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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">Prelim01</font></span>: <a NAME="T1"><span class="comment"><font color="firebrick">:: GTARSKI4:1</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#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">d</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>,<font color="Olive" title="b3">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font> holds <br/>( <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Olive" title="b5">d</font>,<font color="Olive" title="b4">c</font> &amp; <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">a</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font> &amp; <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">a</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Olive" title="b5">d</font>,<font color="Olive" title="b4">c</font> &amp; <font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b5">d</font>,<font color="Olive" title="b4">c</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">a</font> &amp; <font color="Olive" title="b5">d</font>,<font color="Olive" title="b4">c</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">a</font> )</div></div>
