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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p2</font>, <font color="Olive" title="b2">p3</font>, <font color="Olive" title="b3">p1</font>, <font color="Olive" title="b4">q2</font>, <font color="Olive" title="b5">q3</font>, <font color="Olive" title="b6">q1</font>, <font color="Olive" title="b7">r3</font>, <font color="Olive" title="b8">r2</font>, <font color="Olive" title="b9">r1</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">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">p3</font> &amp; <font color="Olive" title="b3">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">p3</font> &amp; <font color="Olive" title="b4">q2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">q3</font> &amp; <font color="Olive" title="b6">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">q2</font> &amp; <font color="Olive" title="b6">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">q3</font> &amp; not <font color="Olive" title="b3">p1</font>,<font color="Olive" title="b1">p2</font>,<font color="Olive" title="b6">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">p1</font>,<font color="Olive" title="b1">p2</font>,<font color="Olive" title="b2">p3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b6">q1</font>,<font color="Olive" title="b4">q2</font>,<font color="Olive" title="b5">q3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">p1</font>,<font color="Olive" title="b4">q2</font>,<font color="Olive" title="b7">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b6">q1</font>,<font color="Olive" title="b1">p2</font>,<font color="Olive" title="b7">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">p1</font>,<font color="Olive" title="b5">q3</font>,<font color="Olive" title="b8">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">p3</font>,<font color="Olive" title="b6">q1</font>,<font color="Olive" title="b8">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">p2</font>,<font color="Olive" title="b5">q3</font>,<font color="Olive" title="b9">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">p3</font>,<font color="Olive" title="b4">q2</font>,<font color="Olive" title="b9">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  holds <br/><font color="Olive" title="b9">r1</font>,<font color="Olive" title="b8">r2</font>,<font color="Olive" title="b7">r3</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">p2</font>, <font color="Maroon" title="c3">p3</font>, <font color="Maroon" title="c4">p1</font>, <font color="Maroon" title="c5">q2</font>, <font color="Maroon" title="c6">q3</font>, <font color="Maroon" title="c7">q1</font>, <font color="Maroon" title="c8">r3</font>, <font color="Maroon" title="c9">r2</font>, <font color="Maroon" title="c10">r1</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"> ( <font color="Maroon" title="c2">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">p3</font> &amp; <font color="Maroon" title="c4">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">p3</font> &amp; <font color="Maroon" title="c5">q2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q3</font> &amp; <font color="Maroon" title="c7">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q2</font> &amp; <font color="Maroon" title="c7">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q3</font> &amp; not <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c7">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c6">q3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c9">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c9">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c10">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c10">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  implies <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="E1:20"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
<font color="Maroon" title="c2">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">p3</font>
 <span class="kw">and </span><br/><a NAME="E2:20"/><span class="lab"><font color="Green" title="E15">A2</font></span>: 
<font color="Maroon" title="c4">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">p3</font>
 <span class="kw">and </span><br/><a NAME="E3:20"/><span class="lab"><font color="Green" title="E16">A3</font></span>: 
<font color="Maroon" title="c5">q2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q3</font>
 <span class="kw">and </span><br/><a NAME="E4:20"/><span class="lab"><font color="Green" title="E17">A4</font></span>: 
<font color="Maroon" title="c7">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q2</font>
 <span class="kw">and </span><br/><a NAME="E5:20"/><span class="lab"><font color="Green" title="E18">A5</font></span>: 
<font color="Maroon" title="c7">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q3</font>
 <span class="kw">and </span><br/><a NAME="E6:20"/><span class="lab"><font color="Green" title="E19">A6</font></span>: 
not <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c7">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E7:20"/><span class="lab"><font color="Green" title="E20">A7</font></span>: 
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E8:20"/><span class="lab"><font color="Green" title="E21">A8</font></span>: 
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c6">q3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E9:20"/><span class="lab"><font color="Green" title="E22">A9</font></span>: 
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E10:20"/><span class="lab"><font color="Green" title="E23">A10</font></span>: 
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E11:20"/><span class="lab"><font color="Green" title="E24">A11</font></span>: 
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c9">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E12:20"/><span class="lab"><font color="Green" title="E25">A12</font></span>: 
<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c9">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E13:20"/><span class="lab"><font color="Green" title="E26">A13</font></span>: 
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c10">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E14:20"/><span class="lab"><font color="Green" title="E27">A14</font></span>: 
<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c10">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/>

<a NAME="E15:20"/><span class="lab"><font color="Green" title="E28">A15</font></span>: 
<font color="Maroon" title="c4">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E29">A16</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:20_1"/><span class="lab"><font color="Green" title="E30">A17</font></span>: 
not <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c5">q2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><div><span class="lab"><font color="Green" title="E31">A18</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:20_1_1"/><span class="lab"><font color="Green" title="E32">A19</font></span>: 
