<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th24</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: DUALSP01:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font>, <font color="Olive" title="b4">h</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <span class="p1">(<span class="default"><a href="dualsp01.html#K12" title="DUALSP01:func.12">R_VectorSpace_of_BoundedLinearFunctionals</a> <font color="Olive" title="b1">X</font></span>)</span> holds <br/> ( <font color="Olive" title="b4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b3">g</font> iff  for <font color="Olive" title="b5">x</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b1">X</font> holds  <font color="Olive" title="b4">h</font> <a href="dualsp01.html#K13" title="DUALSP01:func.13">.</a> <font color="Olive" title="b5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="dualsp01.html#K13" title="DUALSP01:func.13">.</a> <font color="Olive" title="b5">x</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">g</font> <a href="dualsp01.html#K13" title="DUALSP01:func.13">.</a> <font color="Olive" title="b5">x</font></span>)</span> )</div></div>
