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<div><span class="kw">theorem </span><a NAME="T28"><span class="comment"><font color="firebrick">:: DUALSP03:28</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">X0</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font>  st  not <font color="Olive" title="b1">X</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  &amp; <font color="Olive" title="b1">X</font> is  <a href="dualsp02.html#V1" title="DUALSP02:attr.1">Reflexive</a>  holds <br/>( <font color="Olive" title="b2">X0</font> is  <a href="dualsp03.html#V3" title="DUALSP03:attr.3">weakly-sequentially-compact</a>  iff  ex <font color="Olive" title="b3">S</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> st <br/>( <font color="Olive" title="b3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b4">x</font></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> where <font color="Olive" title="b4">x</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">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">X0</font> </span> } </span>  &amp; <font color="Olive" title="b3">S</font> is  <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a>  ) )</div></div>