not <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c6">q3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><div><span class="lab"><font color="Green" title="E33">A20</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1"><span class="kw">now </span></a><div class="add"><div><span class="lab"><font color="Green" title="E34">A21</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:20_1_1_1_1"/>
( not <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">q2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</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="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E1:20_1"><span class="lab"><font color="Green" title="E30">A17</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E2:20_1_1_1_1"/><span class="kw">then </span>
not <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c5">q2</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="#E1:20"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/><a NAME="E3:20_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A22</font></span>: 
not <font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</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/><span class="kw">assume </span><a NAME="E4:20_1_1_1_1"/><span class="lab"><font color="Green" title="E36">A23</font></span>: 
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c2">p2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E5:20_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A24</font></span>: 
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</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="E6:20_1_1_1_1"/>
( <font color="Maroon" title="c2">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">q1</font> &amp; <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c8">r3</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="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E10:20"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a>, <a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</a></span>;<br/><a NAME="E7:20_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c8">r3</font>,<font color="Maroon" title="c5">q2</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="#E5:20_1_1_1_1"><span class="lab"><font color="Green" title="E37">A24</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E8:20_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A25</font></span>: 
<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c8">r3</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="E9:20_1_1_1_1"/>
( <font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</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="#E9:20"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="txt" href="#E1:20_1"><span class="lab"><font color="Green" title="E30">A17</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E10:20_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A26</font></span>: 
<font color="Maroon" title="c5">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">r3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:20_1_1_1_1"><span class="lab"><font color="Green" title="E38">A25</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><a NAME="E11:20_1_1_1_1"/><span class="lab"><font color="Green" title="E40">A27</font></span>: 
<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c6">q3</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="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E12:20_1_1_1_1"/>
<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c2">p2</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="#E4:20_1_1_1_1"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E13:20_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c6">q3</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="#E4:20"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E11:20_1_1_1_1"><span class="lab"><font color="Green" title="E40">A27</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E14:20_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A28</font></span>: 
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c5">q2</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="E15:20_1_1_1_1"/>
<font color="Maroon" title="c2">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1_1"><span class="lab"><font color="Green" title="E32">A19</font></span></a>, <a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</a></span>;<br/><a NAME="E16:20_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c5">q2</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="#E13:20"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="txt" href="#E14:20_1_1_1_1"><span class="lab"><font color="Green" title="E41">A28</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E17:20_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A29</font></span>: 
<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c10">r1</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="E18:20_1_1_1_1"/>
<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c10">r1</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="#E14:20"><span class="lab"><font color="Green" title="E27">A14</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E19:20_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">r1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:20_1_1_1_1"><span class="lab"><font color="Green" title="E42">A29</font></span></a>, <a class="txt" href="#E3:20_1_1_1_1"><span class="lab"><font color="Green" title="E35">A22</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><span class="kw">hence </span><a NAME="E20:20_1_1_1_1"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E10:20_1_1_1_1"><span class="lab"><font color="Green" title="E39">A26</font></span></a>, <a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</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/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E35">A30</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:20_1_1_1_2"/>
( not <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c6">q3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</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="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E1:20_1_1"><span class="lab"><font color="Green" title="E32">A19</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E2:20_1_1_1_2"/><span class="kw">then </span>
not <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c6">q3</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="#E1:20"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/><a NAME="E3:20_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A31</font></span>: 
not <font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</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/><span class="kw">assume </span><a NAME="E4:20_1_1_1_2"/><span class="lab"><font color="Green" title="E37">A32</font></span>: 
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c3">p3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E5:20_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A33</font></span>: 
<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c3">p3</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="E6:20_1_1_1_2"/>
