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<span class="kw">let </span><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font> be    <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; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font> <a href="euclidlp.html#R7" title="EUCLIDLP:pred.7">are_coplane</a> </span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">OO</font> = <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>,<a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>, <font color="Maroon" title="c4">Ox</font> = <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default">1,<a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>, <font color="Maroon" title="c5">Oy</font> = <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>,1</span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> as    <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 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" onmouseover="rs('euclid/T22')" onmouseout="rh()">EUCLID:22</a></span>;<br/>
<a NAME="E2:39"/>
 <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclidlp.html#K4" title="EUCLIDLP:func.4">plane</a> (<font color="Maroon" title="c3">OO</font>,<font color="Maroon" title="c4">Ox</font>,<font color="Maroon" title="c5">Oy</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid12.html#T15" target="_self" onmouseover="rs('euclid12/T15')" onmouseout="rh()">Th12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:39"/>
<font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font> <a href="euclidlp.html#R7" title="EUCLIDLP:pred.7">are_coplane</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclidlp.html#D12" onmouseover="rs('euclidlp/D12')" onmouseout="rh()">EUCLIDLP:def 12</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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