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<span class="kw">let </span><font color="Maroon" title="c1">PCPP</font> be   <a href="anproj_2.html#NM1" title="ANPROJ_2:NM.1">CollProjectiveSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">b2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PCPP</font>  st not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a1</font>,<font color="Olive" title="b3">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a1</font>,<font color="Olive" title="b4">b1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">a2</font>,<font color="Olive" title="b5">b2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">b1</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">b2</font> holds <br/> not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">b1</font>,<font color="Olive" title="b5">b2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c5">b1</font>, <font color="Maroon" title="c6">b2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PCPP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">b1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b2</font> implies  not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:19"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
( not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">b1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <span class="kw">and </span><br/><a NAME="E2:19"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E3:19"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b1</font>
 <span class="kw">and </span><br/><a NAME="E4:19"/><span class="lab"><font color="Green" title="E16">A4</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/>

<a NAME="E5:19"/>
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c4">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E3:19"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/>
<a NAME="E6:19"/><span class="kw">then </span>
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">b1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/>
<a NAME="E7:19"/><span class="kw">then </span>
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b2</font>,<font color="Maroon" title="c5">b1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E4:19"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:19"/>
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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