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<div><span class="kw">theorem </span><a NAME="T30"><span class="comment"><font color="firebrick">:: GTARSKI3:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   <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">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">p</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Olive" title="b1">S</font>  st  <a href="gtarski1.html#R1" title="GTARSKI1:pred.1">between</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> &amp;  <a href="gtarski1.html#R1" title="GTARSKI1:pred.1">between</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">p</font> holds <br/>(  <a href="gtarski3.html#R2" title="GTARSKI3:pred.2">between4</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">p</font> &amp; ( <font color="Olive" title="b2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">c</font> implies  <a href="gtarski3.html#R2" title="GTARSKI3:pred.2">between4</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">p</font> ) ) <span class="kw">by</span> <span class="lab"><a class="txt" href="gtarski3.html#E20"><span class="lab"><font color="Green" title="E17">Satz3p6p1</font></span></a>, <a class="txt" href="gtarski3.html#E23"><span class="lab"><font color="Green" title="E20">Satz3p6p2</font></span></a></span>;<br/></div></div>
