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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E37">Th40</font></span>: <a NAME="T40"><span class="comment"><font color="firebrick">:: EUCLIDLP:40</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">x0</font>, <font color="Olive" title="b3">x1</font>, <font color="Olive" title="b4">x2</font>, <font color="Olive" title="b5">x3</font>, <font color="Olive" title="b6">y0</font>, <font color="Olive" title="b7">y1</font>, <font color="Olive" title="b8">y2</font>, <font color="Olive" title="b9">y3</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 <font color="Olive" title="b3">x1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Olive" title="b2">x0</font>,<font color="Olive" title="b5">x3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Olive" title="b4">x2</font> <a href="euclidlp.html#R3" title="EUCLIDLP:pred.3">are_lindependent2</a>  &amp; <font color="Olive" title="b6">y0</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid_4.html#K2" title="EUCLID_4:func.2">Line</a> (<font color="Olive" title="b2">x0</font>,<font color="Olive" title="b3">x1</font>) &amp; <font color="Olive" title="b7">y1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid_4.html#K2" title="EUCLID_4:func.2">Line</a> (<font color="Olive" title="b2">x0</font>,<font color="Olive" title="b3">x1</font>) &amp; <font color="Olive" title="b6">y0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">y1</font> &amp; <font color="Olive" title="b8">y2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid_4.html#K2" title="EUCLID_4:func.2">Line</a> (<font color="Olive" title="b4">x2</font>,<font color="Olive" title="b5">x3</font>) &amp; <font color="Olive" title="b9">y3</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid_4.html#K2" title="EUCLID_4:func.2">Line</a> (<font color="Olive" title="b4">x2</font>,<font color="Olive" title="b5">x3</font>) &amp; <font color="Olive" title="b8">y2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b9">y3</font> holds <br/><font color="Olive" title="b7">y1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Olive" title="b6">y0</font>,<font color="Olive" title="b9">y3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Olive" title="b8">y2</font> <a href="euclidlp.html#R3" title="EUCLIDLP:pred.3">are_lindependent2</a> </div></div>
