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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="anproj_2.html#V1" title="ANPROJ_2:attr.1">up-3-dimensional</a>  <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font> is  <a href="anproj_2.html#V5" title="ANPROJ_2:attr.5">Desarguesian</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">p1</font>, <font color="Maroon" title="c4">p2</font>, <font color="Maroon" title="c5">p3</font>, <font color="Maroon" title="c6">q1</font>, <font color="Maroon" title="c7">q2</font>, <font color="Maroon" title="c8">q3</font>, <font color="Maroon" title="c9">r1</font>, <font color="Maroon" title="c10">r2</font>, <font color="Maroon" title="c11">r3</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="anproj_2.html#D12" target="_self" title="ANPROJ_2:def.12">ANPROJ_2:def 12</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="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q1</font> &amp; <font color="Maroon" title="c3">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q1</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">q2</font> &amp; <font color="Maroon" title="c4">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">q2</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">q3</font> &amp; <font color="Maroon" title="c5">p3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">q3</font> &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</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="c3">p1</font>,<font color="Maroon" title="c5">p3</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">p2</font>,<font color="Maroon" title="c5">p3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font>,<font color="Maroon" title="c11">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c6">q1</font>,<font color="Maroon" title="c7">q2</font>,<font color="Maroon" title="c11">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">p2</font>,<font color="Maroon" title="c5">p3</font>,<font color="Maroon" title="c9">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">q2</font>,<font color="Maroon" title="c8">q3</font>,<font color="Maroon" title="c9">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p3</font>,<font color="Maroon" title="c10">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c6">q1</font>,<font color="Maroon" title="c8">q3</font>,<font color="Maroon" title="c10">r2</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">p1</font>,<font color="Maroon" title="c6">q1</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">p2</font>,<font color="Maroon" title="c7">q2</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">p3</font>,<font color="Maroon" title="c8">q3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  implies <font color="Maroon" title="c9">r1</font>,<font color="Maroon" title="c10">r2</font>,<font color="Maroon" title="c11">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="E1:88"/><span class="lab"><font color="Green" title="E76">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="c6">q1</font>
 <span class="kw">and </span><br/><a NAME="E2:88"/><span class="lab"><font color="Green" title="E77">A2</font></span>: 
<font color="Maroon" title="c3">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q1</font>
 <span class="kw">and </span><br/><a NAME="E3:88"/><span class="lab"><font color="Green" title="E78">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="c7">q2</font>
 <span class="kw">and </span><br/><a NAME="E4:88"/><span class="lab"><font color="Green" title="E79">A4</font></span>: 
<font color="Maroon" title="c4">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">q2</font>
 <span class="kw">and </span><br/><a NAME="E5:88"/><span class="lab"><font color="Green" title="E80">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="c8">q3</font>
 <span class="kw">and </span><br/><a NAME="E6:88"/><span class="lab"><font color="Green" title="E81">A6</font></span>: 
<font color="Maroon" title="c5">p3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">q3</font>
 <span class="kw">and </span><br/><a NAME="E7:88"/><span class="lab"><font color="Green" title="E82">A7</font></span>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E8:88"/><span class="lab"><font color="Green" title="E83">A8</font></span>: 
( not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p3</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">p2</font>,<font color="Maroon" title="c5">p3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <span class="kw">and </span><br/><a NAME="E9:88"/><span class="lab"><font color="Green" title="E84">A9</font></span>: 
<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font>,<font color="Maroon" title="c11">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E10:88"/><span class="lab"><font color="Green" title="E85">A10</font></span>: 
