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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">Satz2p12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: GTARSKI3:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   <a href="gtarski1.html#V2" title="GTARSKI1:attr.2">satisfying_CongruenceSymmetry</a>   <a href="gtarski1.html#V3" title="GTARSKI1:attr.3">satisfying_CongruenceEquivalenceRelation</a>   <a href="gtarski1.html#V4" title="GTARSKI1:attr.4">satisfying_CongruenceIdentity</a>   <a href="gtarski1.html#V5" title="GTARSKI1:attr.5">satisfying_SegmentConstruction</a>   <a href="gtarski1.html#V6" title="GTARSKI1:attr.6">satisfying_SAS</a>   <a href="gtarski1.html#L1" title="GTARSKI1:struct.1">TarskiGeometryStruct</a> <br/>  for <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">c</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">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">a</font> holds <br/> for <font color="Olive" title="b6">x1</font>, <font color="Olive" title="b7">x2</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">q</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b6">x1</font> &amp; <font color="Olive" title="b3">a</font>,<font color="Olive" title="b6">x1</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Olive" title="b4">b</font>,<font color="Olive" title="b5">c</font> &amp;  <a href="gtarski1.html#R1" title="GTARSKI1:pred.1">between</a> <font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b7">x2</font> &amp; <font color="Olive" title="b3">a</font>,<font color="Olive" title="b7">x2</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Olive" title="b4">b</font>,<font color="Olive" title="b5">c</font> holds <br/><font color="Olive" title="b6">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">x2</font></div></div>
