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<div><span class="kw">theorem </span><a NAME="T19"><span class="comment"><font color="firebrick">:: METRIC_6:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</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">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</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 <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b3">S</font> <a href="metric_6.html#R1" title="METRIC_6:pred.1">is_convergent_in_metrspace_to</a> <font color="Olive" title="b2">x</font> iff  for <font color="Olive" title="b4">V</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">V</font> &amp; <font color="Olive" title="b4">V</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="pcomps_1.html#K2" title="PCOMPS_1:func.2">Family_open_set</a> <font color="Olive" title="b1">X</font> holds <br/><font color="Olive" title="b4">V</font> <a href="metric_6.html#R2" title="METRIC_6:pred.2">contains_almost_all_sequence</a> <font color="Olive" title="b3">S</font> )</div></div>
