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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E57">Th54</font></span>: <a NAME="T65"><span class="comment"><font color="firebrick">:: EUCLID13:65</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>  st <font color="Olive" title="b3">C</font>,<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font> <a href="euclid_6.html#NR1" title="EUCLID_6:NR.1">is_a_triangle</a>  &amp; <font color="Olive" title="b3">C</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid13.html#K1" title="EUCLID13:func.1">the_altitude</a> (<font color="Olive" title="b3">C</font>,<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>) &amp; <font color="Olive" title="b3">C</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid13.html#K1" title="EUCLID13:func.1">the_altitude</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font>) holds <br/><span class="p1">(<span class="default"><a href="euclid13.html#K1" title="EUCLID13:func.1">the_altitude</a> (<font color="Olive" title="b3">C</font>,<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>)</span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="euclid13.html#K1" title="EUCLID13:func.1">the_altitude</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font>)</span>)</span> is  <a href="euclid12.html#V1" title="EUCLID12:attr.1">being_point</a> </div></div>
