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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E1">Th1</font></span>: <a NAME="T1"><span class="comment"><font color="firebrick">:: METRIC_6:1</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="metric_1.html#NM1" title="METRIC_1:NM.1">MetrSpace</a><br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font>, <font color="Olive" title="b4">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</font> holds  <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b4">z</font>)</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b3">y</font>,<font color="Olive" title="b4">z</font>)</span>)</span></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font>)</div></div>
