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<div><span class="kw">theorem </span><a NAME="T45"><span class="comment"><font color="firebrick">:: RMOD_3:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">V</font> being   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">RightMod</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">W1</font>, <font color="Olive" title="b4">W2</font> being    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b5">v</font> being   <a href="vectsp_2.html#NM4" title="VECTSP_2:NM.4">Vector</a> of <font color="Olive" title="b2">V</font>  st <font color="Olive" title="b2">V</font> <a href="rmod_3.html#R1" title="RMOD_3:pred.1">is_the_direct_sum_of</a> <font color="Olive" title="b3">W1</font>,<font color="Olive" title="b4">W2</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="rmod_3.html#K4" title="RMOD_3:func.4">|--</a> (<font color="Olive" title="b3">W1</font>,<font color="Olive" title="b4">W2</font>)</span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="rmod_3.html#K4" title="RMOD_3:func.4">|--</a> (<font color="Olive" title="b4">W2</font>,<font color="Olive" title="b3">W1</font>)</span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </div></div>