<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c6">q3</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="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E7:20_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c3">p3</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="#E4:20"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E5:20_1_1_1_2"><span class="lab"><font color="Green" title="E38">A33</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E8:20_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c6">q3</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="E9:20_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c6">q3</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="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E14:20"><span class="lab"><font color="Green" title="E27">A14</font></span></a>, <a class="txt" href="#E1:20_1"><span class="lab"><font color="Green" title="E30">A17</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E10:20_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A34</font></span>: 
<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c10">r1</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="E11:20_1_1_1_2"/>
not <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c6">q3</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="#E2:20"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E1:20_1_1"><span class="lab"><font color="Green" title="E32">A19</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/><a NAME="E12:20_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A35</font></span>: 
not <font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</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="E13:20_1_1_1_2"/>
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c3">p3</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="#E4:20"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E4:20_1_1_1_2"><span class="lab"><font color="Green" title="E37">A32</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E14:20_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c6">q3</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="E15:20_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c6">q3</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="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E12:20"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E16:20_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A36</font></span>: 
<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c9">r2</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="E17:20_1_1_1_2"/>
<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c10">r1</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="#E13:20"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E18:20_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A37</font></span>: 
<font color="Maroon" title="c6">q3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">r1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:20_1_1_1_2"><span class="lab"><font color="Green" title="E39">A34</font></span></a>, <a class="txt" href="#E3:20_1_1_1_2"><span class="lab"><font color="Green" title="E36">A31</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><a NAME="E19:20_1_1_1_2"/>
<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c9">r2</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="#E11:20"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E20:20_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">q3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:20_1_1_1_2"><span class="lab"><font color="Green" title="E41">A36</font></span></a>, <a class="txt" href="#E12:20_1_1_1_2"><span class="lab"><font color="Green" title="E40">A35</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><span class="kw">hence </span><a NAME="E21:20_1_1_1_2"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E18:20_1_1_1_2"><span class="lab"><font color="Green" title="E42">A37</font></span></a>, <a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</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/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E36">A38</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_3"><span class="kw">now </span></a><div class="add"><a NAME="E1:20_1_1_1_3"/>
not <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c7">q1</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="#E2:20"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/><a NAME="E2:20_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A39</font></span>: 
not <font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</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/><span class="kw">assume </span><a NAME="E3:20_1_1_1_3"/><span class="lab"><font color="Green" title="E38">A40</font></span>: 
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c4">p1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E4:20_1_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c6">q3</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="#E4:20"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E5:20_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A41</font></span>: 
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c7">q1</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="E6:20_1_1_1_3"/>
<font color="Maroon" title="c4">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1_1"><span class="lab"><font color="Green" title="E32">A19</font></span></a>, <a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</a></span>;<br/><a NAME="E7:20_1_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c7">q1</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="#E11:20"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="txt" href="#E5:20_1_1_1_3"><span class="lab"><font color="Green" title="E39">A41</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E8:20_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A42</font></span>: 
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c9">r2</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="E9:20_1_1_1_3"/><span class="lab"><font color="Green" title="E41">A43</font></span>: 
<font color="Maroon" title="c4">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1"><span class="lab"><font color="Green" title="E30">A17</font></span></a>, <a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</a></span>;<br/><a NAME="E10:20_1_1_1_3"/>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c7">q1</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="#E3:20_1_1_1_3"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E11:20_1_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c8">r3</font>,<font color="Maroon" title="c7">q1</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="#E9:20"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="txt" href="#E9:20_1_1_1_3"><span class="lab"><font color="Green" title="E41">A43</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E12:20_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A44</font></span>: 
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c8">r3</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="E13:20_1_1_1_3"/>
not <font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</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="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E14:20_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A45</font></span>: 
