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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="incsp_1.html#NM4">IncSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="incsp_1.html#NM3">PLANE</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:71"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:71"/><i><font color="Green">E47</font></i>: 
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E4:71"/><i><font color="Green">E48</font></i>: 
not <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#NR6" target="_self">is_collinear</a> 
 <b>by </b><i><a class="ref" href="incsp_1.html#T76" target="_self">Th76</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:71"/><i><font color="Green">E49</font></i>: 
not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></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="txt" href="incsp_1.html#E4:71"><i><font color="Green">E48</font></i></a>, <a class="ref" href="incsp_1.html#T75" target="_self">Th75</a></i>;<br/>
<b>take </b><font color="Maroon">c<sub>7</sub></font> =  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/>

<b>take </b><font color="Maroon">c<sub>8</sub></font> =  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>

<b>take </b><font color="Maroon">c<sub>9</sub></font> =  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>

<a NAME="E7:71"/><i><font color="Green">E50</font></i>: 
not <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#NR6" target="_self">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="incsp_1.html#E4:71"><i><font color="Green">E48</font></i></a>, <a class="ref" href="enumset1.html#T98">ENUMSET1:98</a></i>;<br/>
<a NAME="E8:71"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T36" target="_self">Th36</a></i>;<br/>
<a NAME="E9:71"/><b>then </b><i><font color="Green">E52</font></i>: 
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#D9" target="_self">Def9</a></i>;<br/>
<a NAME="E10:71"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">c<sub>9</sub></font> implies <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></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<sub>4</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="ref" href="incsp_1.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E11:71"/><b>then </b><i><font color="Green">E53</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">c<sub>9</sub></font> implies <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>;<br/>
<a NAME="E12:71"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="incsp_1.html#E4:71"><i><font color="Green">E48</font></i></a>, <a class="ref" href="incsp_1.html#T36" target="_self">Th36</a></i>;<br/>
<a NAME="E13:71"/><b>then </b><i><font color="Green">E55</font></i>: 
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#D9" target="_self">Def9</a></i>;<br/>
<b>hence </b><a NAME="E14:71"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E7:71"><i><font color="Green">E50</font></i></a>, <a class="txt" href="incsp_1.html#E11:71"><i><font color="Green">E53</font></i></a>, <a class="ref" href="incsp_1.html#D6" target="_self">Def6</a>, <a class="ref" href="incsp_1.html#T11" target="_self">Th11</a></i>;<br/>

<a NAME="E15:71"/><i><font color="Green">E56</font></i>: 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</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<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="incsp_1.html#E1:71"><i><font color="Green">E46</font></i></a>, <a class="txt" href="incsp_1.html#E3:71"><i><font color="Green">E47</font></i></a>, <a class="ref" href="incsp_1.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E16:71"/><b>then </b><i><font color="Green">E57</font></i>: 
<span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="enumset1.html#T42">ENUMSET1:42</a></i>;<br/>
<a NAME="E17:71"/><b>then </b>
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></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<sub>5</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>;<br/>
<a NAME="E18:71"/><b>then </b>
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T21" target="_self">Th21</a></i>;<br/>
<b>hence </b><a NAME="E19:71"/>
<font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E12:71"><i><font color="Green">E54</font></i></a>, <a class="txt" href="incsp_1.html#E13:71"><i><font color="Green">E55</font></i></a>, <a class="ref" href="incsp_1.html#D8" target="_self">Def8</a></i>;<br/>

<a NAME="E20:71"/>
<span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="incsp_1.html#E15:71"><i><font color="Green">E56</font></i></a>, <a class="ref" href="enumset1.html#T42">ENUMSET1:42</a></i>;<br/>
<a NAME="E21:71"/><b>then </b>
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></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<sub>4</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>;<br/>
<a NAME="E22:71"/><b>then </b>
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T19" target="_self">Th19</a></i>;<br/>
<b>hence </b><a NAME="E23:71"/>
<font color="Maroon">c<sub>9</sub></font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E8:71"><i><font color="Green">E51</font></i></a>, <a class="txt" href="incsp_1.html#E9:71"><i><font color="Green">E52</font></i></a>, <a class="ref" href="incsp_1.html#D8" target="_self">Def8</a></i>;<br/>

<a NAME="E24:71"/>
not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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="txt" href="incsp_1.html#E6:71"><i><font color="Green">E49</font></i></a>, <a class="ref" href="enumset1.html#T105">ENUMSET1:105</a></i>;<br/>
<a NAME="E25:71"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T37" target="_self">Th37</a></i>;<br/>
<a NAME="E26:71"/><b>then </b><i><font color="Green">E58</font></i>: 
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#D9" target="_self">Def9</a></i>;<br/>
<a NAME="E27:71"/><b>then </b>
( <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font> implies <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="incsp_1.html#T35" target="_self">Th35</a></i>;<br/>
<a NAME="E28:71"/><b>then </b>
( <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="incsp_1.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E29:71"/><b>then </b>
( <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font> implies <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K8">}</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<sub>6</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="incsp_1.html#E16:71"><i><font color="Green">E57</font></i></a>, <a class="ref" href="incsp_1.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E30:71"/><b>then </b>
( <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font> implies <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="enumset1.html#T46">ENUMSET1:46</a></i>;<br/>
<b>hence </b><a NAME="E31:71"/>
not <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E6:71"><i><font color="Green">E49</font></i></a>, <a class="ref" href="incsp_1.html#D7" target="_self">Def7</a></i>;<br/>

<b>thus </b><a NAME="E32:71"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="txt" href="incsp_1.html#E9:71"><i><font color="Green">E52</font></i></a>, <a class="txt" href="incsp_1.html#E13:71"><i><font color="Green">E55</font></i></a>, <a class="txt" href="incsp_1.html#E26:71"><i><font color="Green">E58</font></i></a>, <a class="ref" href="incsp_1.html#T11" target="_self">Th11</a></i>;<br/>


</div>
