<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">EQCL3</font></span>: <a NAME="T6"><span class="comment"><font color="firebrick">:: NORMSP_3:6</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b2">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">v</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <font color="Olive" title="b3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normsp_3.html#K1" title="NORMSP_3:func.1">Cl</a> <font color="Olive" title="b2">Y</font> iff  ex <font color="Olive" title="b4">seq</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">X</font> st <br/>(  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b4">seq</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">Y</font> &amp; <font color="Olive" title="b4">seq</font> is  <a href="normsp_1.html#V3" title="NORMSP_1:attr.3">convergent</a>  &amp;  <a href="normsp_1.html#K5" title="NORMSP_1:func.5">lim</a> <font color="Olive" title="b4">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v</font> ) )</div></div>
