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





















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:23"/><span class="lab"><font color="Green" title="E17">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="E2:23"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font>
 <span class="kw">and </span><br/><a NAME="E3:23"/><span class="lab"><font color="Green" title="E19">A3</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font>
 <span class="kw">and </span><br/><a NAME="E4:23"/><span class="lab"><font color="Green" title="E20">A4</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="c5">b2</font>
 <span class="kw">and </span><br/><a NAME="E5:23"/><span class="lab"><font color="Green" title="E21">A5</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="c7">b3</font>
 <span class="kw">and </span><br/><a NAME="E6:23"/><span class="lab"><font color="Green" title="E22">A6</font></span>: 
<font color="Maroon" title="c8">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font>
 <span class="kw">and </span><br/><a NAME="E7:23"/><span class="lab"><font color="Green" title="E23">A7</font></span>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E8:23"/><span class="lab"><font color="Green" title="E24">A8</font></span>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E9:23"/><span class="lab"><font color="Green" title="E25">A9</font></span>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E10:23"/><span class="lab"><font color="Green" title="E26">A10</font></span>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E11:23"/><span class="lab"><font color="Green" title="E27">A11</font></span>: 
( <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <span class="kw">and </span><br/><a NAME="E12:23"/><span class="lab"><font color="Green" title="E28">A12</font></span>: 
<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E13:23"/><span class="lab"><font color="Green" title="E29">A13</font></span>: 
<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">b3</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E14:23"/><span class="lab"><font color="Green" title="E30">A14</font></span>: 
( <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c7">b3</font>,<font color="Maroon" title="c11">c2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <span class="kw">and </span><br/><a NAME="E15:23"/><span class="lab"><font color="Green" title="E31">A15</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c3">b1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E16:23"/><span class="lab"><font color="Green" title="E32">A16</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c5">b2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E17:23"/><span class="lab"><font color="Green" title="E33">A17</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c7">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <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="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/>

<a NAME="E18:23"/><span class="lab"><font color="Green" title="E34">A18</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E23">A7</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="E19:23"/><span class="lab"><font color="Green" title="E35">A19</font></span>: 
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E24">A8</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="E20:23"/><span class="lab"><font color="Green" title="E36">A20</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">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">a3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><span class="kw">now </span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c12">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PCPP</font>;<br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:23_1"/>
not <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E3:23_1"/>
not <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">b3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  implies <font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )</span><br/><span class="kw">consider </span><font color="Maroon" title="c13">x</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="E5:23_1"/><span class="lab"><font color="Green" title="E37">A21</font></span>: 
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c13">x</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E6:23_1"/><span class="lab"><font color="Green" title="E38">A22</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c13">x</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/><span class="kw">consider </span><font color="Maroon" title="c14">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PCPP</font>;<br/><span class="kw">consider </span><font color="Maroon" title="c15">y</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="E9:23_1"/><span class="lab"><font color="Green" title="E39">A23</font></span>: 
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c7">b3</font>,<font color="Maroon" title="c15">y</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E10:23_1"/><span class="lab"><font color="Green" title="E40">A24</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c15">y</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/><span class="kw">assume </span><a NAME="E11:23_1"/><span class="lab"><font color="Green" title="E41">A25</font></span>: 
not <font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <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="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><div><span class="lab"><font color="Green" title="E42">A26</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:23_1_1"/>
( not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c6">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">b3</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c9">c1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:23"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E13:23"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E2:23_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A27</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="c9">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:23"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E5:23"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E16:23"><span class="lab"><font color="Green" title="E32">A16</font></span></a>, <a class="txt" href="#E17:23"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="ref" href="hessenbe.html#T10" target="_self" title="HESSENBE:th.10">Th10</a></span>;<br/><a NAME="E3:23_1_1"/>
