<?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#NM3">PLANE</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>consider </b><font color="Maroon">c<sub>3</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="E2:63"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="incsp_1.html#D8" target="_self">Def8</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</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="E4:63"/><i><font color="Green">E41</font></i>: 
not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</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="ref" href="incsp_1.html#D8" target="_self">Def8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_1"/><i><font color="Green">E42</font></i>: 
not <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div><i><font color="Green">E43</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_1_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1" target="_self">on</a>  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/><b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/><a NAME="E2:63_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>4</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="txt" href="incsp_1.html#E4:63"><i><font color="Green">E41</font></i></a>, <a class="ref" href="incsp_1.html#T37" target="_self">Th37</a></i>;<br/><a NAME="E3:63_1_1"/><b>then </b><i><font color="Green">E46</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#R4" target="_self">on</a>  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="incsp_1.html#D9" target="_self">Def9</a></i>;<br/><a NAME="E4:63_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1" target="_self">on</a>  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="incsp_1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E5:63_1_1"/><b>then </b><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>3</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>  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E1:63_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="incsp_1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E6:63_1_1"/><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>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#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#E4:63"><i><font color="Green">E41</font></i></a>, <a class="ref" href="incsp_1.html#T38" target="_self">Th38</a></i>;<br/><a NAME="E7:63_1_1"/><b>then </b><i><font color="Green">E49</font></i>: 
<span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><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#K8">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="incsp_1.html#D10" target="_self">Def10</a></i>;<br/><a NAME="E8:63_1_1"/><b>then </b>
( <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R2" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> implies <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><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#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>7</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="ref" href="incsp_1.html#T19" target="_self">Th19</a></i>;<br/><a NAME="E9:63_1_1"/><b>then </b><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R2" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> implies <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="ref" href="enumset1.html#T46">ENUMSET1:46</a></i>;<br/><a NAME="E10:63_1_1"/>
<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#R4" target="_self">on</a>  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E2:63_1_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="incsp_1.html#D9" target="_self">Def9</a></i>;<br/><a NAME="E11:63_1_1"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1" target="_self">on</a>  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> implies <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="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#R4" target="_self">on</a>  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="incsp_1.html#T18" target="_self">Th18</a></i>;<br/><a NAME="E12:63_1_1"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1" target="_self">on</a>  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> implies <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><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#K8">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a>  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>;<br/><a NAME="E13:63_1_1"/><b>then </b><i><font color="Green">E51</font></i>: 
not <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</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#E2:63"><i><font color="Green">E40</font></i></a>, <a class="txt" href="incsp_1.html#E1:63_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="incsp_1.html#E5:63_1_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="incsp_1.html#E6:63_1_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="incsp_1.html#D6" target="_self">Def6</a>, <a class="ref" href="incsp_1.html#T39" target="_self">Th39</a></i>;<br/><a NAME="E14:63_1_1"/>
<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="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>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E7:63_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>;<br/><a NAME="E15:63_1_1"/><b>then </b>
<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>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="incsp_1.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E16:63_1_1"/><b>then </b>
(  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R3" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><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#K8">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="incsp_1.html#E2:63_1_1"><i><font color="Green">E45</font></i></a>, <a class="txt" href="incsp_1.html#E3:63_1_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="incsp_1.html#E6:63_1_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="incsp_1.html#D8" target="_self">Def8</a>, <a class="ref" href="incsp_1.html#D10" target="_self">Def10</a></i>;<br/><a NAME="E17:63_1_1"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R2" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R2" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R2" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="incsp_1.html#E1:63_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="incsp_1.html#D8" target="_self">Def8</a>, <a class="ref" href="incsp_1.html#T14" target="_self">Th14</a></i>;<br/><a NAME="E18:63_1_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="incsp_1.html#T14" target="_self">Th14</a></i>;<br/><a NAME="E19:63_1_1"/><b>then </b>
not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</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#E4:63"><i><font color="Green">E41</font></i></a>, <a class="txt" href="incsp_1.html#E9:63_1_1"><i><font color="Green">E50</font></i></a>, <a class="txt" href="incsp_1.html#E13:63_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="incsp_1.html#D7" target="_self">Def7</a>, <a class="ref" href="incsp_1.html#T40" target="_self">Th40</a></i>;<br/><b>hence </b><a NAME="E20:63_1_1"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font> &amp; not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</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#E2:63"><i><font color="Green">E40</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_1_2"/><i><font color="Green">E44</font></i>: 
not <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1" target="_self">on</a>  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/><b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><a NAME="E2:63_1_2"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>4</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="txt" href="incsp_1.html#E4:63"><i><font color="Green">E41</font></i></a>, <a class="ref" href="incsp_1.html#T37" target="_self">Th37</a></i>;<br/><a NAME="E3:63_1_2"/><b>then </b>
<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#R4" target="_self">on</a>  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="incsp_1.html#D9" target="_self">Def9</a></i>;<br/><a NAME="E4:63_1_2"/><b>then </b><i><font color="Green">E46</font></i>: 
not <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</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#E1:63_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="incsp_1.html#E2:63_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="incsp_1.html#T39" target="_self">Th39</a></i>;<br/><a NAME="E5:63_1_2"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="incsp_1.html#D10" target="_self">Def10</a></i>;<br/><a NAME="E6:63_1_2"/><b>then </b>
<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="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<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="E7:63_1_2"/><b>then </b>
<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>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<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/><a NAME="E8:63_1_2"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<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>4</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#K7">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<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/><a NAME="E9:63_1_2"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<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>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="enumset1.html#T45">ENUMSET1:45</a></i>;<br/><a NAME="E10:63_1_2"/><b>then </b>
(  not <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R2" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> or  not <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R2" target="_self">on</a>  <a href="incsp_1.html#K2" target="_self">Plane</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="incsp_1.html#E4:63"><i><font color="Green">E41</font></i></a>, <a class="ref" href="incsp_1.html#D7" target="_self">Def7</a>, <a class="ref" href="incsp_1.html#T13" target="_self">Th13</a></i>;<br/><a NAME="E11:63_1_2"/><b>then </b>
(  not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</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>  or  not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</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#E4:63_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="incsp_1.html#E5:63_1_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="incsp_1.html#T40" target="_self">Th40</a></i>;<br/><a NAME="E12:63_1_2"/><b>then </b>
(  not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>3</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>  or  not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</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="ref" href="enumset1.html#T110">ENUMSET1:110</a></i>;<br/><b>hence </b><a NAME="E13:63_1_2"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font> &amp; not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</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#E2:63"><i><font color="Green">E40</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:63_1"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font> &amp; not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</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#E2:63_1"><i><font color="Green">E43</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:63"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>2</sub></font> &amp; not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</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#E4:63"><i><font color="Green">E41</font></i></a></i>;<br/>


</div>
