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<b>let </b><font color="Maroon" title="c1">FCPS</font> be  <a href="anproj_2.html#NV10" title="ANPROJ_2:NV.10">up-3-dimensional</a> <a href="anproj_2.html#NM1" title="ANPROJ_2:NM.1">CollProjectiveSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">o</font>, <font color="Maroon" title="c6">d</font>, <font color="Maroon" title="c7">d'</font>, <font color="Maroon" title="c8">a'</font>, <font color="Maroon" title="c9">b'</font>, <font color="Maroon" title="c10">c'</font>, <font color="Maroon" title="c11">s</font>, <font color="Maroon" title="c12">t</font>, <font color="Maroon" title="c13">u</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FCPS</font>;<br/>

























<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E23">A1</font></i>: 
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">o</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp; not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp; not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c5">o</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp; not <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c5">o</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp; not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c5">o</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c7">d'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c8">a'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c9">b'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c10">c'</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c11">s</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c8">a'</font>,<font color="Maroon" title="c7">d'</font>,<font color="Maroon" title="c11">s</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c12">t</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c9">b'</font>,<font color="Maroon" title="c7">d'</font>,<font color="Maroon" title="c12">t</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c13">u</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">a'</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d'</font> &amp; <font color="Maroon" title="c6">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d'</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b'</font> )
 ;<br/>

<a NAME="E2:27"/><b>then </b>
not <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">a</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="projdes1.html#T10" target="_self" title="PROJDES1:th.10">Th10</a></i>;<br/>
<a NAME="E3:27"/><b>then </b>
not <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="projdes1.html#T1" target="_self" title="PROJDES1:th.1">Th1</a></i>;<br/>
<a NAME="E4:27"/><b>then </b><i><font color="Green" title="E24">A2</font></i>: 
<font color="Maroon" title="c11">s</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="txt" href="projdes1.html#E1:27"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="projdes1.html#T8" target="_self" title="PROJDES1:th.8">Th8</a></i>;<br/>
<a NAME="E5:27"/><i><font color="Green" title="E25">A3</font></i>: 
not <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 
<b>by </b><i><a class="txt" href="projdes1.html#E1:27"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="projdes1.html#T11" target="_self" title="PROJDES1:th.11">Th11</a></i>;<br/>
<a NAME="E6:27"/><b>then </b><i><font color="Green" title="E26">A4</font></i>: 
not <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c11">s</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 
<b>by </b><i><a class="txt" href="projdes1.html#E1:27"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="projdes1.html#E4:27"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="projdes1.html#T19" target="_self" title="PROJDES1:th.19">Th19</a></i>;<br/>
<a NAME="E7:27"/><i><font color="Green" title="E27">A5</font></i>: 
( <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp; <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp; <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  )
 
<b>by </b><i><a class="ref" href="projdes1.html#T18" target="_self" title="PROJDES1:th.18">Th18</a></i>;<br/>
<a NAME="E8:27"/>
<font color="Maroon" title="c3">b</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="txt" href="projdes1.html#E1:27"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="projdes1.html#T18" target="_self" title="PROJDES1:th.18">Th18</a></i>;<br/>
<a NAME="E9:27"/><b>then </b><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">t</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 
<b>by </b><i><a class="txt" href="projdes1.html#E1:27"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="projdes1.html#E7:27"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="projdes1.html#T14" target="_self" title="PROJDES1:th.14">Th14</a></i>;<br/>
<a NAME="E10:27"/><i><font color="Green" title="E29">A7</font></i>: 
<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">u</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 
<b>by </b><i><a class="txt" href="projdes1.html#E1:27"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="projdes1.html#E7:27"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="projdes1.html#T14" target="_self" title="PROJDES1:th.14">Th14</a></i>;<br/>
<a NAME="E11:27"/><i><font color="Green" title="E30">A8</font></i>: 
not <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="projdes1.html#E5:27"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="projdes1.html#T10" target="_self" title="PROJDES1:th.10">Th10</a></i>;<br/>
<a NAME="E12:27"/>
not <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c5">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="projdes1.html#E1:27"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="projdes1.html#T10" target="_self" title="PROJDES1:th.10">Th10</a></i>;<br/>
<a NAME="E13:27"/><b>then </b>
not <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="projdes1.html#T1" target="_self" title="PROJDES1:th.1">Th1</a></i>;<br/>
<a NAME="E14:27"/><b>then </b><i><font color="Green" title="E31">A9</font></i>: 
<font color="Maroon" title="c12">t</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="txt" href="projdes1.html#E1:27"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="projdes1.html#T8" target="_self" title="PROJDES1:th.8">Th8</a></i>;<br/>
<a NAME="E15:27"/><i><font color="Green" title="E32">A10</font></i>: 
<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c12">t</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="projdes1.html#E1:27"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="projdes1.html#T1" target="_self" title="PROJDES1:th.1">Th1</a></i>;<br/>
<a NAME="E16:27"/>
<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">u</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="projdes1.html#E1:27"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="projdes1.html#T1" target="_self" title="PROJDES1:th.1">Th1</a></i>;<br/>
<a NAME="E17:27"/><b>then </b>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">u</font>
 
<b>by </b><i><a class="txt" href="projdes1.html#E11:27"><i><font color="Green" title="E30">A8</font></i></a>, <a class="txt" href="projdes1.html#E14:27"><i><font color="Green" title="E31">A9</font></i></a>, <a class="txt" href="projdes1.html#E15:27"><i><font color="Green" title="E32">A10</font></i></a>, <a class="txt" href="projdes1.html#E9"><i><font color="Green" title="E3">Lm1</font></i></a></i>;<br/>
<a NAME="E18:27"/><b>then </b>
not <font color="Maroon" title="c12">t</font>,<font color="Maroon" title="c13">u</font>,<font color="Maroon" title="c11">s</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="projdes1.html#E6:27"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="projdes1.html#E9:27"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="projdes1.html#E10:27"><i><font color="Green" title="E29">A7</font></i></a>, <a class="ref" href="projdes1.html#T14" target="_self" title="PROJDES1:th.14">Th14</a></i>;<br/>
<b>hence </b><a NAME="E19:27"/>
not <font color="Maroon" title="c11">s</font>,<font color="Maroon" title="c12">t</font>,<font color="Maroon" title="c13">u</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="projdes1.html#T1" target="_self" title="PROJDES1:th.1">Th1</a></i>;<br/>


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