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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th47</font></span>: <a NAME="T47"><span class="comment"><font color="firebrick">:: ZMODUL02:47</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> holds  <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p2">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Olive" title="b2">V</font></span>)</span>,<font color="Olive" title="b3">L1</font>)</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p2">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Olive" title="b2">V</font></span>)</span>,<font color="Olive" title="b4">L2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">L1</font> <a href="vectsp_6.html#K5" title="VECTSP_6:func.5">+</a> <font color="Olive" title="b4">L2</font></div></div>
