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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="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<a NAME="E1:43"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="lmod_6.html#R1" target="_self">c=</a> <font color="Maroon">c<sub>4</sub></font> iff <font color="Maroon">c<sub>3</sub></font> is    <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="lmod_6.html#D7" target="_self">Def7</a></i>;<br/>
<b>hence </b><a NAME="E2:43"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="lmod_6.html#R1" target="_self">c=</a> <font color="Maroon">c<sub>4</sub></font> iff for <font color="Olive">b<sub>1</sub></font> being  <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>3</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="vectsp_4.html#T16">VECTSP_4:16</a>, <a class="ref" href="vectsp_4.html#T36">VECTSP_4:36</a></i>;<br/>


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