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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E6">Th6</font></span>: <a NAME="T6"><span class="comment"><font color="firebrick">:: CARDFIL4:6</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="metric_1.html#K7" title="METRIC_1:func.7">RealSpace</a>  ex <font color="Olive" title="b3">xr</font>, <font color="Olive" title="b4">yr</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">xr</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">yr</font> &amp;  <a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="metric_1.html#K6" title="METRIC_1:func.6">real_dist</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) &amp;  <a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid.html#K13" title="EUCLID:func.13">Pitag_dist</a> 1</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1"><a href="srings_5.html#K24" title="SRINGS_5:func.24">&lt;*</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="srings_5.html#K24" title="SRINGS_5:func.24">*&gt;</a></span>,<span class="p1"><a href="srings_5.html#K24" title="SRINGS_5:func.24">&lt;*</a><span class="default"><font color="Olive" title="b2">y</font></span><a href="srings_5.html#K24" title="SRINGS_5:func.24">*&gt;</a></span>) &amp;  <a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">xr</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b4">yr</font></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> )</div></div>
