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<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font>] <span class="kw">means </span> <a href="seq_4.html#K24" title="SEQ_4:func.24">dist</a> ($1,<font color="Maroon" title="c2">A</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">r</font>;<br/>
<a NAME="E1:131_1_1"/>
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">z</font> where <font color="Olive" title="b1">z</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">z</font>] </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="fraenkel.html#S10" title="FRAENKEL:sch.10">FRAENKEL:sch 10</a>();<br/></span>
<span class="kw">hence </span><a NAME="E2:131_1_1"/>
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">z</font> where <font color="Olive" title="b1">z</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font> :  <a href="seq_4.html#K24" title="SEQ_4:func.24">dist</a> (<font color="Olive" title="b1">z</font>,<font color="Maroon" title="c2">A</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">r</font> </span> } </span>  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>
 ; <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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