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<b>let </b><font color="Maroon">R</font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="vectsp_2.html#NM7">RightMod</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">W1</font> be    <a href="rmod_2.html#M1">Submodule</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">W2</font> be    <a href="rmod_2.html#M1">Submodule</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">W3</font> be    <a href="rmod_2.html#M1">Submodule</a> of <font color="Maroon">V</font>;<br/>









<b>assume </b><a NAME="E1:24"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">W1</font> is    <a href="rmod_2.html#M1">Submodule</a> of <font color="Maroon">W2</font> &amp; <font color="Maroon">W1</font> is    <a href="rmod_2.html#M1">Submodule</a> of <font color="Maroon">W3</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">v</font> be   <a href="vectsp_2.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/><b>assume </b><a NAME="E1:24_1"/>
<font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W1</font>
 ;<br/><a NAME="E2:24_1"/><b>then </b>
( <font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W2</font> &amp; <font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W3</font> )
 <b>by </b><i>, <a class="ref" href="rmod_2.html#T16">RMOD_2:16</a></i>;<br/><b>hence </b><a NAME="E3:24_1"/>
<font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W2</font> <a href="rmod_3.html#K2" target="_self">/\</a> <font color="Maroon">W3</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:24"/>
<font color="Maroon">W1</font> is    <a href="rmod_2.html#M1">Submodule</a> of <font color="Maroon">W2</font> <a href="rmod_3.html#K2" target="_self">/\</a> <font color="Maroon">W3</font>
 <b>by </b><i><a class="ref" href="rmod_2.html#T36">RMOD_2:36</a></i>;<br/>


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