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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="realset2.html#V3">trivial</a> <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/>

<b>given </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><a NAME="E1:91"/><i><font color="Green">E81</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>3</sub></font>
 <b>and </b><br/><a NAME="E2:91"/><i><font color="Green">E82</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>ex <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 ;<br/>

<b>let </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> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>







<b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E4:91"/><i><font color="Green">E83</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E2:91"><i><font color="Green">E82</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E6:91"/><i><font color="Green">E84</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E2:91"><i><font color="Green">E82</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E8:91"/><i><font color="Green">E85</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E2:91"><i><font color="Green">E82</font></i></a></i>;<br/>
<a NAME="E9:91"/>
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E1:91"><i><font color="Green">E81</font></i></a>, <a class="txt" href="anproj_2.html#E4:91"><i><font color="Green">E83</font></i></a>, <a class="txt" href="anproj_2.html#E6:91"><i><font color="Green">E84</font></i></a>, <a class="txt" href="anproj_2.html#E8:91"><i><font color="Green">E85</font></i></a>, <a class="ref" href="anproj_2.html#D8" target="_self">Def8</a>, <a class="ref" href="anproj_2.html#T25" target="_self">Th25</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E11:91"/><i><font color="Green">E86</font></i>: 
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="ref" href="anproj_2.html#D9" target="_self">Def9</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E13:91"/><i><font color="Green">E87</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E2:91"><i><font color="Green">E82</font></i></a></i>;<br/>
<a NAME="E14:91"/>
( <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E1:91"><i><font color="Green">E81</font></i></a>, <a class="txt" href="anproj_2.html#E4:91"><i><font color="Green">E83</font></i></a>, <a class="txt" href="anproj_2.html#E6:91"><i><font color="Green">E84</font></i></a>, <a class="txt" href="anproj_2.html#E13:91"><i><font color="Green">E87</font></i></a>, <a class="ref" href="anproj_2.html#D8" target="_self">Def8</a>, <a class="ref" href="anproj_2.html#T25" target="_self">Th25</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E16:91"/><i><font color="Green">E88</font></i>: 
( <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="ref" href="anproj_2.html#D9" target="_self">Def9</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>14</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E18:91"/><i><font color="Green">E89</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E2:91"><i><font color="Green">E82</font></i></a></i>;<br/>
<a NAME="E19:91"/>
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E1:91"><i><font color="Green">E81</font></i></a>, <a class="txt" href="anproj_2.html#E4:91"><i><font color="Green">E83</font></i></a>, <a class="txt" href="anproj_2.html#E6:91"><i><font color="Green">E84</font></i></a>, <a class="txt" href="anproj_2.html#E18:91"><i><font color="Green">E89</font></i></a>, <a class="ref" href="anproj_2.html#D8" target="_self">Def8</a>, <a class="ref" href="anproj_2.html#T25" target="_self">Th25</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>15</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E21:91"/><i><font color="Green">E90</font></i>: 
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="ref" href="anproj_2.html#D9" target="_self">Def9</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>16</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E23:91"/><i><font color="Green">E91</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E2:91"><i><font color="Green">E82</font></i></a></i>;<br/>
<a NAME="E24:91"/>
( <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E1:91"><i><font color="Green">E81</font></i></a>, <a class="txt" href="anproj_2.html#E4:91"><i><font color="Green">E83</font></i></a>, <a class="txt" href="anproj_2.html#E6:91"><i><font color="Green">E84</font></i></a>, <a class="txt" href="anproj_2.html#E23:91"><i><font color="Green">E91</font></i></a>, <a class="ref" href="anproj_2.html#D8" target="_self">Def8</a>, <a class="ref" href="anproj_2.html#T25" target="_self">Th25</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>17</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E26:91"/><i><font color="Green">E92</font></i>: 
( <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="ref" href="anproj_2.html#D9" target="_self">Def9</a></i>;<br/>
<div><i><font color="Green">E93</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_1"/><i><font color="Green">E94</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div><i><font color="Green">E95</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_1_1"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><b>take </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>8</sub></font>;<br/><a NAME="E2:91_1_1"/>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:91_1_1"><i><font color="Green">E96</font></i></a>, <a class="ref" href="anproj_2.html#D7" target="_self">Def7</a></i>;<br/><b>hence </b><a NAME="E3:91_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E4:91"><i><font color="Green">E83</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_1_2"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><b>take </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>9</sub></font>;<br/><a NAME="E2:91_1_2"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:91_1_2"><i><font color="Green">E96</font></i></a>, <a class="ref" href="anproj_2.html#D7" target="_self">Def7</a></i>;<br/><b>hence </b><a NAME="E3:91_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:91"><i><font color="Green">E84</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:91_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:91_1"><i><font color="Green">E94</font></i></a>, <a class="txt" href="anproj_2.html#E2:91_1"><i><font color="Green">E95</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_2"/><i><font color="Green">E94</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> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div><i><font color="Green">E95</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="91_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_2_1"/><i><font color="Green">E96</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><b>take </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>13</sub></font>;<br/><a NAME="E2:91_2_1"/>
