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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E23">Def10</font></span>   defines <a href="gtarski5.html#K3" title="GTARSKI5:func.3">Plane</a> <a onclick="hs(this)" href="javascript:()">GTARSKI5:def 10 : <br/></a><span> 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> 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="b3">r</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="b2">A</font> <a href="gtarski3.html#R8" title="GTARSKI3:pred.8">is_line</a>  &amp;  not <font color="Olive" title="b3">r</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> holds <br/> for <font color="Olive">b<sub>4</sub></font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">S</font> holds <br/> ( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gtarski5.html#K3" title="GTARSKI5:func.3">Plane</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">r</font>) iff  ex <font color="Olive" title="b5">r9</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Olive" title="b1">S</font> st <br/>(  <a href="gtarski5.html#R1" title="GTARSKI5:pred.1">between</a> <font color="Olive" title="b3">r</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b5">r9</font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gtarski5.html#K1" title="GTARSKI5:func.1">half-plane</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">r</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="gtarski5.html#K1" title="GTARSKI5:func.1">half-plane</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b5">r9</font>)</span>)</span> ) );<br/></span></div>