not <font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c2">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="#E9:23"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E4:23_1_1"/><span class="kw">then </span>
not <font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c2">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="#E12:23"><span class="lab"><font color="Green" title="E28">A12</font></span></a>, <a class="txt" href="#E2:23_1_1"><span class="lab"><font color="Green" title="E43">A27</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/><a NAME="E5:23_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A28</font></span>: 
not <font color="Maroon" title="c2">o</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="E6:23_1_1"/><span class="lab"><font color="Green" title="E45">A29</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="c7">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E15:23"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="txt" href="#E17:23"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="ref" href="hessenbe.html#T9" target="_self" title="HESSENBE:th.9">Th9</a></span>;<br/><a NAME="E7:23_1_1"/>
( not <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">a3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c2">o</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="txt" href="#E8:23"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E15:23"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E8:23_1_1"/><span class="kw">then </span>
not <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c8">a3</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="#E2:23"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="hessenbe.html#T8" target="_self" title="HESSENBE:th.8">Th8</a></span>;<br/><a NAME="E9:23_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A30</font></span>: 
not <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">a3</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/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E10:23_1_1"/><span class="lab"><font color="Green" title="E47">A31</font></span>: 
<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c10">c3</font>,<font color="Maroon" title="c13">x</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E11:23_1_1"/><span class="lab"><font color="Green" title="E48">A32</font></span>: 
<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c10">c3</font>,<font color="Maroon" title="c15">y</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"> contradiction</span><br/><a NAME="E12:23_1_1"/>
( <font color="Maroon" title="c9">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">c3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E10:23"><span class="lab"><font color="Green" title="E26">A10</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="E13:23_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c7">b3</font>,<font color="Maroon" title="c13">x</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="#E6:23_1"><span class="lab"><font color="Green" title="E38">A22</font></span></a>, <a class="txt" href="#E9:23_1"><span class="lab"><font color="Green" title="E39">A23</font></span></a>, <a class="txt" href="#E10:23_1"><span class="lab"><font color="Green" title="E40">A24</font></span></a>, <a class="txt" href="#E10:23_1_1"><span class="lab"><font color="Green" title="E47">A31</font></span></a>, <a class="txt" href="#E11:23_1_1"><span class="lab"><font color="Green" title="E48">A32</font></span></a>, <a class="txt" href="#E5:23_1_1"><span class="lab"><font color="Green" title="E44">A28</font></span></a>, <a class="ref" href="hessenbe.html#T17" target="_self" title="HESSENBE:th.17">Th17</a></span>;<br/><a NAME="E14:23_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c10">c3</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="#E14:23"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E19:23"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="txt" href="#E5:23_1"><span class="lab"><font color="Green" title="E37">A21</font></span></a>, <a class="txt" href="#E10:23_1_1"><span class="lab"><font color="Green" title="E47">A31</font></span></a>, <a class="txt" href="#E6:23_1_1"><span class="lab"><font color="Green" title="E45">A29</font></span></a>, <a class="txt" href="#E9:23_1_1"><span class="lab"><font color="Green" title="E46">A30</font></span></a>, <a class="ref" href="hessenbe.html#T17" target="_self" title="HESSENBE:th.17">Th17</a></span>;<br/><span class="kw">hence </span><a NAME="E15:23_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:23_1"><span class="lab"><font color="Green" title="E41">A25</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="23_1_2"><span class="kw">now </span></a><div class="add"><div><span class="lab"><font color="Green" title="E43">A33</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:23_1_2_1"/><span class="lab"><font color="Green" title="E44">A34</font></span>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c7">b3</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="#E1:23"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E5:23"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E15:23"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="txt" href="#E17:23"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="ref" href="hessenbe.html#T19" target="_self" title="HESSENBE:th.19">Th19</a></span>;<br/><a NAME="E2:23_1_2_1"/><span class="lab"><font color="Green" title="E45">A35</font></span>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c6">a2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b3</font>,<font color="Maroon" title="c8">a3</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="#E16:23"><span class="lab"><font color="Green" title="E32">A16</font></span></a>, <a class="txt" href="#E17:23"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></span>;<br/><a NAME="E3:23_1_2_1"/><span class="lab"><font color="Green" title="E46">A36</font></span>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c15">y</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">a1</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="#E15:23"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="txt" href="#E16:23"><span class="lab"><font color="Green" title="E32">A16</font></span></a>, <a class="txt" href="#E18:23"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="txt" href="#E10:23_1"><span class="lab"><font color="Green" title="E40">A24</font></span></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></span>;<br/><span class="kw">assume </span><a NAME="E4:23_1_2_1"/><span class="lab"><font color="Green" title="E47">A37</font></span>: 
