<?xml version="1.0"?>
<div class="add">

<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">A</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c3">P</font> be   <a href="incsp_1.html#NM3" title="INCSP_1:NM.3">PLANE</a> of <font color="Maroon" title="c1">S</font>;<br/>





<b>assume </b><a NAME="E1:74"/><i><font color="Green" title="E56">A1</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a> <font color="Maroon" title="c3">P</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c4">B</font>, <font color="Maroon" title="c5">C</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="E3:74"/><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="c4">B</font>,<font color="Maroon" title="c5">C</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="c3">P</font>
 <b>and </b><br/><a NAME="E4:74"/><i><font color="Green" title="E58">A3</font></i>: 
not <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#NR6" title="INCSP_1:NR.6">is_collinear</a> 
 <b>by </b><i><a class="ref" href="incsp_1.html#T76" target="_self" title="INCSP_1:th.76">Th76</a></i>;<br/>
<b>consider </b><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="E6:74"/><i><font color="Green" title="E59">A4</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="c2">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#E4:74"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="incsp_1.html#T75" target="_self" title="INCSP_1:th.75">Th75</a></i>;<br/>
<b>take </b><font color="Maroon" title="c7">L3</font> =  <a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c6">D</font>;<br/>

<b>take </b><font color="Maroon" title="c8">L1</font> =  <a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">B</font>;<br/>

<b>take </b><font color="Maroon" title="c9">L2</font> =  <a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c5">C</font>;<br/>

<a NAME="E7:74"/><i><font color="Green" title="E60">A5</font></i>: 
not <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c4">B</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#NR6" title="INCSP_1:NR.6">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="incsp_1.html#E4:74"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="enumset1.html#T98" title="ENUMSET1:th.98">ENUMSET1:98</a></i>;<br/>
<a NAME="E8:74"/><b>then </b><i><font color="Green" title="E61">A6</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">C</font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T36" target="_self" title="INCSP_1:th.36">Th36</a></i>;<br/>
<a NAME="E9:74"/><b>then </b><i><font color="Green" title="E62">A7</font></i>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c5">C</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="c9">L2</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="E10:74"/><b>then </b>
( <font color="Maroon" title="c4">B</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L2</font> implies <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c5">C</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#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">B</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c9">L2</font> )
 
<b>by </b><i><a class="ref" href="incsp_1.html#T18" target="_self" title="INCSP_1:th.18">Th18</a></i>;<br/>
<a NAME="E11:74"/><b>then </b><i><font color="Green" title="E63">A8</font></i>: 
( <font color="Maroon" title="c4">B</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L2</font> implies <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c4">B</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c9">L2</font> )
 
<b>by </b><i><a class="ref" href="enumset1.html#T43" title="ENUMSET1:th.43">ENUMSET1:43</a></i>;<br/>
<a NAME="E12:74"/><i><font color="Green" title="E64">A9</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">B</font>
 
<b>by </b><i><a class="txt" href="incsp_1.html#E4:74"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="incsp_1.html#T36" target="_self" title="INCSP_1:th.36">Th36</a></i>;<br/>
<a NAME="E13:74"/><b>then </b><i><font color="Green" title="E65">A10</font></i>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">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="c8">L1</font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#D19" target="_self" title="INCSP_1:def.19">Def19</a></i>;<br/>
<b>hence </b><a NAME="E14:74"/>
<font color="Maroon" title="c8">L1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">L2</font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E7:74"><i><font color="Green" title="E60">A5</font></i></a>, <a class="txt" href="incsp_1.html#E11:74"><i><font color="Green" title="E63">A8</font></i></a>, <a class="ref" href="incsp_1.html#D6" target="_self" title="INCSP_1:def.6">Def6</a>, <a class="ref" href="incsp_1.html#T11" target="_self" title="INCSP_1:th.11">Th11</a></i>;<br/>

<a NAME="E15:74"/><i><font color="Green" title="E66">A11</font></i>: 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">A</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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="c4">B</font>,<font color="Maroon" title="c5">C</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="c3">P</font>
 
<b>by </b><i><a class="txt" href="incsp_1.html#E1:74"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="incsp_1.html#E3:74"><i><font color="Green" title="E57">A2</font></i></a>, <a class="ref" href="incsp_1.html#T19" target="_self" title="INCSP_1:th.19">Th19</a></i>;<br/>
<a NAME="E16:74"/><b>then </b><i><font color="Green" title="E67">A12</font></i>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c3">P</font>
 
<b>by </b><i><a class="ref" href="enumset1.html#T42" title="ENUMSET1:th.42">ENUMSET1:42</a></i>;<br/>
<a NAME="E17:74"/><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="c2">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#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">C</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c3">P</font>
 
