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<b>let </b><font color="Maroon" title="c1">S</font> be   <a href="incsp_1.html#NM4" title="INCSP_1:NM.4">IncSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">L</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">S</font>;<br/>



<b>consider </b><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E2:78"/><i><font color="Green" title="E56">A1</font></i>: 
<font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">B</font>
 <b>and </b><br/><a NAME="E3:78"/><i><font color="Green" title="E57">A2</font></i>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c2">L</font>
 <b>by </b><i><a class="ref" href="incsp_1.html#D8" target="_self" title="INCSP_1:def.8">Def8</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">C</font>, <font color="Maroon" title="c6">D</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E5:78"/><i><font color="Green" title="E58">A3</font></i>: 
not <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c6">D</font></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span> <a href="incsp_1.html#NR7" title="INCSP_1:NR.7">is_coplanar</a> 
 <b>by </b><i><a class="txt" href="incsp_1.html#E2:78"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="incsp_1.html#T77" target="_self" title="INCSP_1:th.77">Th77</a></i>;<br/>
<b>take </b><font color="Maroon" title="c7">K</font> =  <a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c6">D</font>;<br/>

<b>given </b><font color="Maroon" title="c8">P</font> being   <a href="incsp_1.html#NM3" title="INCSP_1:NM.3">PLANE</a> of <font color="Maroon" title="c1">S</font><b> such that </b><a NAME="E7:78"/><i><font color="Green" title="E59">A4</font></i>: 
( <font color="Maroon" title="c2">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c8">P</font> &amp; <font color="Maroon" title="c7">K</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c8">P</font> )
 ;<br/>

<a NAME="E8:78"/>
not <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c6">D</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span> <a href="incsp_1.html#NR7" title="INCSP_1:NR.7">is_coplanar</a> 
 
<b>by </b><i><a class="txt" href="incsp_1.html#E5:78"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="enumset1.html#T118" title="ENUMSET1:th.118">ENUMSET1:118</a></i>;<br/>
<a NAME="E9:78"/><b>then </b>
<font color="Maroon" title="c5">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">D</font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T37" target="_self" title="INCSP_1:th.37">Th37</a></i>;<br/>
<a NAME="E10:78"/><b>then </b>
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c6">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c7">K</font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#D19" target="_self" title="INCSP_1:def.19">Def19</a></i>;<br/>
<a NAME="E11:78"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c8">P</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c6">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c8">P</font> )
 
<b>by </b><i><a class="txt" href="incsp_1.html#E3:78"><i><font color="Green" title="E57">A2</font></i></a>, <a class="txt" href="incsp_1.html#E7:78"><i><font color="Green" title="E59">A4</font></i></a>, <a class="ref" href="incsp_1.html#T35" target="_self" title="INCSP_1:th.35">Th35</a></i>;<br/>
<a NAME="E12:78"/><b>then </b>
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c6">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c8">P</font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T21" target="_self" title="INCSP_1:th.21">Th21</a></i>;<br/>
<a NAME="E13:78"/><b>then </b>
<span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c6">D</font></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c8">P</font>
 
<b>by </b><i><a class="ref" href="enumset1.html#T45" title="ENUMSET1:th.45">ENUMSET1:45</a></i>;<br/>
<b>hence </b><a NAME="E14:78"/>
contradiction
 <b>by </b><i><a class="txt" href="incsp_1.html#E5:78"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="incsp_1.html#D7" target="_self" title="INCSP_1:def.7">Def7</a></i>;<br/>


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