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<div>:: <span class="kw">deftheorem </span>   defines <a href="seq_4.html#V2" title="SEQ_4:attr.2">closed</a> <a onclick="hs(this)" href="javascript:()">SEQ_4:def 15 : <br/></a><span> 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">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="seq_4.html#K12" title="SEQ_4:func.12">COMPLEX</a> <font color="Olive" title="b1">n</font></span>)</span> holds <br/> ( <font color="Olive" title="b2">A</font> is  <a href="seq_4.html#V2" title="SEQ_4:attr.2">closed</a>  iff  for <font color="Olive" title="b3">x</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="seq_4.html#K12" title="SEQ_4:func.12">COMPLEX</a> <font color="Olive" title="b1">n</font>  st (  for <font color="Olive" title="b4">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b4">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> ex <font color="Olive" title="b5">z</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="seq_4.html#K12" title="SEQ_4:func.12">COMPLEX</a> <font color="Olive" title="b1">n</font> st <br/>( <span class="p1"><a href="seq_4.html#K20" title="SEQ_4:func.20">|.</a><span class="default"><font color="Olive" title="b5">z</font></span><a href="seq_4.html#K20" title="SEQ_4:func.20">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b4">r</font> &amp; <font color="Olive" title="b3">x</font> <a href="seq_4.html#K13" title="SEQ_4:func.13">+</a> <font color="Olive" title="b5">z</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> ) ) holds <br/><font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> );<br/></span></div>