<font color="Maroon" title="c6">q1</font>,<font color="Maroon" title="c7">q2</font>,<font color="Maroon" title="c11">r3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E11:88"/><span class="lab"><font color="Green" title="E86">A11</font></span>: 
<font color="Maroon" title="c4">p2</font>,<font color="Maroon" title="c5">p3</font>,<font color="Maroon" title="c9">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E12:88"/><span class="lab"><font color="Green" title="E87">A12</font></span>: 
<font color="Maroon" title="c7">q2</font>,<font color="Maroon" title="c8">q3</font>,<font color="Maroon" title="c9">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E13:88"/><span class="lab"><font color="Green" title="E88">A13</font></span>: 
<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p3</font>,<font color="Maroon" title="c10">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E14:88"/><span class="lab"><font color="Green" title="E89">A14</font></span>: 
<font color="Maroon" title="c6">q1</font>,<font color="Maroon" title="c8">q3</font>,<font color="Maroon" title="c10">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E15:88"/><span class="lab"><font color="Green" title="E90">A15</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c6">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E16:88"/><span class="lab"><font color="Green" title="E91">A16</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p2</font>,<font color="Maroon" title="c7">q2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E17:88"/><span class="lab"><font color="Green" title="E92">A17</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">p3</font>,<font color="Maroon" title="c8">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="c9">r1</font>,<font color="Maroon" title="c10">r2</font>,<font color="Maroon" title="c11">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="c12">q19</font>, <font color="Maroon" title="c13">q29</font>, <font color="Maroon" title="c14">r399</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E19:88"/><span class="lab"><font color="Green" title="E93">A18</font></span>: 
<font color="Maroon" title="c6">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c12">q19</font>
 <span class="kw">and </span><br/><a NAME="E20:88"/><span class="lab"><font color="Green" title="E94">A19</font></span>: 
<font color="Maroon" title="c7">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c13">q29</font>
 <span class="kw">and </span><br/><a NAME="E21:88"/><span class="lab"><font color="Green" title="E95">A20</font></span>: 
<font color="Maroon" title="c11">r3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c14">r399</font>
 <span class="kw">and </span><br/><a NAME="E22:88"/><span class="lab"><font color="Green" title="E96">A21</font></span>: 
not <font color="Maroon" title="c12">q19</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E23:88"/><span class="lab"><font color="Green" title="E97">A22</font></span>: 
not <font color="Maroon" title="c13">q29</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E24:88"/><span class="lab"><font color="Green" title="E98">A23</font></span>: 
not <font color="Maroon" title="c14">r399</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E25:88"/><span class="lab"><font color="Green" title="E99">A24</font></span>: 
<font color="Maroon" title="c12">q19</font>,<font color="Maroon" title="c13">q29</font>,<font color="Maroon" title="c14">r399</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:88"><span class="lab"><font color="Green" title="E85">A10</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c15">q299</font>, <font color="Maroon" title="c16">q39</font>, <font color="Maroon" title="c17">r199</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E27:88"/><span class="lab"><font color="Green" title="E100">A25</font></span>: 
<font color="Maroon" title="c7">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c15">q299</font>
 <span class="kw">and </span><br/><a NAME="E28:88"/><span class="lab"><font color="Green" title="E101">A26</font></span>: 
<font color="Maroon" title="c8">q3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c16">q39</font>
 <span class="kw">and </span><br/><a NAME="E29:88"/><span class="lab"><font color="Green" title="E102">A27</font></span>: 
<font color="Maroon" title="c9">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c17">r199</font>
 <span class="kw">and </span><br/><a NAME="E30:88"/><span class="lab"><font color="Green" title="E103">A28</font></span>: 
not <font color="Maroon" title="c15">q299</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E31:88"/><span class="lab"><font color="Green" title="E104">A29</font></span>: 
not <font color="Maroon" title="c16">q39</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E32:88"/><span class="lab"><font color="Green" title="E105">A30</font></span>: 
not <font color="Maroon" title="c17">r199</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E33:88"/><span class="lab"><font color="Green" title="E106">A31</font></span>: 