<font color="Maroon" title="c7">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">r3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:20"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="txt" href="#E12:20_1_1_1_3"><span class="lab"><font color="Green" title="E42">A44</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><a NAME="E15:20_1_1_1_3"/>
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c9">r2</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="#E12:20"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E16:20_1_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c7">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:20_1_1_1_3"><span class="lab"><font color="Green" title="E40">A42</font></span></a>, <a class="txt" href="#E2:20_1_1_1_3"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><span class="kw">hence </span><a NAME="E17:20_1_1_1_3"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E14:20_1_1_1_3"><span class="lab"><font color="Green" title="E43">A45</font></span></a>, <a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</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/></div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E4:20_1_1_1"/>
( <font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c4">p1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c2">p2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c3">p3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><span class="kw">hence </span><a NAME="E5:20_1_1_1"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E3:20_1_1_1"><span class="lab"><font color="Green" title="E36">A38</font></span></a>, <a class="txt" href="#E1:20_1_1_1"><span class="lab"><font color="Green" title="E34">A21</font></span></a>, <a class="txt" href="#E2:20_1_1_1"><span class="lab"><font color="Green" title="E35">A30</font></span></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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:20_1_1_2"/><span class="lab"><font color="Green" title="E34">A46</font></span>: 
not <font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c4">p1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E2:20_1_1_2"/><span class="lab"><font color="Green" title="E35">A47</font></span>: 
( not <font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c2">p2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c3">p3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><span class="kw">consider </span><font color="Maroon" title="c11">o</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PCPP</font><span class="kw"> such that </span><br/><a NAME="E4:20_1_1_2"/><span class="lab"><font color="Green" title="E36">A48</font></span>: 
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c11">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E5:20_1_1_2"/><span class="lab"><font color="Green" title="E37">A49</font></span>: 
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c11">o</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="anproj_2.html#D14" title="ANPROJ_2:def.14">ANPROJ_2:def 14</a></span>;<br/><a NAME="E6:20_1_1_2"/>
not <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c7">q1</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="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E1:20_1_1_2"><span class="lab"><font color="Green" title="E34">A46</font></span></a>, <a class="txt" href="#E4:20_1_1_2"><span class="lab"><font color="Green" title="E36">A48</font></span></a>, <a class="txt" href="#E5:20_1_1_2"><span class="lab"><font color="Green" title="E37">A49</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/><a NAME="E7:20_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A50</font></span>: 
not <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c7">q1</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="E8:20_1_1_2"/>
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c11">o</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="#E4:20"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E5:20_1_1_2"><span class="lab"><font color="Green" title="E37">A49</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E9:20_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A51</font></span>: 
<font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c6">q3</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="E10:20_1_1_2"/>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c11">o</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="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E15:20"><span class="lab"><font color="Green" title="E28">A15</font></span></a>, <a class="txt" href="#E4:20_1_1_2"><span class="lab"><font color="Green" title="E36">A48</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E11:20_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A52</font></span>: 
<font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</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="E12:20_1_1_2"/>
( <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</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="#E4:20_1_1_2"><span class="lab"><font color="Green" title="E36">A48</font></span></a>, <a class="txt" href="#E5:20_1_1_2"><span class="lab"><font color="Green" title="E37">A49</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><span class="kw">hence </span><a NAME="E13:20_1_1_2"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E1:20"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:20"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="txt" href="#E9:20"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="txt" href="#E10:20"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="txt" href="#E11:20"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="txt" href="#E12:20"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="txt" href="#E13:20"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="txt" href="#E14:20"><span class="lab"><font color="Green" title="E27">A14</font></span></a>, <a class="txt" href="#E15:20"><span class="lab"><font color="Green" title="E28">A15</font></span></a>, <a class="txt" href="#E1:20_1"><span class="lab"><font color="Green" title="E30">A17</font></span></a>, <a class="txt" href="#E1:20_1_1"><span class="lab"><font color="Green" title="E32">A19</font></span></a>, <a class="txt" href="#E2:20_1_1_2"><span class="lab"><font color="Green" title="E35">A47</font></span></a>, <a class="txt" href="#E4:20_1_1_2"><span class="lab"><font color="Green" title="E36">A48</font></span></a>, <a class="txt" href="#E5:20_1_1_2"><span class="lab"><font color="Green" title="E37">A49</font></span></a>, <a class="txt" href="#E11:20_1_1_2"><span class="lab"><font color="Green" title="E40">A52</font></span></a>, <a class="txt" href="#E9:20_1_1_2"><span class="lab"><font color="Green" title="E39">A51</font></span></a>, <a class="txt" href="#E7:20_1_1_2"><span class="lab"><font color="Green" title="E38">A50</font></span></a>, <a class="ref" href="anproj_2.html#D13" title="ANPROJ_2:def.13">ANPROJ_2:def 13</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/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:20_1_1"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E2:20_1_1"><span class="lab"><font color="Green" title="E33">A20</font></span></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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:20_1_2"/><span class="lab"><font color="Green" title="E32">A53</font></span>: 
