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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">v1</font>, <font color="Maroon" title="c5">v2</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="c6">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="E1:58"/><i><font color="Green" title="E41">A1</font></i>: 
<font color="Maroon" title="c3">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v1</font> <a href="rmod_2.html#K3" title="RMOD_2:func.3">+</a> <font color="Maroon" title="c6">W</font>
 <b>and </b><br/><a NAME="E2:58"/><i><font color="Green" title="E42">A2</font></i>: 
<font color="Maroon" title="c3">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">v2</font> <a href="rmod_2.html#K3" title="RMOD_2:func.3">+</a> <font color="Maroon" title="c6">W</font>
 ;<br/>

<b>thus </b><font color="Maroon" title="c4">v1</font> <a href="rmod_2.html#K3" title="RMOD_2:func.3">+</a> <font color="Maroon" title="c6">W</font> = 
<font color="Maroon" title="c3">u</font> <a href="rmod_2.html#K3" title="RMOD_2:func.3">+</a> <font color="Maroon" title="c6">W</font>
<b>by </b><i><a class="txt" href="rmod_2.html#E1:58"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="rmod_2.html#T68" target="_self" title="RMOD_2:th.68">Th68</a></i>
<br/>.= 
<font color="Maroon" title="c5">v2</font> <a href="rmod_2.html#K3" title="RMOD_2:func.3">+</a> <font color="Maroon" title="c6">W</font>
<b>by </b><i><a class="txt" href="rmod_2.html#E2:58"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="rmod_2.html#T68" target="_self" title="RMOD_2:th.68">Th68</a></i>
;<br/>


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