<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E29">Th35</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: NORMSP_4:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="lopban_1.html#NM2" title="LOPBAN_1:NM.2">RealBanachSpace</a><br/>  for <font color="Olive" title="b2">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font>  ex <font color="Olive" title="b3">Z</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font> st <br/>( <font color="Olive" title="b3">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <font color="Olive" title="b2">Y</font></span>)</span> &amp;  <a href="normsp_3.html#K19" title="NORMSP_3:func.19">ClNLin</a> <font color="Olive" title="b2">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normsp_3.html#K4" title="NORMSP_3:func.4">NLin</a> <span class="p1">(<span class="default"><a href="normsp_3.html#K1" title="NORMSP_3:func.1">Cl</a> <font color="Olive" title="b3">Z</font></span>)</span> &amp;  <a href="normsp_3.html#K1" title="NORMSP_3:func.1">Cl</a> <font color="Olive" title="b3">Z</font> is  <a href="rlsub_1.html#V1" title="RLSUB_1:attr.1">linearly-closed</a>  &amp;  <a href="normsp_3.html#K1" title="NORMSP_3:func.1">Cl</a> <font color="Olive" title="b3">Z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</div></div>