<font color="Maroon" title="c15">q299</font>,<font color="Maroon" title="c16">q39</font>,<font color="Maroon" title="c17">r199</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:88"><span class="lab"><font color="Green" title="E87">A12</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E34:88"/><span class="lab"><font color="Green" title="E107">A32</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c15">q299</font>,<font color="Maroon" title="c13">q29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:88"><span class="lab"><font color="Green" title="E94">A19</font></span></a>, <a class="txt" href="#E23:88"><span class="lab"><font color="Green" title="E97">A22</font></span></a>, <a class="txt" href="#E27:88"><span class="lab"><font color="Green" title="E100">A25</font></span></a>, <a class="txt" href="#E30:88"><span class="lab"><font color="Green" title="E103">A28</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c18">p299</font>, <font color="Maroon" title="c19">p39</font>, <font color="Maroon" title="c20">r19</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E36:88"/><span class="lab"><font color="Green" title="E108">A33</font></span>: 
<font color="Maroon" title="c4">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c18">p299</font>
 <span class="kw">and </span><br/><a NAME="E37:88"/><span class="lab"><font color="Green" title="E109">A34</font></span>: 
<font color="Maroon" title="c5">p3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c19">p39</font>
 <span class="kw">and </span><br/><a NAME="E38:88"/><span class="lab"><font color="Green" title="E110">A35</font></span>: 
<font color="Maroon" title="c9">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c20">r19</font>
 <span class="kw">and </span><br/><a NAME="E39:88"/><span class="lab"><font color="Green" title="E111">A36</font></span>: 
not <font color="Maroon" title="c18">p299</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E40:88"/><span class="lab"><font color="Green" title="E112">A37</font></span>: 
not <font color="Maroon" title="c19">p39</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E41:88"/><span class="lab"><font color="Green" title="E113">A38</font></span>: 
not <font color="Maroon" title="c20">r19</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E42:88"/><span class="lab"><font color="Green" title="E114">A39</font></span>: 
<font color="Maroon" title="c18">p299</font>,<font color="Maroon" title="c19">p39</font>,<font color="Maroon" title="c20">r19</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:88"><span class="lab"><font color="Green" title="E86">A11</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E43:88"/><span class="lab"><font color="Green" title="E115">A40</font></span>: 
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c19">p39</font>,<font color="Maroon" title="c16">q39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:88"><span class="lab"><font color="Green" title="E81">A6</font></span></a>, <a class="txt" href="#E37:88"><span class="lab"><font color="Green" title="E109">A34</font></span></a>, <a class="txt" href="#E40:88"><span class="lab"><font color="Green" title="E112">A37</font></span></a>, <a class="txt" href="#E28:88"><span class="lab"><font color="Green" title="E101">A26</font></span></a>, <a class="txt" href="#E31:88"><span class="lab"><font color="Green" title="E104">A29</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E44:88"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c17">r199</font>,<font color="Maroon" title="c20">r19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:88"><span class="lab"><font color="Green" title="E110">A35</font></span></a>, <a class="txt" href="#E41:88"><span class="lab"><font color="Green" title="E113">A38</font></span></a>, <a class="txt" href="#E29:88"><span class="lab"><font color="Green" title="E102">A27</font></span></a>, <a class="txt" href="#E32:88"><span class="lab"><font color="Green" title="E105">A30</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E45:88"/><span class="kw">then </span><span class="lab"><font color="Green" title="E116">A41</font></span>: 
<font color="Maroon" title="c13">q29</font>,<font color="Maroon" title="c16">q39</font>,<font color="Maroon" title="c20">r19</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:88"><span class="lab"><font color="Green" title="E106">A31</font></span></a>, <a class="txt" href="#E34:88"><span class="lab"><font color="Green" title="E107">A32</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c21">p199</font>, <font color="Maroon" title="c22">p399</font>, <font color="Maroon" title="c23">r29</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E47:88"/><span class="lab"><font color="Green" title="E117">A42</font></span>: 
<font color="Maroon" title="c3">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c21">p199</font>
 <span class="kw">and </span><br/><a NAME="E48:88"/><span class="lab"><font color="Green" title="E118">A43</font></span>: 
