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<div><span class="kw">theorem </span><a NAME="T56"><span class="comment"><font color="firebrick">:: EUCLIDLP:56</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>, <font color="Olive" title="b3">x1</font>, <font color="Olive" title="b4">x2</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="b5">L</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="b5">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_4.html#K2" title="EUCLID_4:func.2">Line</a> (<font color="Olive" title="b3">x1</font>,<font color="Olive" title="b4">x2</font>) holds <br/><span class="p1"> { <span class="default"> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">x</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Olive" title="b6">x0</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> where <font color="Olive" title="b6">x0</font> is    <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> : <font color="Olive" title="b6">x0</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="b3">x1</font>,<font color="Olive" title="b4">x2</font>) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclidlp.html#K2" title="EUCLIDLP:func.2">dist_v</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b5">L</font>) ;<br/></div></div>
