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<div><span class="kw">theorem </span><a NAME="T70"><span class="comment"><font color="firebrick">:: GTARSKI5:70</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="gtarski1.html#V9" title="GTARSKI1:attr.9">satisfying_Tarski-model</a>   <a href="gtarski2.html#NV5" title="GTARSKI2:NV.5">satisfying_Lower_Dimension_Axiom</a>   <a href="gtarski1.html#L1" title="GTARSKI1:struct.1">TarskiGeometryStruct</a> <br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Olive" title="b1">S</font>  st  not  <a href="gtarski1.html#R6" title="GTARSKI1:pred.6">Collinear</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> holds <br/> for <font color="Olive" title="b5">E</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b2">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">E</font> &amp; <font color="Olive" title="b3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">E</font> &amp; <font color="Olive" title="b4">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">E</font> &amp; (  for <font color="Olive" title="b6">u</font>, <font color="Olive" title="b7">v</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b6">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">E</font> &amp; <font color="Olive" title="b7">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">E</font> &amp; <font color="Olive" title="b6">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">v</font> holds <br/> <a href="gtarski4.html#K1" title="GTARSKI4:func.1">Line</a> (<font color="Olive" title="b6">u</font>,<font color="Olive" title="b7">v</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">E</font> ) holds <br/> <a href="gtarski5.html#K4" title="GTARSKI5:func.4">Plane</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">E</font></div></div>
