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<div class="add">

<b>let </b><font color="Maroon" title="c4">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</a>;<br/><b>let </b><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">X</font>;<br/>





<b>thus </b><a NAME="E1:80"/>
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">y</font> implies  <a href="csspace.html#K15" title="CSSPACE:func.15">dist</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:80_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">y</font>
 ;<br/>

<a NAME="E2:80_1"/><b>then </b>
 <a href="csspace.html#K15" title="CSSPACE:func.15">dist</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="csspace.html#T55" target="_self" title="CSSPACE:th.55">Th55</a></i>;<br/>
<b>hence </b><a NAME="E3:80_1"/>
 <a href="csspace.html#K15" title="CSSPACE:func.15">dist</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="ref" href="csspace.html#T56" target="_self" title="CSSPACE:th.56">Th56</a></i>;<br/>


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

<b>thus </b><a NAME="E2:80"/>
(  <a href="csspace.html#K15" title="CSSPACE:func.15">dist</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 implies <font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">y</font> )
 <b>by </b><i><a class="ref" href="csspace.html#T53" target="_self" title="CSSPACE:th.53">Th53</a></i>;<br/>


</div>
