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<div><span class="kw">theorem </span><a NAME="T29"><span class="comment"><font color="firebrick">:: RMOD_3:29</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>, <font color="Olive" title="b5">W3</font> being    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Olive" title="b2">V</font> holds  <font color="Olive" title="b4">W2</font> <a href="rmod_3.html#K1" title="RMOD_3:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">W1</font> <a href="rmod_3.html#K2" title="RMOD_3:func.2">/\</a> <font color="Olive" title="b5">W3</font></span>)</span> is    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <span class="p1">(<span class="default"><font color="Olive" title="b3">W1</font> <a href="rmod_3.html#K1" title="RMOD_3:func.1">+</a> <font color="Olive" title="b4">W2</font></span>)</span> <a href="rmod_3.html#K2" title="RMOD_3:func.2">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">W2</font> <a href="rmod_3.html#K1" title="RMOD_3:func.1">+</a> <font color="Olive" title="b5">W3</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="rmod_3.html#E42"><span class="lab"><font color="Green" title="E27">Lm12</font></span></a>, <a class="ref" href="rmod_2.html#T27" onmouseover="rs('rmod_2/T27')" onmouseout="rh()">RMOD_2:27</a></span>;<br/></div></div>
