<?xml version="1.0"?>
<div class="add">

<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>, <font color="Maroon">c<sub>4</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="E1:24"/>
( <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> &amp; <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> )
 ;<br/>

<a NAME="E2:24"/><b>then </b>
( <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> &amp; <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/>
<a NAME="E3:24"/><b>then </b>
<font color="Maroon">c<sub>2</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="vectsp_4.html#T34">VECTSP_4:34</a></i>;<br/>
<b>hence </b><a NAME="E4:24"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lmod_6.html#R1" target="_self">c=</a> <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/>


</div>
