<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E26">Th24</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: RLAFFIN1:24</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">R</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">vector-distributive</a>   <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">scalar-distributive</a>   <a href="rlvect_1.html#V7" title="RLVECT_1:attr.7">scalar-associative</a>   <a href="rlvect_1.html#V8" title="RLVECT_1:attr.8">scalar-unital</a>   <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">RLSStruct</a> <br/>  for <font color="Olive" title="b3">LR1</font>, <font color="Olive" title="b4">LR2</font> being    <a href="rlvect_2.html#M1" title="RLVECT_2:mode.1">Linear_Combination</a> of <font color="Olive" title="b2">R</font> holds  <font color="Olive" title="b1">r</font> <a href="rlaffin1.html#K2" title="RLAFFIN1:func.2">(*)</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">LR1</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <font color="Olive" title="b4">LR2</font></span>)</span> <a href="rlvect_2.html#R1" title="RLVECT_2:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">r</font> <a href="rlaffin1.html#K2" title="RLAFFIN1:func.2">(*)</a> <font color="Olive" title="b3">LR1</font></span>)</span> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">r</font> <a href="rlaffin1.html#K2" title="RLAFFIN1:func.2">(*)</a> <font color="Olive" title="b4">LR2</font></span>)</span></div></div>
