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

<b>let </b><font color="Maroon" title="c1">PCPP</font> be  <a href="anproj_2.html#V6" title="ANPROJ_2:attr.6">Pappian</a> <a href="anproj_2.html#NM2" title="ANPROJ_2:NM.2">CollProjectivePlane</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">b1</font>, <font color="Olive" title="b3">a1</font>, <font color="Olive" title="b4">b2</font>, <font color="Olive" title="b5">a2</font>, <font color="Olive" title="b6">b3</font>, <font color="Olive" title="b7">a3</font>, <font color="Olive" title="b8">c1</font>, <font color="Olive" title="b9">c3</font>, <font color="Olive" title="b10">c2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PCPP</font>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b1</font> &amp; <font color="Olive" title="b3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">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="b4">b2</font> &amp; <font color="Olive" title="b5">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">b2</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="b6">b3</font> &amp; <font color="Olive" title="b7">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">b3</font> &amp; not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">a1</font>,<font color="Olive" title="b5">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">a1</font>,<font color="Olive" title="b7">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">a2</font>,<font color="Olive" title="b7">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b8">c1</font>,<font color="Olive" title="b9">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">a1</font>,<font color="Olive" title="b5">a2</font>,<font color="Olive" title="b9">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">b1</font>,<font color="Olive" title="b4">b2</font>,<font color="Olive" title="b9">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b5">a2</font>,<font color="Olive" title="b7">a3</font>,<font color="Olive" title="b8">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b4">b2</font>,<font color="Olive" title="b6">b3</font>,<font color="Olive" title="b8">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">a1</font>,<font color="Olive" title="b7">a3</font>,<font color="Olive" title="b10">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">b1</font>,<font color="Olive" title="b6">b3</font>,<font color="Olive" title="b10">c2</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">a1</font>,<font color="Olive" title="b2">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="b5">a2</font>,<font color="Olive" title="b4">b2</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="b7">a3</font>,<font color="Olive" title="b6">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; ( <font color="Olive" title="b3">a1</font>,<font color="Olive" title="b5">a2</font>,<font color="Olive" title="b7">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Olive" title="b2">b1</font>,<font color="Olive" title="b4">b2</font>,<font color="Olive" title="b6">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  ) holds <br/><font color="Olive" title="b8">c1</font>,<font color="Olive" title="b10">c2</font>,<font color="Olive" title="b9">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><b>let </b><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">b1</font>, <font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c5">b2</font>, <font color="Maroon" title="c6">a2</font>, <font color="Maroon" title="c7">b3</font>, <font color="Maroon" title="c8">a3</font>, <font color="Maroon" title="c9">c1</font>, <font color="Maroon" title="c10">c3</font>, <font color="Maroon" title="c11">c2</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">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="c5">b2</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</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="c7">b3</font> &amp; <font color="Maroon" title="c8">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">b3</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c7">b3</font>,<font color="Maroon" title="c11">c2</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">a1</font>,<font color="Maroon" title="c3">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="c6">a2</font>,<font color="Maroon" title="c5">b2</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="c8">a3</font>,<font color="Maroon" title="c7">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; ( <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  ) implies <font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )</span><br/>





















<b>assume </b><b>that </b><br/><a NAME="E1:17"/><i><font color="Green" title="E15">A1</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">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="c5">b2</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</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="c7">b3</font> &amp; <font color="Maroon" title="c8">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> )
 <b>and </b><br/><a NAME="E2:17"/><i><font color="Green" title="E16">A2</font></i>: 
( not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <b>and </b><br/><a NAME="E3:17"/>
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>and </b><br/><a NAME="E4:17"/><i><font color="Green" title="E17">A3</font></i>: 
( <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">b3</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c7">b3</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <b>and </b><br/><a NAME="E5:17"/><i><font color="Green" title="E18">A4</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c3">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="c6">a2</font>,<font color="Maroon" title="c5">b2</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="c8">a3</font>,<font color="Maroon" title="c7">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <b>and </b><br/><a NAME="E6:17"/><i><font color="Green" title="E19">A5</font></i>: 
( <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/>

<a NAME="E7:17"/><i><font color="Green" title="E20">A6</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a1</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">a2</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a2</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="c8">a3</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">a3</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">a3</font> )
 
<b>by </b><i><a class="txt" href="#E2:17"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</a></i>;<br/>
<a NAME="E8:17"/><i><font color="Green" title="E21">A7</font></i>: 
( <font color="Maroon" title="c3">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> )
 
<b>by </b><i><a class="txt" href="#E1:17"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="#E2:17"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E5:17"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></i>;<br/>
<div><i><font color="Green" title="E22">A8</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_1"/><i><font color="Green" title="E23">A9</font></i>: 
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E2:17_1"/><i><font color="Green" title="E24">A10</font></i>: 
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_1_1"/>
<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c4">a1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="#E1:17_1"><i><font color="Green" title="E23">A9</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></i>;<br/>
<a NAME="E2:17_1_1"/><b>then </b>
<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="#E4:17"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E7:17"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></i>;<br/>
<b>hence </b><a NAME="E3:17_1_1"/>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:17_1"/>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_1_2"/>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c6">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="#E1:17_1"><i><font color="Green" title="E23">A9</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></i>;<br/>
<b>hence </b><a NAME="E2:17_1_2"/>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="#E4:17"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E7:17"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:17_1"/>
<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="#E4:17"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E7:17"><i><font color="Green" title="E20">A6</font></i></a>, <a class="txt" href="#E2:17_1"><i><font color="Green" title="E24">A10</font></i></a>, <a class="ref" href="anproj_2.html#D8" title="ANPROJ_2:def.8">ANPROJ_2:def 8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_2"/><i><font color="Green" title="E23">A11</font></i>: 
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E2:17_2"/><i><font color="Green" title="E24">A12</font></i>: 
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_2_1"/>
<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">b3</font>,<font color="Maroon" title="c3">b1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="#E1:17_2"><i><font color="Green" title="E23">A11</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></i>;<br/>
<a NAME="E2:17_2_1"/><b>then </b>
<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="#E4:17"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E8:17"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></i>;<br/>
<b>hence </b><a NAME="E3:17_2_1"/>
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:17_2"/>
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_2_2"/>
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c7">b3</font>,<font color="Maroon" title="c5">b2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="#E1:17_2"><i><font color="Green" title="E23">A11</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></i>;<br/>
<b>hence </b><a NAME="E2:17_2_2"/>
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="#E4:17"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E8:17"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:17_2"/>
<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="#E4:17"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E8:17"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="#E2:17_2"><i><font color="Green" title="E24">A12</font></i></a>, <a class="ref" href="anproj_2.html#D8" title="ANPROJ_2:def.8">ANPROJ_2:def 8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:17"/>
<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="#E6:17"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E9:17"><i><font color="Green" title="E22">A8</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
