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<div><span class="kw">theorem </span><a NAME="T21"><span class="comment"><font color="firebrick">:: KURATO_2:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">S</font> being   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</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="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span><br/>  for <font color="Olive" title="b3">p</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span>  st  ex <font color="Olive" title="b4">s</font> being   <a href="toprns_1.html#NM1" title="TOPRNS_1:NM.1">Real_Sequence</a> of <font color="Olive" title="b1">n</font> st <br/>( <font color="Olive" title="b4">s</font> is  <a href="toprns_1.html#V3" title="TOPRNS_1:attr.3">convergent</a>  &amp; (  for <font color="Olive" title="b5">x</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b4">s</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b5">x</font> ) &amp; <font color="Olive" title="b3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="toprns_1.html#K6" title="TOPRNS_1:func.6">lim</a> <font color="Olive" title="b4">s</font> ) holds <br/><font color="Olive" title="b3">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="kurato_2.html#K1" title="KURATO_2:func.1">Lim_inf</a> <font color="Olive" title="b2">S</font></div></div>