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c6">q3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><div><span class="lab"><font color="Green" title="E33">A54</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:20_1_2_1"/><span class="lab"><font color="Green" title="E34">A55</font></span>: 
<font color="Maroon" title="c2">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q3</font>
 <span class="kw">and </span><br/><a NAME="E2:20_1_2_1"/><span class="lab"><font color="Green" title="E35">A56</font></span>: 
<font color="Maroon" title="c4">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E3:20_1_2_1"/>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c2">p2</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="#E1:20_1_2"><span class="lab"><font color="Green" title="E32">A53</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E4:20_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c9">r2</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="#E11:20"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="txt" href="#E2:20_1_2_1"><span class="lab"><font color="Green" title="E35">A56</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E5:20_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c3">p3</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="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E15:20"><span class="lab"><font color="Green" title="E28">A15</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E6:20_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A57</font></span>: 
<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c9">r2</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="E7:20_1_2_1"/>
not <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c7">q1</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="#E2:20"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/><a NAME="E8:20_1_2_1"/><span class="kw">then </span>
not <font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c4">p1</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="E9:20_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A58</font></span>: 
<font color="Maroon" title="c3">p3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:20"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="txt" href="#E6:20_1_2_1"><span class="lab"><font color="Green" title="E36">A57</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><a NAME="E10:20_1_2_1"/><span class="lab"><font color="Green" title="E38">A59</font></span>: 
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</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="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E11:20_1_2_1"/>
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c4">p1</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="#E1:20_1_2"><span class="lab"><font color="Green" title="E32">A53</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E12:20_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c10">r1</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="#E13:20"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="txt" href="#E1:20_1_2_1"><span class="lab"><font color="Green" title="E34">A55</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E13:20_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c3">p3</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="#E15:20"><span class="lab"><font color="Green" title="E28">A15</font></span></a>, <a class="txt" href="#E10:20_1_2_1"><span class="lab"><font color="Green" title="E38">A59</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E14:20_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A60</font></span>: 
<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c10">r1</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="E15:20_1_2_1"/>
( not <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">q2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</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="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E1:20_1"><span class="lab"><font color="Green" title="E30">A17</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E16:20_1_2_1"/><span class="kw">then </span>
not <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c5">q2</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="#E1:20"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/><a NAME="E17:20_1_2_1"/><span class="kw">then </span>
not <font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c2">p2</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="E18:20_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">p3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">r1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:20"><span class="lab"><font color="Green" title="E27">A14</font></span></a>, <a class="txt" href="#E14:20_1_2_1"><span class="lab"><font color="Green" title="E39">A60</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><span class="kw">hence </span><a NAME="E19:20_1_2_1"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E9:20_1_2_1"><span class="lab"><font color="Green" title="E37">A58</font></span></a>, <a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</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/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E34">A61</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:20_1_2_2"/>
not <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c7">q1</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="#E2:20"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/><a NAME="E2:20_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A62</font></span>: 
not <font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c7">q1</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="E3:20_1_2_2"/><span class="lab"><font color="Green" title="E36">A63</font></span>: 
not <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c4">p1</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="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E4:20_1_2_2"/><span class="lab"><font color="Green" title="E37">A64</font></span>: 
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c8">r3</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="#E10:20"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><span class="kw">assume </span><a NAME="E5:20_1_2_2"/><span class="lab"><font color="Green" title="E38">A65</font></span>: 
<font color="Maroon" title="c2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E6:20_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</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="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E7:20_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c8">r3</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="#E5:20"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="txt" href="#E5:20_1_2_2"><span class="lab"><font color="Green" title="E38">A65</font></span></a>, <a class="txt" href="#E4:20_1_2_2"><span class="lab"><font color="Green" title="E37">A64</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E8:20_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A66</font></span>: 
