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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: EUCLID12:51</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font>, <font color="Olive" title="b3">C</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="b4">L1</font>, <font color="Olive" title="b5">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="b4">L1</font> <a href="euclidlp.html#R6" title="EUCLIDLP:pred.6">_|_</a> <font color="Olive" title="b5">L2</font> &amp; <font color="Olive" title="b3">C</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">L1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b5">L2</font> &amp; <font color="Olive" title="b1">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">L1</font> &amp; <font color="Olive" title="b2">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">L2</font> &amp; <font color="Olive" title="b1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">C</font> &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">C</font> holds <br/><font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font> <a href="euclid_6.html#NR1" title="EUCLID_6:NR.1">is_a_triangle</a> </div></div>
