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<div><span class="kw">theorem </span><a NAME="T41"><span class="comment"><font color="firebrick">:: ZMODUL02:41</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">L1</font>, <font color="Olive" title="b4">L2</font> being    <a href="vectsp_6.html#M1" title="VECTSP_6:mode.1">Linear_Combination</a> of <font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b5">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">V</font>  st <font color="Olive" title="b3">L1</font> is    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Olive" title="b5">A</font> &amp; <font color="Olive" title="b4">L2</font> is    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Olive" title="b5">A</font> holds <br/><font color="Olive" title="b3">L1</font> <a href="vectsp_6.html#K8" title="VECTSP_6:func.8">-</a> <font color="Olive" title="b4">L2</font> is    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Olive" title="b5">A</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_6.html#T42" onmouseover="rs('vectsp_6/T42')" onmouseout="rh()">VECTSP_6:42</a></span>;<br/></div></div>
