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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th10</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: COMPL_SP:10</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> holds <br/> ( <font color="Olive" title="b1">M</font> is  <a href="tbsp_1.html#V4" title="TBSP_1:attr.4">complete</a>  iff  for <font color="Olive" title="b2">S</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="compl_sp.html#V1" title="COMPL_SP:attr.1">pointwise_bounded</a>   <a href="compl_sp.html#V7" title="COMPL_SP:attr.7">closed</a>  <a href="kurato_2.html#NM1" title="KURATO_2:NM.1">SetSequence</a> of <font color="Olive" title="b1">M</font>  st <font color="Olive" title="b2">S</font> is <a href="prob_1.html#V2" title="PROB_1:attr.2">V176</a>() &amp;  <a href="seq_2.html#K1" title="SEQ_2:func.1">lim</a> <span class="p1">(<span class="default"><a href="compl_sp.html#K1" title="COMPL_SP:func.1">diameter</a> <font color="Olive" title="b2">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> not  <a href="kurato_0.html#K2" title="KURATO_0:func.2">meet</a> <font color="Olive" title="b2">S</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )</div></div>
