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<b>let </b><font color="Maroon">S</font> be   <a href="incsp_1.html#NM4">IncSpace</a>;<br/><b>let </b><font color="Maroon">L</font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">S</font>;<br/>



<b>consider </b><font color="Maroon">A</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font>, <font color="Maroon">B</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E2:75"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">B</font>
 <b>and </b><br/><a NAME="E3:75"/><i><font color="Green">E24</font></i>: 
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="incsp_1.html#D5" target="_self">Def5</a></i>;<br/>
<b>consider </b><font color="Maroon">C</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font>, <font color="Maroon">D</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E5:75"/><i><font color="Green">E36</font></i>: 
not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#NR7" target="_self">is_coplanar</a> 
 <b>by </b><i>, </i>;<br/>
<b>take </b><font color="Maroon">K</font> =  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">C</font>,<font color="Maroon">D</font>;<br/>

<b>given </b><font color="Maroon">P</font> being   <a href="incsp_1.html#NM3">PLANE</a> of <font color="Maroon">S</font><b> such that </b><a NAME="E6:75"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">L</font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">P</font> &amp; <font color="Maroon">K</font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">P</font> )
 ;<br/>

<a NAME="E7:75"/>
not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#NR7" target="_self">is_coplanar</a> 
 
<b>by </b><i>, <a class="ref" href="enumset1.html#T118">ENUMSET1:118</a></i>;<br/>
<a NAME="E8:75"/><b>then </b>
<font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E9:75"/><b>then </b>
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">K</font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E10:75"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">P</font> &amp; <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">P</font> )
 
<b>by </b><i>, , <a class="ref" href="incsp_1.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E11:75"/><b>then </b>
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K7">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E12:75"/><b>then </b>
<span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="ref" href="enumset1.html#T45">ENUMSET1:45</a></i>;<br/>
<b>hence </b><a NAME="E13:75"/>
contradiction
 <b>by </b><i>, </i>;<br/>


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