not <font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c10">c3</font>,<font color="Maroon" title="c15">y</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"> contradiction</span><br/><a NAME="E5:23_1_2_1"/>
( not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c5">b2</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">b2</font>,<font color="Maroon" title="c7">b3</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="#E1:23"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E5:23"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E9:23"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E15:23"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="txt" href="#E16:23"><span class="lab"><font color="Green" title="E32">A16</font></span></a>, <a class="txt" href="#E17:23"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="ref" href="hessenbe.html#T19" target="_self" title="HESSENBE:th.19">Th19</a></span>;<br/><span class="kw">hence </span><a NAME="E6:23_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E4:23"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E6:23"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E10:23"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="txt" href="#E11:23"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="txt" href="#E12:23"><span class="lab"><font color="Green" title="E28">A12</font></span></a>, <a class="txt" href="#E13:23"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E14:23"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E18:23"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="txt" href="#E20:23"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="txt" href="#E9:23_1"><span class="lab"><font color="Green" title="E39">A23</font></span></a>, <a class="txt" href="#E11:23_1"><span class="lab"><font color="Green" title="E41">A25</font></span></a>, <a class="txt" href="#E4:23_1_2_1"><span class="lab"><font color="Green" title="E47">A37</font></span></a>, <a class="txt" href="#E3:23_1_2_1"><span class="lab"><font color="Green" title="E46">A36</font></span></a>, <a class="txt" href="#E2:23_1_2_1"><span class="lab"><font color="Green" title="E45">A35</font></span></a>, <a class="txt" href="#E1:23_1_2_1"><span class="lab"><font color="Green" title="E44">A34</font></span></a>, <a class="txt" href="hessenbe.html#E22"><span class="lab"><font color="Green" title="E15">Lm2</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">assume </span><a NAME="E2:23_1_2"/>
(  not <font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c10">c3</font>,<font color="Maroon" title="c13">x</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or  not <font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c10">c3</font>,<font color="Maroon" title="c15">y</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="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><span class="kw">hence </span><a NAME="E3:23_1_2"/>
<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E4:23"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E5:23"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E6:23"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E9:23"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E10:23"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="txt" href="#E11:23"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="txt" href="#E12:23"><span class="lab"><font color="Green" title="E28">A12</font></span></a>, <a class="txt" href="#E13:23"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E14:23"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E15:23"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="txt" href="#E16:23"><span class="lab"><font color="Green" title="E32">A16</font></span></a>, <a class="txt" href="#E17:23"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="txt" href="#E5:23_1"><span class="lab"><font color="Green" title="E37">A21</font></span></a>, <a class="txt" href="#E6:23_1"><span class="lab"><font color="Green" title="E38">A22</font></span></a>, <a class="txt" href="#E1:23_1_2"><span class="lab"><font color="Green" title="E43">A33</font></span></a>, <a class="txt" href="hessenbe.html#E22"><span class="lab"><font color="Green" title="E15">Lm2</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="E14:23_1"/>
<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:23_1"><span class="lab"><font color="Green" title="E42">A26</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="E22:23"/>
<font color="Maroon" title="c9">c1</font>,<font color="Maroon" title="c11">c2</font>,<font color="Maroon" title="c10">c3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E9:23"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E11:23"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="txt" href="#E12:23"><span class="lab"><font color="Green" title="E28">A12</font></span></a>, <a class="txt" href="#E13:23"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E14:23"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E15:23"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="txt" href="#E16:23"><span class="lab"><font color="Green" title="E32">A16</font></span></a>, <a class="txt" href="#E17:23"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="txt" href="hessenbe.html#E21"><span class="lab"><font color="Green" title="E14">Lm1</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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