<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c8">r3</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="E9:20_1_2_2"/>
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</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="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E5:20_1_2_2"><span class="lab"><font color="Green" title="E38">A65</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E10:20_1_2_2"/><span class="kw">then </span>
not <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c4">p1</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="#E3:20"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E5:20_1_2_2"><span class="lab"><font color="Green" title="E38">A65</font></span></a>, <a class="txt" href="#E3:20_1_2_2"><span class="lab"><font color="Green" title="E36">A63</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/><a NAME="E11:20_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A67</font></span>: 
not <font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</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="E12:20_1_2_2"/>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c9">r2</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="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E11:20"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="txt" href="#E15:20"><span class="lab"><font color="Green" title="E28">A15</font></span></a>, <a class="txt" href="#E5:20_1_2_2"><span class="lab"><font color="Green" title="E38">A65</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E13:20_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c9">r2</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="E14:20_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A68</font></span>: 
<font color="Maroon" title="c3">p3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:20"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="txt" href="#E2:20_1_2_2"><span class="lab"><font color="Green" title="E35">A62</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><a NAME="E15:20_1_2_2"/>
<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c8">r3</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="#E9:20"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E16:20_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">r3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:20_1_2_2"><span class="lab"><font color="Green" title="E39">A66</font></span></a>, <a class="txt" href="#E11:20_1_2_2"><span class="lab"><font color="Green" title="E40">A67</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><span class="kw">hence </span><a NAME="E17:20_1_2_2"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E14:20"><span class="lab"><font color="Green" title="E27">A14</font></span></a>, <a class="txt" href="#E14:20_1_2_2"><span class="lab"><font color="Green" title="E41">A68</font></span></a>, <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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:20_1_2_3"/><span class="lab"><font color="Green" title="E35">A69</font></span>: 
<font color="Maroon" title="c4">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E2:20_1_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c10">r1</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="#E13:20"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E3:20_1_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c10">r1</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="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E15:20"><span class="lab"><font color="Green" title="E28">A15</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E4:20_1_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A70</font></span>: 
<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c10">r1</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="E5:20_1_2_3"/>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c7">q1</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="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E1:20_1_2_3"><span class="lab"><font color="Green" title="E35">A69</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E6:20_1_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c8">r3</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="#E3:20"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E9:20"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="txt" href="#E1:20_1_2_3"><span class="lab"><font color="Green" title="E35">A69</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E7:20_1_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A71</font></span>: 
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c8">r3</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="E8:20_1_2_3"/>
not <font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">q2</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="#E2:20"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E1:20_1_2_3"><span class="lab"><font color="Green" title="E35">A69</font></span></a>, <a class="ref" href="hessenbe.html#T16" target="_self" title="HESSENBE:th.16">Th16</a></span>;<br/><a NAME="E9:20_1_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A72</font></span>: 
<font color="Maroon" title="c3">p3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">r1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:20"><span class="lab"><font color="Green" title="E27">A14</font></span></a>, <a class="txt" href="#E4:20_1_2_3"><span class="lab"><font color="Green" title="E36">A70</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><a NAME="E10:20_1_2_3"/>
not <font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</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="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E11:20_1_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c7">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">r3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:20"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="txt" href="#E7:20_1_2_3"><span class="lab"><font color="Green" title="E37">A71</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><span class="kw">hence </span><a NAME="E12:20_1_2_3"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E12:20"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="txt" href="#E9:20_1_2_3"><span class="lab"><font color="Green" title="E38">A72</font></span></a>, <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/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:20_1_2"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E3:20_1_2"><span class="lab"><font color="Green" title="E34">A61</font></span></a>, <a class="txt" href="#E2:20_1_2"><span class="lab"><font color="Green" title="E33">A54</font></span></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/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:20_1"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E2:20_1"><span class="lab"><font color="Green" title="E31">A18</font></span></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/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><span class="kw">now </span></a><div class="add"><div><span class="lab"><font color="Green" title="E30">A73</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:20_2_1"/>
