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<a NAME="E1:5_1_1"/>
 ex <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> <font color="Maroon" title="c2">n</font></span>)</span> st <br/>( <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> &amp;  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topreal6.html#D1" title="TOPREAL6:def.1">TOPREAL6:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:5_1_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xxreal_0.html#D7" title="XXREAL_0:def.7">XXREAL_0:def 7</a> <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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