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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th10</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: METRIC_1:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being    <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>  holds  <a href="metric_1.html#K6" title="METRIC_1:func.6">real_dist</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="metric_1.html#K6" title="METRIC_1:func.6">real_dist</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font>)</span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="metric_1.html#K6" title="METRIC_1:func.6">real_dist</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b3">z</font>,<font color="Olive" title="b2">y</font>)</span>)</span></div></div>
