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<div class="add">

<b>let </b><font color="Maroon">X</font> be   <a href="csspace.html#NM1">ComplexUnitarySpace</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/>





<b>thus </b><a NAME="E1:79"/>
( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> implies  <a href="csspace.html#K15" target="_self">dist</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1"><b>proof </b></a><div class="add">

<b>assume </b><b>that </b><br/><a NAME="E1:79_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 <b>and </b><br/><a NAME="E2:79_1"/><i><font color="Green">E33</font></i>: 
 <a href="csspace.html#K15" target="_self">dist</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E3:79_1"/>
<span class="p1"><a href="csspace.html#K13" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">y</font></span>)</span></span><a href="csspace.html#K13" target="_self">.||</a></span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="csspace.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E4:79_1"/><b>then </b>
<font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">X</font>)
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:79_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="rlvect_1.html#T35">RLVECT_1:35</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:79"/>
(  <a href="csspace.html#K15" target="_self">dist</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 implies <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="csspace.html#T4" target="_self">Th4</a></i>;<br/>


</div>
