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<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: EUCLID_4:42</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">p1</font>, <font color="Olive" title="b3">p2</font>, <font color="Olive" title="b4">q1</font>, <font color="Olive" title="b5">q2</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>  st <font color="Olive" title="b4">q1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rltopsp1.html#K5" title="RLTOPSP1:func.5">Line</a> (<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>) &amp; <font color="Olive" title="b5">q2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rltopsp1.html#K5" title="RLTOPSP1:func.5">Line</a> (<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>) holds <br/> <a href="rltopsp1.html#K5" title="RLTOPSP1:func.5">Line</a> (<font color="Olive" title="b4">q1</font>,<font color="Olive" title="b5">q2</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="rltopsp1.html#K5" title="RLTOPSP1:func.5">Line</a> (<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>) <span class="kw">by</span> <span class="lab"><a class="ref" href="rltopsp1.html#T74" onmouseover="rs('rltopsp1/T74')" onmouseout="rh()">RLTOPSP1:74</a></span>;<br/></div></div>
