.html#K1" target="_self">Lin</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="mod_3.html#E1:13"><i><font color="Green">E11</font></i></a>, <a class="ref" href="vectsp_4.html#T33">VECTSP_4:33</a></i>;<br/>


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