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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">Satz8p12</font></span>: <a NAME="T23"><span class="comment"><font color="firebrick">:: GTARSKI4:23</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="gtarski1.html#L1" title="GTARSKI1:struct.1">TarskiGeometryStruct</a> <br/>  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">A9</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b4">x</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Olive" title="b1">S</font> holds <br/> (  <a href="gtarski4.html#R2" title="GTARSKI4:pred.2">are_orthogonal</a> <font color="Olive" title="b2">A</font>,<font color="Olive" title="b4">x</font>,<font color="Olive" title="b3">A9</font> iff  <a href="gtarski4.html#R2" title="GTARSKI4:pred.2">are_orthogonal</a> <font color="Olive" title="b3">A9</font>,<font color="Olive" title="b4">x</font>,<font color="Olive" title="b2">A</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski4.html#T13" target="_self" onmouseover="rs('gtarski4/T13')" onmouseout="rh()">Satz8p2</a></span>;<br/></div></div>
