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<div><span class="kw">theorem </span><a NAME="T111"><span class="comment"><font color="firebrick">:: ZMODUL01:111</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#NM5" title="VECTSP_2:NM.5">LeftMod</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="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b2">V</font> holds  <font color="Olive" title="b3">W1</font> <a href="vectsp_5.html#K2" title="VECTSP_5:func.2">/\</a> <font color="Olive" title="b4">W2</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b3">W1</font> <a href="zmodul01.html#K1" title="ZMODUL01:func.1">+</a> <font color="Olive" title="b4">W2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="zmodul01.html#E128"><span class="lab"><font color="Green" title="E34">Lm9</font></span></a>, <a class="ref" href="zmodul01.html#T43" target="_self" onmouseover="rs('zmodul01/T43')" onmouseout="rh()">Th43</a></span>;<br/></div></div>