<font color="Maroon" title="c5">p3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c22">p399</font>
 <span class="kw">and </span><br/><a NAME="E49:88"/><span class="lab"><font color="Green" title="E119">A44</font></span>: 
<font color="Maroon" title="c10">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c23">r29</font>
 <span class="kw">and </span><br/><a NAME="E50:88"/><span class="lab"><font color="Green" title="E120">A45</font></span>: 
not <font color="Maroon" title="c21">p199</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E51:88"/><span class="lab"><font color="Green" title="E121">A46</font></span>: 
not <font color="Maroon" title="c22">p399</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E52:88"/><span class="lab"><font color="Green" title="E122">A47</font></span>: 
not <font color="Maroon" title="c23">r29</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E53:88"/><span class="lab"><font color="Green" title="E123">A48</font></span>: 
<font color="Maroon" title="c21">p199</font>,<font color="Maroon" title="c22">p399</font>,<font color="Maroon" title="c23">r29</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:88"><span class="lab"><font color="Green" title="E88">A13</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E54:88"/><span class="lab"><font color="Green" title="E124">A49</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c22">p399</font>,<font color="Maroon" title="c19">p39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:88"><span class="lab"><font color="Green" title="E109">A34</font></span></a>, <a class="txt" href="#E40:88"><span class="lab"><font color="Green" title="E112">A37</font></span></a>, <a class="txt" href="#E48:88"><span class="lab"><font color="Green" title="E118">A43</font></span></a>, <a class="txt" href="#E51:88"><span class="lab"><font color="Green" title="E121">A46</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c24">o9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E56:88"/><span class="lab"><font color="Green" title="E125">A50</font></span>: 
not <font color="Maroon" title="c24">o9</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E57:88"/><span class="lab"><font color="Green" title="E126">A51</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c24">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_1.html#T42" title="ANPROJ_1:th.42">ANPROJ_1:42</a></span>;<br/>
<a NAME="E58:88"/><span class="lab"><font color="Green" title="E127">A52</font></span>: 
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c24">o9</font>,<font color="Maroon" title="c16">q39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:88"><span class="lab"><font color="Green" title="E80">A5</font></span></a>, <a class="txt" href="#E56:88"><span class="lab"><font color="Green" title="E125">A50</font></span></a>, <a class="txt" href="#E57:88"><span class="lab"><font color="Green" title="E126">A51</font></span></a>, <a class="txt" href="#E28:88"><span class="lab"><font color="Green" title="E101">A26</font></span></a>, <a class="txt" href="#E31:88"><span class="lab"><font color="Green" title="E104">A29</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c25">p19</font>, <font color="Maroon" title="c26">p29</font>, <font color="Maroon" title="c27">r39</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E60:88"/><span class="lab"><font color="Green" title="E128">A53</font></span>: 
<font color="Maroon" title="c3">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c25">p19</font>
 <span class="kw">and </span><br/><a NAME="E61:88"/><span class="lab"><font color="Green" title="E129">A54</font></span>: 
<font color="Maroon" title="c4">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c26">p29</font>
 <span class="kw">and </span><br/><a NAME="E62:88"/><span class="lab"><font color="Green" title="E130">A55</font></span>: 
<font color="Maroon" title="c11">r3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c27">r39</font>
 <span class="kw">and </span><br/><a NAME="E63:88"/><span class="lab"><font color="Green" title="E131">A56</font></span>: 
not <font color="Maroon" title="c25">p19</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E64:88"/><span class="lab"><font color="Green" title="E132">A57</font></span>: 
not <font color="Maroon" title="c26">p29</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E65:88"/><span class="lab"><font color="Green" title="E133">A58</font></span>: 
not <font color="Maroon" title="c27">r39</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E66:88"/><span class="lab"><font color="Green" title="E134">A59</font></span>: 
<font color="Maroon" title="c25">p19</font>,<font color="Maroon" title="c26">p29</font>,<font color="Maroon" title="c27">r39</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:88"><span class="lab"><font color="Green" title="E84">A9</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E67:88"/><span class="lab"><font color="Green" title="E135">A60</font></span>: 
