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<div><span class="kw">theorem </span><a NAME="T47"><span class="comment"><font color="firebrick">:: RMOD_4:47</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#NM6" title="VECTSP_2:NM.6">RightMod</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">a</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b4">L1</font>, <font color="Olive" title="b5">L2</font> being    <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Olive" title="b2">V</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b4">L1</font> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <font color="Olive" title="b5">L2</font></span>)</span> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Olive" title="b3">a</font> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">L1</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Olive" title="b3">a</font></span>)</span> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">L2</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Olive" title="b3">a</font></span>)</span></div></div>
