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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E8">Th8</font></span>: <a NAME="T11"><span class="comment"><font color="firebrick">:: CARDFIL3:11</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">s</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="pcomps_1.html#K3" title="PCOMPS_1:func.3">TopSpaceMetr</a> <font color="Olive" title="b1">M</font></span>)</span><br/>  for <font color="Olive" title="b3">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="pcomps_1.html#K3" title="PCOMPS_1:func.3">TopSpaceMetr</a> <font color="Olive" title="b1">M</font></span>)</span> holds <br/> ( <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="frechet.html#K2" title="FRECHET:func.2">Lim</a> <font color="Olive" title="b2">s</font> iff  for <font color="Olive" title="b4">b</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="frechet.html#K1" title="FRECHET:func.1">Balls</a> <font color="Olive" title="b3">x</font>  ex <font color="Olive" title="b5">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/> for <font color="Olive" title="b6">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b5">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b6">m</font> holds <br/><font color="Olive" title="b2">s</font> <a href="normsp_0.html#K1" title="NORMSP_0:func.1">.</a> <font color="Olive" title="b6">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">b</font> )</div></div>
