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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E68">Th81</font></span>: <a NAME="T81"><span class="comment"><font color="firebrick">:: EUCLIDLP:81</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">x</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Olive" title="b1">n</font><br/>  for <font color="Olive" title="b3">L1</font>, <font color="Olive" title="b4">L2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="euclidlp.html#K1" title="EUCLIDLP:func.1">line_of_REAL</a> <font color="Olive" title="b1">n</font>  st <font color="Olive" title="b2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">L2</font> &amp; <font color="Olive" title="b3">L1</font> <a href="euclidlp.html#R6" title="EUCLIDLP:pred.6">_|_</a> <font color="Olive" title="b4">L2</font> holds <br/> ex <font color="Olive" title="b5">x0</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Olive" title="b1">n</font> st <br/>( <font color="Olive" title="b2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">x0</font> &amp; <font color="Olive" title="b5">x0</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">L1</font> &amp;  not <font color="Olive" title="b5">x0</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">L2</font> )</div></div>