<b>by </b><i><a class="ref" href="enumset1.html#T43" title="ENUMSET1:th.43">ENUMSET1:43</a></i>;<br/>
<a NAME="E18:74"/><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="c2">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="c3">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/>
<b>hence </b><a NAME="E19:74"/>
<font color="Maroon" title="c8">L1</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c3">P</font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E12:74"><i><font color="Green" title="E64">A9</font></i></a>, <a class="txt" href="incsp_1.html#E13:74"><i><font color="Green" title="E65">A10</font></i></a>, <a class="ref" href="incsp_1.html#D14" target="_self" title="INCSP_1:def.14">Def14</a></i>;<br/>

<a NAME="E20:74"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c4">B</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c3">P</font>
 
<b>by </b><i><a class="txt" href="incsp_1.html#E15:74"><i><font color="Green" title="E66">A11</font></i></a>, <a class="ref" href="enumset1.html#T42" title="ENUMSET1:th.42">ENUMSET1:42</a></i>;<br/>
<a NAME="E21:74"/><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="c2">A</font>,<font color="Maroon" title="c5">C</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#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">B</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c3">P</font>
 
<b>by </b><i><a class="ref" href="enumset1.html#T43" title="ENUMSET1:th.43">ENUMSET1:43</a></i>;<br/>
<a NAME="E22:74"/><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="c2">A</font>,<font color="Maroon" title="c5">C</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="c3">P</font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T19" target="_self" title="INCSP_1:th.19">Th19</a></i>;<br/>
<b>hence </b><a NAME="E23:74"/>
<font color="Maroon" title="c9">L2</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c3">P</font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E8:74"><i><font color="Green" title="E61">A6</font></i></a>, <a class="txt" href="incsp_1.html#E9:74"><i><font color="Green" title="E62">A7</font></i></a>, <a class="ref" href="incsp_1.html#D14" target="_self" title="INCSP_1:def.14">Def14</a></i>;<br/>

<a NAME="E24:74"/>
not <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c6">D</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</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#E6:74"><i><font color="Green" title="E59">A4</font></i></a>, <a class="ref" href="enumset1.html#T105" title="ENUMSET1:th.105">ENUMSET1:105</a></i>;<br/>
<a NAME="E25:74"/><b>then </b>
<font color="Maroon" title="c2">A</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="E26:74"/><b>then </b><i><font color="Green" title="E68">A13</font></i>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">A</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">L3</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="E27:74"/><b>then </b>
( <font color="Maroon" title="c7">L3</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c3">P</font> implies <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">A</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="c3">P</font> )
 
<b>by </b><i><a class="ref" href="incsp_1.html#T35" target="_self" title="INCSP_1:th.35">Th35</a></i>;<br/>
<a NAME="E28:74"/><b>then </b>
( <font color="Maroon" title="c7">L3</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c3">P</font> implies <font color="Maroon" title="c6">D</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a> <font color="Maroon" title="c3">P</font> )
 
<b>by </b><i><a class="ref" href="incsp_1.html#T13" target="_self" title="INCSP_1:th.13">Th13</a></i>;<br/>
<a NAME="E29:74"/><b>then </b>
( <font color="Maroon" title="c7">L3</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c3">P</font> implies <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c6">D</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c3">P</font> )
 
<b>by </b><i><a class="txt" href="incsp_1.html#E16:74"><i><font color="Green" title="E67">A12</font></i></a>, <a class="ref" href="incsp_1.html#T19" target="_self" title="INCSP_1:th.19">Th19</a></i>;<br/>
<a NAME="E30:74"/><b>then </b>
( <font color="Maroon" title="c7">L3</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c3">P</font> implies <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c2">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="c3">P</font> )
 
<b>by </b><i><a class="ref" href="enumset1.html#T46" title="ENUMSET1:th.46">ENUMSET1:46</a></i>;<br/>
<b>hence </b><a NAME="E31:74"/>
not <font color="Maroon" title="c7">L3</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a> <font color="Maroon" title="c3">P</font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E6:74"><i><font color="Green" title="E59">A4</font></i></a>, <a class="ref" href="incsp_1.html#D7" target="_self" title="INCSP_1:def.7">Def7</a></i>;<br/>

<b>thus </b><a NAME="E32:74"/>
( <font color="Maroon" title="c2">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">L3</font> &amp; <font color="Maroon" title="c2">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">L1</font> &amp; <font color="Maroon" title="c2">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L2</font> )
 <b>by </b><i><a class="txt" href="incsp_1.html#E9:74"><i><font color="Green" title="E62">A7</font></i></a>, <a class="txt" href="incsp_1.html#E13:74"><i><font color="Green" title="E65">A10</font></i></a>, <a class="txt" href="incsp_1.html#E26:74"><i><font color="Green" title="E68">A13</font></i></a>, <a class="ref" href="incsp_1.html#T11" target="_self" title="INCSP_1:th.11">Th11</a></i>;<br/>


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