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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span><br/>

<span class="kw">thus </span><a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) = 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">y</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="metric_1.html#D12" target="_self" title="METRIC_1:def.12">Def13</a></span>
<br/>.= 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T52" title="COMPLEX1:th.52">COMPLEX1:52</a></span>
<br/>.= 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c1">x</font></span>)</span>

<br/>.= 
<a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="metric_1.html#D12" target="_self" title="METRIC_1:def.12">Def13</a></span>
; <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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