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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">o</font>, <font color="Olive" title="b2">b1</font>, <font color="Olive" title="b3">b2</font>, <font color="Olive" title="b4">a1</font>, <font color="Olive" title="b5">a2</font>, <font color="Olive" title="b6">a3</font>, <font color="Olive" title="b7">c3</font>, <font color="Olive" title="b8">c1</font>, <font color="Olive" title="b9">b3</font>, <font color="Olive" title="b10">c2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PCPP</font>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b1</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b2</font> &amp; not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">a1</font>,<font color="Olive" title="b5">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">a1</font>,<font color="Olive" title="b6">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">a2</font>,<font color="Olive" title="b6">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b4">a1</font>,<font color="Olive" title="b5">a2</font>,<font color="Olive" title="b7">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">b1</font>,<font color="Olive" title="b3">b2</font>,<font color="Olive" title="b7">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b5">a2</font>,<font color="Olive" title="b6">a3</font>,<font color="Olive" title="b8">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">b2</font>,<font color="Olive" title="b9">b3</font>,<font color="Olive" title="b8">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b4">a1</font>,<font color="Olive" title="b6">a3</font>,<font color="Olive" title="b10">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">b1</font>,<font color="Olive" title="b9">b3</font>,<font color="Olive" title="b10">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">a1</font>,<font color="Olive" title="b2">b1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">a2</font>,<font color="Olive" title="b3">b2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b6">a3</font>,<font color="Olive" title="b9">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; ( <font color="Olive" title="b4">a1</font>,<font color="Olive" title="b5">a2</font>,<font color="Olive" title="b6">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Olive" title="b2">b1</font>,<font color="Olive" title="b3">b2</font>,<font color="Olive" title="b9">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  ) holds <br/><font color="Olive" title="b8">c1</font>,<font color="Olive" title="b10">c2</font>,<font color="Olive" title="b7">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">b1</font>, <font color="Maroon" title="c4">b2</font>, <font color="Maroon" title="c5">a1</font>, <font color="Maroon" title="c6">a2</font>, <font color="Maroon" title="c7">a3</font>, <font color="Maroon" title="c8">c3</font>, <font color="Maroon" title="c9">c1</font>, <font color="Maroon" title="c10">b3</font>, <font color="Maroon" title="c11">c2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PCPP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b2</font> &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c6">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c7">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c7">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c8">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c7">a3</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c10">b3</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c7">a3</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c10">b3</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c3">b1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c4">b2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a3</font>,<font color="Maroon" title="c10">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; ( <font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c7">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c10">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  ) implies <font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c8">c3</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="E1:21"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font>
 <span class="kw">and </span><br/><a NAME="E2:21"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b2</font>
 <span class="kw">and </span><br/><a NAME="E3:21"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c6">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E4:21"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c7">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E5:21"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c7">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E6:21"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E7:21"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c8">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E8:21"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c7">a3</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E9:21"/><span class="lab"><font color="Green" title="E23">A9</font></span>: 
<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c10">b3</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E10:21"/><span class="lab"><font color="Green" title="E24">A10</font></span>: 
<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c7">a3</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E11:21"/><span class="lab"><font color="Green" title="E25">A11</font></span>: 
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c10">b3</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E12:21"/><span class="lab"><font color="Green" title="E26">A12</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c3">b1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E13:21"/><span class="lab"><font color="Green" title="E27">A13</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c4">b2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E14:21"/><span class="lab"><font color="Green" title="E28">A14</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a3</font>,<font color="Maroon" title="c10">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E15:21"/><span class="lab"><font color="Green" title="E29">A15</font></span>: 
( <font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c7">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c10">b3</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="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c8">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/>

<a NAME="E16:21"/><span class="lab"><font color="Green" title="E30">A16</font></span>: 
<font color="Maroon" title="c5">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:21"><span class="lab"><font color="Green" title="E18">A4</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="E17:21"/><span class="lab"><font color="Green" title="E31">A17</font></span>: 
<font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:21"><span class="lab"><font color="Green" title="E19">A5</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="E18:21"/><span class="lab"><font color="Green" title="E32">A18</font></span>: 
<font color="Maroon" title="c5">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E17">A3</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="E33">A19</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:21_1"/><span class="lab"><font color="Green" title="E34">A20</font></span>: 
<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c7">a3</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="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c8">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E2:21_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c7">a3</font>,<font color="Maroon" title="c5">a1</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="E3:21_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c9">c1</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="#E8:21"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E17:21"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E4:21_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A21</font></span>: 
<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <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="E5:21_1"/>
<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c7">a3</font>,<font color="Maroon" title="c6">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_1"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E6:21_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:21"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E16:21"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><span class="kw">hence </span><a NAME="E7:21_1"/>
<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c8">c3</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="#E6:21"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E18:21"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E4:21_1"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="anproj_2.html#D8" title="ANPROJ_2:def.8">ANPROJ_2:def 8</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>
<a NAME="E20:21"/><span class="lab"><font color="Green" title="E34">A22</font></span>: 
<font color="Maroon" title="c4">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E5:21"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E13:21"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E14:21"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/>
<a NAME="E21:21"/><span class="lab"><font color="Green" title="E35">A23</font></span>: 
<font color="Maroon" title="c3">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E4:21"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E12:21"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E14:21"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/>
<a NAME="E22:21"/><span class="lab"><font color="Green" title="E36">A24</font></span>: 
<font color="Maroon" title="c3">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E12:21"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E13:21"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:21_2"/><span class="lab"><font color="Green" title="E37">A25</font></span>: 
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c10">b3</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="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c8">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E2:21_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c10">b3</font>,<font color="Maroon" title="c3">b1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E3:21_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:21"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E20:21"><span class="lab"><font color="Green" title="E34">A22</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><a NAME="E4:21_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A26</font></span>: 
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c9">c1</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="E5:21_2"/>
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c10">b3</font>,<font color="Maroon" title="c4">b2</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="#E1:21_2"><span class="lab"><font color="Green" title="E37">A25</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E6:21_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c11">c2</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="#E11:21"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E21:21"><span class="lab"><font color="Green" title="E35">A23</font></span></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><span class="kw">hence </span><a NAME="E7:21_2"/>
<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c8">c3</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="#E7:21"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E22:21"><span class="lab"><font color="Green" title="E36">A24</font></span></a>, <a class="txt" href="#E4:21_2"><span class="lab"><font color="Green" title="E38">A26</font></span></a>, <a class="ref" href="anproj_2.html#D8" title="ANPROJ_2:def.8">ANPROJ_2:def 8</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="E24:21"/>
<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c8">c3</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="#E15:21"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E19:21"><span class="lab"><font color="Green" title="E33">A19</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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