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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: ZMODUL02:25</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">L</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="b4">v1</font>, <font color="Olive" title="b5">v2</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b2">V</font>  st  <a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <font color="Olive" title="b3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b4">v1</font>,<font color="Olive" title="b5">v2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp; <font color="Olive" title="b4">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">v2</font> holds <br/> <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Olive" title="b3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">v1</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b4">v1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">v2</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b5">v2</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_6.html#T21" onmouseover="rs('vectsp_6/T21')" onmouseout="rh()">VECTSP_6:21</a></span>;<br/></div></div>