( not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c25">p19</font>,<font color="Maroon" title="c12">q19</font> &amp; not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c26">p29</font>,<font color="Maroon" title="c13">q29</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:88"><span class="lab"><font color="Green" title="E77">A2</font></span></a>, <a class="txt" href="#E4:88"><span class="lab"><font color="Green" title="E79">A4</font></span></a>, <a class="txt" href="#E60:88"><span class="lab"><font color="Green" title="E128">A53</font></span></a>, <a class="txt" href="#E61:88"><span class="lab"><font color="Green" title="E129">A54</font></span></a>, <a class="txt" href="#E63:88"><span class="lab"><font color="Green" title="E131">A56</font></span></a>, <a class="txt" href="#E64:88"><span class="lab"><font color="Green" title="E132">A57</font></span></a>, <a class="txt" href="#E19:88"><span class="lab"><font color="Green" title="E93">A18</font></span></a>, <a class="txt" href="#E20:88"><span class="lab"><font color="Green" title="E94">A19</font></span></a>, <a class="txt" href="#E22:88"><span class="lab"><font color="Green" title="E96">A21</font></span></a>, <a class="txt" href="#E23:88"><span class="lab"><font color="Green" title="E97">A22</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E68:88"/><span class="lab"><font color="Green" title="E136">A61</font></span>: 
( not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c24">o9</font>,<font color="Maroon" title="c12">q19</font> &amp; not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c24">o9</font>,<font color="Maroon" title="c13">q29</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:88"><span class="lab"><font color="Green" title="E76">A1</font></span></a>, <a class="txt" href="#E3:88"><span class="lab"><font color="Green" title="E78">A3</font></span></a>, <a class="txt" href="#E56:88"><span class="lab"><font color="Green" title="E125">A50</font></span></a>, <a class="txt" href="#E57:88"><span class="lab"><font color="Green" title="E126">A51</font></span></a>, <a class="txt" href="#E19:88"><span class="lab"><font color="Green" title="E93">A18</font></span></a>, <a class="txt" href="#E20:88"><span class="lab"><font color="Green" title="E94">A19</font></span></a>, <a class="txt" href="#E22:88"><span class="lab"><font color="Green" title="E96">A21</font></span></a>, <a class="txt" href="#E23:88"><span class="lab"><font color="Green" title="E97">A22</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c28">o999</font>, <font color="Maroon" title="c29">p2999</font>, <font color="Maroon" title="c30">q2999</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E70:88"/><span class="lab"><font color="Green" title="E137">A62</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c28">o999</font>
 <span class="kw">and </span><br/><a NAME="E71:88"/><span class="lab"><font color="Green" title="E138">A63</font></span>: 
<font color="Maroon" title="c4">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c29">p2999</font>
 <span class="kw">and </span><br/><a NAME="E72:88"/><span class="lab"><font color="Green" title="E139">A64</font></span>: 
<font color="Maroon" title="c7">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c30">q2999</font>
 <span class="kw">and </span><br/><a NAME="E73:88"/><span class="lab"><font color="Green" title="E140">A65</font></span>: 
not <font color="Maroon" title="c28">o999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E74:88"/><span class="lab"><font color="Green" title="E141">A66</font></span>: 
not <font color="Maroon" title="c29">p2999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E75:88"/><span class="lab"><font color="Green" title="E142">A67</font></span>: 
not <font color="Maroon" title="c30">q2999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E76:88"/><span class="lab"><font color="Green" title="E143">A68</font></span>: 
<font color="Maroon" title="c28">o999</font>,<font color="Maroon" title="c29">p2999</font>,<font color="Maroon" title="c30">q2999</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:88"><span class="lab"><font color="Green" title="E91">A16</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E77:88"/><span class="lab"><font color="Green" title="E144">A69</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c30">q2999</font>,<font color="Maroon" title="c13">q29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:88"><span class="lab"><font color="Green" title="E94">A19</font></span></a>, <a class="txt" href="#E23:88"><span class="lab"><font color="Green" title="E97">A22</font></span></a>, <a class="txt" href="#E72:88"><span class="lab"><font color="Green" title="E139">A64</font></span></a>, <a class="txt" href="#E75:88"><span class="lab"><font color="Green" title="E142">A67</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E78:88"/><span class="lab"><font color="Green" title="E145">A70</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c28">o999</font>,<font