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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">A</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font>;<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>assume </b><b>that </b><br/><a NAME="E1:34"/><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> &amp; <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>and </b><br/><a NAME="E2:34"/><i><font color="Green">E24</font></i>: 
not <font color="Maroon">C</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">L</font>
 ;<br/>

<b>given </b><font color="Maroon">K</font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">S</font><b> such that </b><a NAME="E3:34"/><i><font color="Green">E36</font></i>: 
<span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">K</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="incsp_1.html#D6" target="_self">INCSP_1:def 6</a><br/>

<a NAME="E4:34"/>
<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#K6">{</a><span class="default"><font color="Maroon">C</font></span><a href="domain_1.html#K6">}</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#T14" target="_self">Th14</a>, <a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>;<br/>
<a NAME="E5:34"/><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#R4" target="_self">on</a> <font color="Maroon">K</font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E6:34"/><b>then </b>
<font color="Maroon">L</font> <a href="hidden.html#R1">=</a> <font color="Maroon">K</font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T12" target="_self">Th12</a>, <a class="ref" href="incsp_1.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E7:34"/>
contradiction
 <b>by </b><i><a class="ref" href="incsp_1.html#T13" target="_self">Th13</a>, <a class="ref" href="incsp_1.html#T14" target="_self">Th14</a>, </i>;<br/>


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