( <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E4:91"><i><font color="Green">E83</font></i></a>, <a class="txt" href="anproj_2.html#E16:91"><i><font color="Green">E88</font></i></a>, <a class="ref" href="anproj_2.html#D7" target="_self">Def7</a>, <a class="ref" href="anproj_2.html#T25" target="_self">Th25</a></i>;<br/><a NAME="E3:91_2_1"/><b>then </b><i><font color="Green">E97</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:91_2_1"><i><font color="Green">E96</font></i></a>, <a class="ref" href="anproj_2.html#D8" target="_self">Def8</a></i>;<br/><a NAME="E4:91_2_1"/>
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:91"><i><font color="Green">E84</font></i></a>, <a class="txt" href="anproj_2.html#E16:91"><i><font color="Green">E88</font></i></a>, <a class="ref" href="anproj_2.html#D7" target="_self">Def7</a>, <a class="ref" href="anproj_2.html#T25" target="_self">Th25</a></i>;<br/><a NAME="E5:91_2_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:91_2_1"><i><font color="Green">E96</font></i></a>, <a class="ref" href="anproj_2.html#D8" target="_self">Def8</a></i>;<br/><b>hence </b><a NAME="E6:91_2_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E3:91_2_1"><i><font color="Green">E97</font></i></a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E96</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="91_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_2_2"/><i><font color="Green">E97</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><b>take </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>15</sub></font>;<br/><a NAME="E2:91_2_2"/>
( <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E4:91"><i><font color="Green">E83</font></i></a>, <a class="txt" href="anproj_2.html#E21:91"><i><font color="Green">E90</font></i></a>, <a class="ref" href="anproj_2.html#D7" target="_self">Def7</a>, <a class="ref" href="anproj_2.html#T25" target="_self">Th25</a></i>;<br/><a NAME="E3:91_2_2"/><b>then </b><i><font color="Green">E98</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:91_2_2"><i><font color="Green">E97</font></i></a>, <a class="ref" href="anproj_2.html#D8" target="_self">Def8</a></i>;<br/><a NAME="E4:91_2_2"/>
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:91"><i><font color="Green">E84</font></i></a>, <a class="txt" href="anproj_2.html#E21:91"><i><font color="Green">E90</font></i></a>, <a class="ref" href="anproj_2.html#D7" target="_self">Def7</a>, <a class="ref" href="anproj_2.html#T25" target="_self">Th25</a></i>;<br/><a NAME="E5:91_2_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:91_2_2"><i><font color="Green">E97</font></i></a>, <a class="ref" href="anproj_2.html#D8" target="_self">Def8</a></i>;<br/><b>hence </b><a NAME="E6:91_2_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E3:91_2_2"><i><font color="Green">E98</font></i></a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E97</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="91_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_2_3"/><i><font color="Green">E98</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><b>take </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>17</sub></font>;<br/><a NAME="E2:91_2_3"/>
( <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E4:91"><i><font color="Green">E83</font></i></a>, <a class="txt" href="anproj_2.html#E26:91"><i><font color="Green">E92</font></i></a>, <a class="ref" href="anproj_2.html#D7" target="_self">Def7</a>, <a class="ref" href="anproj_2.html#T25" target="_self">Th25</a></i>;<br/><a NAME="E3:91_2_3"/><b>then </b><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:91_2_3"><i><font color="Green">E98</font></i></a>, <a class="ref" href="anproj_2.html#D8" target="_self">Def8</a></i>;<br/><a NAME="E4:91_2_3"/>
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:91"><i><font color="Green">E84</font></i></a>, <a class="txt" href="anproj_2.html#E26:91"><i><font color="Green">E92</font></i></a>, <a class="ref" href="anproj_2.html#D7" target="_self">Def7</a>, <a class="ref" href="anproj_2.html#T25" target="_self">Th25</a></i>;<br/><a NAME="E5:91_2_3"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:91_2_3"><i><font color="Green">E98</font></i></a>, <a class="ref" href="anproj_2.html#D8" target="_self">Def8</a></i>;<br/><b>hence </b><a NAME="E6:91_2_3"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E3:91_2_3"><i><font color="Green">E99</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_2_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_2_4"/><i><font color="Green">E98</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><b>take </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>11</sub></font>;<br/><a NAME="E2:91_2_4"/>
( <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E4:91"><i><font color="Green">E83</font></i></a>, <a class="txt" href="anproj_2.html#E11:91"><i><font color="Green">E86</font></i></a>, <a class="ref" href="anproj_2.html#D7" target="_self">Def7</a>, <a class="ref" href="anproj_2.html#T25" target="_self">Th25</a></i>;<br/><a NAME="E3:91_2_4"/><b>then </b><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:91_2_4"><i><font color="Green">E98</font></i></a>, <a class="ref" href="anproj_2.html#D8" target="_self">Def8</a></i>;<br/><a NAME="E4:91_2_4"/>
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:91"><i><font color="Green">E84</font></i></a>, <a class="txt" href="anproj_2.html#E11:91"><i><font color="Green">E86</font></i></a>, <a class="ref" href="anproj_2.html#D7" target="_self">Def7</a>, <a class="ref" href="anproj_2.html#T25" target="_self">Th25</a></i>;<br/><a NAME="E5:91_2_4"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:91_2_4"><i><font color="Green">E98</font></i></a>, <a class="ref" href="anproj_2.html#D8" target="_self">Def8</a></i>;<br/><b>hence </b><a NAME="E6:91_2_4"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E3:91_2_4"><i><font color="Green">E99</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:91_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:91_2"><i><font color="Green">E94</font></i></a>, <a class="txt" href="anproj_2.html#E2:91_2"><i><font color="Green">E95</font></i></a>, <a class="txt" href="anproj_2.html#E3:91_2"><i><font color="Green">E96</font></i></a>, <a class="txt" href="anproj_2.html#E4:91_2"><i><font color="Green">E97</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E29:91"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E27:91"><i><font color="Green">E93</font></i></a></i>;<br/>


</div>
