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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">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#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font></span>)</span> holds <br/> ( <font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="seq_4.html#K27" title="SEQ_4:func.27">ComplexOpenSets</a> <font color="Maroon" title="c1">n</font> iff <font color="Olive" title="b1">A</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">B</font> be   <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#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="seq_4.html#K27" title="SEQ_4:func.27">ComplexOpenSets</a> <font color="Maroon" title="c1">n</font> iff <font color="Maroon" title="c2">B</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a>  )</span><br/>



<a NAME="E1:152"/>
( <font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <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#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font></span>)</span> : <font color="Olive" title="b1">A</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a>  </span> } </span>  iff  ex <font color="Olive" title="b1">C</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#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font></span>)</span> st <br/>( <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">C</font> &amp; <font color="Olive" title="b1">C</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a>  ) )
 
;<br/>
<span class="kw">hence </span><a NAME="E2:152"/>
( <font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="seq_4.html#K27" title="SEQ_4:func.27">ComplexOpenSets</a> <font color="Maroon" title="c1">n</font> iff <font color="Maroon" title="c2">B</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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