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<div><span class="kw">theorem </span><a NAME="T55"><span class="comment"><font color="firebrick">:: EUCLID_3:55</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">p2</font>, <font color="Olive" title="b3">p3</font>, <font color="Olive" title="b4">p</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="b2">p2</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b3">p3</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b1">p1</font> <a href="euclid_3.html#R1" title="EUCLID_3:pred.1">are_lindependent2</a>  holds <br/>( <font color="Olive" title="b4">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid_3.html#K8" title="EUCLID_3:func.8">outside_of_triangle</a> (<font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font>,<font color="Olive" title="b3">p3</font>) iff (  <a href="euclid_3.html#K10" title="EUCLID_3:func.10">tricord1</a> (<font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font>,<font color="Olive" title="b3">p3</font>,<font color="Olive" title="b4">p</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or  <a href="euclid_3.html#K11" title="EUCLID_3:func.11">tricord2</a> (<font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font>,<font color="Olive" title="b3">p3</font>,<font color="Olive" title="b4">p</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or  <a href="euclid_3.html#K12" title="EUCLID_3:func.12">tricord3</a> (<font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font>,<font color="Olive" title="b3">p3</font>,<font color="Olive" title="b4">p</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) )</div></div>