not <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c7">q1</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="#E2:20"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/><a NAME="E2:20_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A74</font></span>: 
not <font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</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="E3:20_2_1"/><span class="lab"><font color="Green" title="E32">A75</font></span>: 
not <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c2">p2</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="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><span class="kw">assume </span><a NAME="E4:20_2_1"/><span class="lab"><font color="Green" title="E33">A76</font></span>: 
<font color="Maroon" title="c4">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E5:20_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c7">q1</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="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E6:20_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c9">r2</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="#E3:20"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E11:20"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="txt" href="#E4:20_2_1"><span class="lab"><font color="Green" title="E33">A76</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E7:20_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A77</font></span>: 
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c9">r2</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="E8:20_2_1"/><span class="lab"><font color="Green" title="E35">A78</font></span>: 
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c2">p2</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="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E9:20_2_1"/>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c10">r1</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="#E14:20"><span class="lab"><font color="Green" title="E27">A14</font></span></a>, <a class="txt" href="#E4:20_2_1"><span class="lab"><font color="Green" title="E33">A76</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E10:20_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c10">r1</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="#E2:20"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E8:20_2_1"><span class="lab"><font color="Green" title="E35">A78</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E11:20_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A79</font></span>: 
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c10">r1</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="E12:20_2_1"/>
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c9">r2</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="#E12:20"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E13:20_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A80</font></span>: 
<font color="Maroon" title="c7">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:20_2_1"><span class="lab"><font color="Green" title="E34">A77</font></span></a>, <a class="txt" href="#E2:20_2_1"><span class="lab"><font color="Green" title="E31">A74</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><a NAME="E14:20_2_1"/>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c6">q3</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="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E4:20_2_1"><span class="lab"><font color="Green" title="E33">A76</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E15:20_2_1"/><span class="kw">then </span>
not <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c2">p2</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="#E3:20"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:20_2_1"><span class="lab"><font color="Green" title="E33">A76</font></span></a>, <a class="txt" href="#E3:20_2_1"><span class="lab"><font color="Green" title="E32">A75</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/><a NAME="E16:20_2_1"/><span class="kw">then </span>
not <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c6">q3</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="E17:20_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:20"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="txt" href="#E11:20_2_1"><span class="lab"><font color="Green" title="E36">A79</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><span class="kw">hence </span><a NAME="E18:20_2_1"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E10:20"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="txt" href="#E13:20_2_1"><span class="lab"><font color="Green" title="E37">A80</font></span></a>, <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/></div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:20_2"/><span class="lab"><font color="Green" title="E31">A81</font></span>: 
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c5">q2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><div><span class="lab"><font color="Green" title="E32">A82</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:20_2_2"/><span class="lab"><font color="Green" title="E33">A83</font></span>: 
<font color="Maroon" title="c4">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q2</font>
 <span class="kw">and </span><br/><a NAME="E2:20_2_2"/><span class="lab"><font color="Green" title="E34">A84</font></span>: 
<font color="Maroon" title="c3">p3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E3:20_2_2"/>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c2">p2</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="#E2:20_2"><span class="lab"><font color="Green" title="E31">A81</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E4:20_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c8">r3</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="#E9:20"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="txt" href="#E1:20_2_2"><span class="lab"><font color="Green" title="E33">A83</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E5:20_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A85</font></span>: 
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c8">r3</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="E6:20_2_2"/>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c3">p3</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="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E15:20"><span class="lab"><font color="Green" title="E28">A15</font></span></a>, <a class="txt" href="#E2:20_2"><span class="lab"><font color="Green" title="E31">A81</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E7:20_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c4">p1</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="E8:20_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c10">r1</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="#E14:20"><span class="lab"><font color="Green" title="E27">A14</font></span></a>, <a class="txt" href="#E2:20_2_2"><span class="lab"><font color="Green" title="E34">A84</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E9:20_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A86</font></span>: 
