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<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c4">v</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font>;<br/><b>let </b><font color="Maroon" title="c5">W</font> be    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c2">V</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:25"/><i><font color="Green" title="E19">A1</font></i>: 
<font color="Maroon" title="c3">u</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 <b>and </b><br/><a NAME="E2:25"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c4">v</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 ;<br/>

<a NAME="E3:25"/>
 <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">v</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 
<b>by </b><i><a class="txt" href="rmod_2.html#E2:25"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="rmod_2.html#T30" target="_self" title="RMOD_2:th.30">Th30</a></i>;<br/>
<a NAME="E4:25"/><b>then </b>
<font color="Maroon" title="c3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 
<b>by </b><i><a class="txt" href="rmod_2.html#E1:25"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="rmod_2.html#T28" target="_self" title="RMOD_2:th.28">Th28</a></i>;<br/>
<b>hence </b><a NAME="E5:25"/>
<font color="Maroon" title="c3">u</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">v</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 ;<br/>


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