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<b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>



<a NAME="E1:22"/>
 ex <font color="Olive">p'</font>, <font color="Olive">q'</font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> 2</span>)</span> st <br/>( <font color="Olive">p'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp; <font color="Olive">q'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> &amp;  <a href="topreal6.html#K1">dist</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="metric_1.html#K4">dist</a> <font color="Olive">p'</font>,<font color="Olive">q'</font> )
 
<b>by </b><i><a class="ref" href="topreal6.html#D1">TOPREAL6:def 1</a></i>;<br/>
<b>hence </b><a NAME="E2:22"/>
( <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> implies  <a href="topreal6.html#K1">dist</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i><a class="ref" href="sub_metr.html#T2">SUB_METR:2</a></i>;<br/>


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