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<div><span class="kw">theorem </span><a NAME="T31"><span class="comment"><font color="firebrick">:: CARDFIL3:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="rltopsp1.html#NM1" title="RLTOPSP1:NM.1">LinearTopSpace</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 <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b4">V</font> being   <a href="rltopsp1.html#NM2" title="RLTOPSP1:NM.2">local_base</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cardfil2.html#K20" title="CARDFIL2:func.20">lim_f</a> <font color="Olive" title="b2">s</font> iff  for <font color="Olive" title="b5">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="b5">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">V</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="yellow19.html#K1" title="YELLOW19:func.1">NeighborhoodSystem</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">X</font></span>)</span></span>)</span> holds <br/> ex <font color="Olive" title="b6">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/> for <font color="Olive" title="b7">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b6">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b7">j</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="b7">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">x</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Olive" title="b5">v</font> )</div></div>
