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<div><span class="kw">theorem </span><a NAME="T13"><span class="comment"><font color="firebrick">:: C0SP3:13</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">T</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">g</font>, <font color="Olive" title="b5">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="c0sp3.html#K5" title="C0SP3:func.5">R_VectorSpace_of_ContinuousFunctions</a> (<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">T</font>)</span>)</span> holds <br/> ( <font color="Olive" title="b5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b4">g</font> iff  for <font color="Olive" title="b6">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font> holds  <font color="Olive" title="b5">h</font> <a href="c0sp3.html#K6" title="C0SP3:func.6">.</a> <font color="Olive" title="b6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="c0sp3.html#K6" title="C0SP3:func.6">.</a> <font color="Olive" title="b6">x</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">g</font> <a href="c0sp3.html#K6" title="C0SP3:func.6">.</a> <font color="Olive" title="b6">x</font></span>)</span> )</div></div>
