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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">u</font> be   <a href="vectsp_2.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/><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>let </b><font color="Maroon">W</font> be    <a href="rmod_2.html#M1" target="_self">Submodule</a> of <font color="Maroon">V</font>;<br/>









<b>assume </b><a NAME="E1:22"/>
( <font color="Maroon">u</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> &amp; <font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> )
 ;<br/>

<a NAME="E2:22"/><b>then </b><i><font color="Green">E33</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font> )
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">VW</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font> <b>by </b><i/>;<br/>
<a NAME="E4:22"/>
<font color="Maroon">VW</font> is <a href="rmod_2.html#V1" target="_self">lineary-closed</a>
 
<b>by </b><i/>;<br/>
<a NAME="E5:22"/><b>then </b>
<font color="Maroon">u</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:22"/>
<font color="Maroon">u</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>


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