color="Maroon" title="c24">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:88"><span class="lab"><font color="Green" title="E125">A50</font></span></a>, <a class="txt" href="#E57:88"><span class="lab"><font color="Green" title="E126">A51</font></span></a>, <a class="txt" href="#E70:88"><span class="lab"><font color="Green" title="E137">A62</font></span></a>, <a class="txt" href="#E73:88"><span class="lab"><font color="Green" title="E140">A65</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E79:88"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c29">p2999</font>,<font color="Maroon" title="c26">p29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:88"><span class="lab"><font color="Green" title="E129">A54</font></span></a>, <a class="txt" href="#E64:88"><span class="lab"><font color="Green" title="E132">A57</font></span></a>, <a class="txt" href="#E71:88"><span class="lab"><font color="Green" title="E138">A63</font></span></a>, <a class="txt" href="#E74:88"><span class="lab"><font color="Green" title="E141">A66</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E80:88"/><span class="kw">then </span><span class="lab"><font color="Green" title="E146">A71</font></span>: 
<font color="Maroon" title="c24">o9</font>,<font color="Maroon" title="c26">p29</font>,<font color="Maroon" title="c13">q29</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E76:88"><span class="lab"><font color="Green" title="E143">A68</font></span></a>, <a class="txt" href="#E78:88"><span class="lab"><font color="Green" title="E145">A70</font></span></a>, <a class="txt" href="#E77:88"><span class="lab"><font color="Green" title="E144">A69</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c31">q199</font>, <font color="Maroon" title="c32">q399</font>, <font color="Maroon" title="c33">r299</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E82:88"/><span class="lab"><font color="Green" title="E147">A72</font></span>: 
<font color="Maroon" title="c6">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c31">q199</font>
 <span class="kw">and </span><br/><a NAME="E83:88"/><span class="lab"><font color="Green" title="E148">A73</font></span>: 
<font color="Maroon" title="c8">q3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c32">q399</font>
 <span class="kw">and </span><br/><a NAME="E84:88"/><span class="lab"><font color="Green" title="E149">A74</font></span>: 
<font color="Maroon" title="c10">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c33">r299</font>
 <span class="kw">and </span><br/><a NAME="E85:88"/><span class="lab"><font color="Green" title="E150">A75</font></span>: 
not <font color="Maroon" title="c31">q199</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E86:88"/><span class="lab"><font color="Green" title="E151">A76</font></span>: 
not <font color="Maroon" title="c32">q399</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E87:88"/><span class="lab"><font color="Green" title="E152">A77</font></span>: 
not <font color="Maroon" title="c33">r299</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E88:88"/><span class="lab"><font color="Green" title="E153">A78</font></span>: 
<font color="Maroon" title="c31">q199</font>,<font color="Maroon" title="c32">q399</font>,<font color="Maroon" title="c33">r299</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:88"><span class="lab"><font color="Green" title="E89">A14</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E89:88"/><span class="lab"><font color="Green" title="E154">A79</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c31">q199</font>,<font color="Maroon" title="c12">q19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:88"><span class="lab"><font color="Green" title="E93">A18</font></span></a>, <a class="txt" href="#E22:88"><span class="lab"><font color="Green" title="E96">A21</font></span></a>, <a class="txt" href="#E82:88"><span class="lab"><font color="Green" title="E147">A72</font></span></a>, <a class="txt" href="#E85:88"><span class="lab"><font color="Green" title="E150">A75</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E90:88"/><span class="lab"><font color="Green" title="E155">A80</font></span>: 
not <font color="Maroon" title="c24">o9</font>,<font color="Maroon" title="c25">p19</font>,<font color="Maroon" title="c26">p29</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:88"><span class="lab"><font color="Green" title="E82">A7</font></span></a>, <a class="txt" href="#E56:88"><span class="lab"><font color="Green" title="E125">A50</font></span></a>, <a class="txt" href="#E57:88"><span class="lab"><font color="Green" title="E126">A51</font></span></a>, <a class="txt" href="#E60:88"><span class="lab"><font color="Green" title="E128">A53</font></span></a>, <a class="txt" href="#E61:88"><span class="lab"><font color="Green" title="E129">A54</font></span></a>, <a class="txt" href="#E63:88"><span class="lab"><font color="Green" title="E131">A56</font></span></a>, <a class="txt" href="#E64:88"><span