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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th16</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: EUCLID12:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L1</font>, <font color="Olive" title="b2">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> 2  holds <br/>( <font color="Olive" title="b1">L1</font> <a href="euclidlp.html#R5" title="EUCLIDLP:pred.5">//</a> <font color="Olive" title="b2">L2</font> or  ex <font color="Olive" title="b3">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> 2 st <br/>( <font color="Olive" title="b1">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or <font color="Olive" title="b2">L2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) or ( <font color="Olive" title="b1">L1</font> is  <a href="euclid_4.html#V1" title="EUCLID_4:attr.1">being_line</a>  &amp; <font color="Olive" title="b2">L2</font> is  <a href="euclid_4.html#V1" title="EUCLID_4:attr.1">being_line</a>  &amp;  ex <font color="Olive" title="b3">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> 2 st <font color="Olive" title="b1">L1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">L2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) )</div></div>
