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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E47">Th42</font></span>: <a NAME="T43"><span class="comment"><font color="firebrick">:: COMPL_SP:43</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#V6" title="METRIC_1:attr.6">Reflexive</a>   <a href="metric_1.html#V8" title="METRIC_1:attr.8">symmetric</a>   <a href="metric_1.html#V9" title="METRIC_1:attr.9">triangle</a>   <a href="metric_1.html#L1" title="METRIC_1:struct.1">MetrStruct</a>   st <font color="Olive" title="b1">M</font> is  <a href="tbsp_1.html#V4" title="TBSP_1:attr.4">complete</a>  holds <br/> for <font color="Olive" title="b2">a</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">M</font>  st  ex <font color="Olive" title="b3">b</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">M</font> st  <a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> for <font color="Olive" title="b3">X</font> being   <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> (  <a href="compl_sp.html#K3" title="COMPL_SP:func.3">WellSpace</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">X</font>) is  <a href="tbsp_1.html#V4" title="TBSP_1:attr.4">complete</a>  &amp;  ex <font color="Olive" title="b4">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="kurato_2.html#NM1" title="KURATO_2:NM.1">SetSequence</a> of <span class="p1">(<span class="default"><a href="compl_sp.html#K3" title="COMPL_SP:func.3">WellSpace</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">X</font>)</span>)</span> st <br/>( <font color="Olive" title="b4">S</font> is  <a href="compl_sp.html#V7" title="COMPL_SP:attr.7">closed</a>  &amp; <font color="Olive" title="b4">S</font> is <a href="prob_1.html#V2" title="PROB_1:attr.2">V176</a>() &amp;  <a href="kurato_0.html#K2" title="KURATO_0:func.2">meet</a> <font color="Olive" title="b4">S</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  ) )</div></div>
