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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E7">Th5</font></span>: <a NAME="T5"><span class="comment"><font color="firebrick">:: EUCLID12:5</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">An</font>, <font color="Olive" title="b3">Bn</font>, <font color="Olive" title="b4">Cn</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span><br/>  for <font color="Olive" title="b5">Ln</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">An</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">Cn</font> &amp; <font color="Olive" title="b4">Cn</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b2">An</font>,<font color="Olive" title="b3">Bn</font>) &amp; <font color="Olive" title="b2">An</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">Ln</font> &amp; <font color="Olive" title="b4">Cn</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">Ln</font> &amp; <font color="Olive" title="b5">Ln</font> is  <a href="euclid_4.html#V1" title="EUCLID_4:attr.1">being_line</a>  holds <br/><font color="Olive" title="b3">Bn</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">Ln</font></div></div>
