<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E16">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: DUALSP06:18</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">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">M</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Olive" title="b1">X</font> holds  <span class="p1"> { <span class="default"> <span class="p2"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">x</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b4">m</font></span>)</span></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> where <font color="Olive" title="b4">m</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">X</font> : <font color="Olive" title="b4">m</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b3">M</font> </span> } </span>  is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="membered.html#V3" title="MEMBERED:attr.3">real-membered</a>   <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> </div></div>
