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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th24</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: DUALSP06:24</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 <span class="p1">(<span class="default"><a href="dualsp01.html#K17" title="DUALSP01:func.17">DualSp</a> <font color="Olive" title="b1">X</font></span>)</span><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">(<span class="default"><font color="Olive" title="b4">y</font> <a href="dualsp06.html#K2" title="DUALSP06:func.2">.|.</a> <font color="Olive" title="b2">x</font></span>)</span> where <font color="Olive" title="b4">y</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">y</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b3">M</font> &amp; <span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b4">y</font></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 ) </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#V4" title="XXREAL_2:attr.4">bounded_above</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> </div></div>
