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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E48">Th44</font></span>: <a NAME="T59"><span class="comment"><font color="firebrick">:: EUCLID12:59</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</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#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span><br/>  for <font color="Olive" title="b3">L1</font>, <font color="Olive" title="b4">L2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="euclidlp.html#K1" title="EUCLIDLP:func.1">line_of_REAL</a> 2  st <font color="Olive" title="b1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">B</font> &amp; <font color="Olive" title="b3">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rltopsp1.html#K5" title="RLTOPSP1:func.5">Line</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>) &amp; <font color="Olive" title="b3">L1</font> <a href="euclidlp.html#R6" title="EUCLIDLP:pred.6">_|_</a> <font color="Olive" title="b4">L2</font> &amp;  <a href="euclid12.html#K2" title="EUCLID12:func.2">the_midpoint_of_the_segment</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">L2</font> holds <br/><font color="Olive" title="b4">L2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid12.html#K3" title="EUCLID12:func.3">the_perpendicular_bisector</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>)</div></div>