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c10">r1</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="E10:20_2_2"/>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c2">p2</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="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E11:20_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c10">r1</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="#E2:20"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E9:20_2_2"><span class="lab"><font color="Green" title="E36">A86</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E12:20_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A87</font></span>: 
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c10">r1</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="E13:20_2_2"/>
not <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c6">q3</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="#E3:20"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E2:20_2"><span class="lab"><font color="Green" title="E31">A81</font></span></a>, <a class="ref" href="hessenbe.html#T14" target="_self" title="HESSENBE:th.14">Th14</a></span>;<br/><a NAME="E14:20_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A88</font></span>: 
<font color="Maroon" title="c2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">r1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:20"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="txt" href="#E12:20_2_2"><span class="lab"><font color="Green" title="E37">A87</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><a NAME="E15:20_2_2"/>
( not <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c7">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c8">r3</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="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E10:20"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E16:20_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">r3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:20_2_2"><span class="lab"><font color="Green" title="E35">A85</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><span class="kw">hence </span><a NAME="E17:20_2_2"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E14:20_2_2"><span class="lab"><font color="Green" title="E38">A88</font></span></a>, <a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:20_2_3"/><span class="lab"><font color="Green" title="E33">A89</font></span>: 
<font color="Maroon" title="c3">p3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E2:20_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c3">p3</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="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E3:20_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A90</font></span>: 
not <font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c7">q1</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="#E2:20"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="hessenbe.html#T13" target="_self" title="HESSENBE:th.13">Th13</a></span>;<br/><a NAME="E4:20_2_3"/>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c2">p2</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="#E7:20"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E5:20_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c8">r3</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="#E2:20"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E9:20"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="txt" href="#E1:20_2_3"><span class="lab"><font color="Green" title="E33">A89</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E6:20_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A91</font></span>: 
<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c8">r3</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="E7:20_2_3"/>
( not <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c7">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c8">r3</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="#E6:20"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E10:20"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E8:20_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A92</font></span>: 
<font color="Maroon" title="c2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">r3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:20_2_3"><span class="lab"><font color="Green" title="E35">A91</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><a NAME="E9:20_2_3"/>
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c9">r2</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="#E12:20"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="txt" href="#E1:20_2_3"><span class="lab"><font color="Green" title="E33">A89</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E10:20_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c9">r2</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="#E4:20"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E11:20_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A93</font></span>: 
<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c7">q1</font>,<font color="Maroon" title="c9">r2</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="E12:20_2_3"/>
<font color="Maroon" title="c6">q3</font>,<font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c9">r2</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="#E11:20"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E13:20_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c8">r3</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c10">r1</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="#E13:20"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="txt" href="#E8:20_2_3"><span class="lab"><font color="Green" title="E36">A92</font></span></a>, <a class="txt" href="#E3:20_2_3"><span class="lab"><font color="Green" title="E34">A90</font></span></a>, <a class="txt" href="#E11:20_2_3"><span class="lab"><font color="Green" title="E37">A93</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><span class="kw">hence </span><a NAME="E14:20_2_3"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:20_2"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E1:20_2"><span class="lab"><font color="Green" title="E30">A73</font></span></a>, <a class="txt" href="#E3:20_2"><span class="lab"><font color="Green" title="E32">A82</font></span></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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E18:20"/>
<font color="Maroon" title="c10">r1</font>,<font color="Maroon" title="c9">r2</font>,<font color="Maroon" title="c8">r3</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="#E16:20"><span class="lab"><font color="Green" title="E29">A16</font></span></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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