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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">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="complsp1.html#K8" title="COMPLSP1:func.8">COMPLEX</a> <font color="Maroon" title="c1">n</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:105"/>
<font color="Maroon" title="c2">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">B</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:105"/><i><font color="Green" title="E84">A1</font></i>: 
( <font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">z</font> = <font color="Maroon" title="c4">z</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="complsp1.html#K8" title="COMPLSP1:func.8">COMPLEX</a> <font color="Maroon" title="c1">n</font> <b>by </b><i><a class="txt" href="complsp1.html#E3:105"><i><font color="Green" title="E84">A1</font></i></a></i>;<br/>
<a NAME="E5:105"/>
(  <a href="complsp1.html#K18" title="COMPLSP1:func.18">dist</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp;  <a href="complsp1.html#K18" title="COMPLSP1:func.18">dist</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 
<b>by </b><i><a class="txt" href="complsp1.html#E3:105"><i><font color="Green" title="E84">A1</font></i></a>, <a class="ref" href="complsp1.html#T87" target="_self" title="COMPLSP1:th.87">Th87</a></i>;<br/>
<a NAME="E6:105"/><b>then </b>
0 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 0 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="complsp1.html#K20" title="COMPLSP1:func.20">dist</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>
 
<b>by </b><i><a class="txt" href="complsp1.html#E3:105"><i><font color="Green" title="E84">A1</font></i></a>, <a class="ref" href="complsp1.html#T100" target="_self" title="COMPLSP1:th.100">Th100</a></i>;<br/>
<b>hence </b><a NAME="E7:105"/>
 <a href="complsp1.html#K20" title="COMPLSP1:func.20">dist</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="complsp1.html#E3:105"><i><font color="Green" title="E84">A1</font></i></a>, <a class="ref" href="complsp1.html#T98" target="_self" title="COMPLSP1:th.98">Th98</a></i>;<br/>


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