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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: COMPL_SP:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">M</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="metric_1.html#NM1" title="METRIC_1:NM.1">MetrSpace</a><br/>  for <font color="Olive" title="b2">A</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">M</font><br/>  for <font color="Olive" title="b3">S</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">M</font> <a href="topmetr.html#K1" title="TOPMETR:func.1">|</a> <font color="Olive" title="b2">A</font></span>)</span><br/>  for <font color="Olive" title="b4">S9</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">M</font>  st <font color="Olive" title="b3">S</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b4">S9</font> holds <br/>( <font color="Olive" title="b4">S9</font> is  <a href="tbsp_1.html#V3" title="TBSP_1:attr.3">Cauchy</a>  iff <font color="Olive" title="b3">S</font> is  <a href="tbsp_1.html#V3" title="TBSP_1:attr.3">Cauchy</a>  )</div></div>
