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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#V2" title="VECTSP_2:attr.2">strict</a> <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font>;<br/>



<a NAME="E1:47"/>
( <span class="p1">(<span class="default"><a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="rmod_3.html#K1" title="RMOD_3:func.1">+</a> <span class="p1">(<span class="default"><a href="rmod_2.html#K2" title="RMOD_2:func.2">(Omega).</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V</font> &amp;  <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Maroon" title="c2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="rmod_3.html#K2" title="RMOD_3:func.2">/\</a> <span class="p1">(<span class="default"><a href="rmod_2.html#K2" title="RMOD_2:func.2">(Omega).</a> <font color="Maroon" title="c2">V</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="rmod_3.html#T13" target="_self" title="RMOD_3:th.13">Th13</a>, <a class="ref" href="rmod_3.html#T25" target="_self" title="RMOD_3:th.25">Th25</a></i>;<br/>
<b>hence </b><a NAME="E2:47"/>
<font color="Maroon" title="c2">V</font> <a href="rmod_3.html#R1" title="RMOD_3:pred.1">is_the_direct_sum_of</a>  <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Maroon" title="c2">V</font>, <a href="rmod_2.html#K2" title="RMOD_2:func.2">(Omega).</a> <font color="Maroon" title="c2">V</font>
 <b>by </b><i><a class="ref" href="rmod_3.html#D4" target="_self" title="RMOD_3:def.4">Def4</a></i>;<br/>

<b>hence </b><a NAME="E3:47"/>
<font color="Maroon" title="c2">V</font> <a href="rmod_3.html#R1" title="RMOD_3:pred.1">is_the_direct_sum_of</a>  <a href="rmod_2.html#K2" title="RMOD_2:func.2">(Omega).</a> <font color="Maroon" title="c2">V</font>, <a href="rmod_2.html#K1" title="RMOD_2:func.1">(0).</a> <font color="Maroon" title="c2">V</font>
 <b>by </b><i><a class="ref" href="rmod_3.html#T46" target="_self" title="RMOD_3:th.46">Th46</a></i>;<br/>


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