class="lab"><font color="Green" title="E132">A57</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E91:88"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c14">r399</font>,<font color="Maroon" title="c27">r39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:88"><span class="lab"><font color="Green" title="E130">A55</font></span></a>, <a class="txt" href="#E65:88"><span class="lab"><font color="Green" title="E133">A58</font></span></a>, <a class="txt" href="#E21:88"><span class="lab"><font color="Green" title="E95">A20</font></span></a>, <a class="txt" href="#E24:88"><span class="lab"><font color="Green" title="E98">A23</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E92:88"/><span class="kw">then </span><span class="lab"><font color="Green" title="E156">A81</font></span>: 
<font color="Maroon" title="c12">q19</font>,<font color="Maroon" title="c13">q29</font>,<font color="Maroon" title="c27">r39</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:88"><span class="lab"><font color="Green" title="E99">A24</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E93:88"/><span class="lab"><font color="Green" title="E157">A82</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c32">q399</font>,<font color="Maroon" title="c16">q39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:88"><span class="lab"><font color="Green" title="E101">A26</font></span></a>, <a class="txt" href="#E31:88"><span class="lab"><font color="Green" title="E104">A29</font></span></a>, <a class="txt" href="#E83:88"><span class="lab"><font color="Green" title="E148">A73</font></span></a>, <a class="txt" href="#E86:88"><span class="lab"><font color="Green" title="E151">A76</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c34">o9999</font>, <font color="Maroon" title="c35">p3999</font>, <font color="Maroon" title="c36">q3999</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E95:88"/><span class="lab"><font color="Green" title="E158">A83</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c34">o9999</font>
 <span class="kw">and </span><br/><a NAME="E96:88"/><span class="lab"><font color="Green" title="E159">A84</font></span>: 
<font color="Maroon" title="c5">p3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c35">p3999</font>
 <span class="kw">and </span><br/><a NAME="E97:88"/><span class="lab"><font color="Green" title="E160">A85</font></span>: 
<font color="Maroon" title="c8">q3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c36">q3999</font>
 <span class="kw">and </span><br/><a NAME="E98:88"/><span class="lab"><font color="Green" title="E161">A86</font></span>: 
not <font color="Maroon" title="c34">o9999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E99:88"/><span class="lab"><font color="Green" title="E162">A87</font></span>: 
not <font color="Maroon" title="c35">p3999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E100:88"/><span class="lab"><font color="Green" title="E163">A88</font></span>: 
not <font color="Maroon" title="c36">q3999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E101:88"/><span class="lab"><font color="Green" title="E164">A89</font></span>: 
<font color="Maroon" title="c34">o9999</font>,<font color="Maroon" title="c35">p3999</font>,<font color="Maroon" title="c36">q3999</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:88"><span class="lab"><font color="Green" title="E92">A17</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E102:88"/><span class="lab"><font color="Green" title="E165">A90</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c36">q3999</font>,<font color="Maroon" title="c16">q39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:88"><span class="lab"><font color="Green" title="E101">A26</font></span></a>, <a class="txt" href="#E31:88"><span class="lab"><font color="Green" title="E104">A29</font></span></a>, <a class="txt" href="#E97:88"><span class="lab"><font color="Green" title="E160">A85</font></span></a>, <a class="txt" href="#E100:88"><span class="lab"><font color="Green" title="E163">A88</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E103:88"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c18">p299</font>,<font color="Maroon" title="c26">p29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:88"><span class="lab"><font color="Green" title="E129">A54</font></span></a>, <a class="txt" href="#E64:88"><span class="lab"><font color="Green" title="E132">A57</font></span></a>, <a class="txt" href="#E36:88"><span class="lab"><font color="Green" title="E108">A33</font></span></a>, <a class="txt" href="#E39:88"><span class="lab"><font color="Green" title="E111">A36</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E104:88"/><span class="kw">then </span><span class="lab"><font color="Green" title="E166">A91</font></span>: 
<font color="Maroon" title="c26">p29</font>,<font color="Maroon" title="c19">p39</font>,<font color="Maroon" title="c20">r19</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:88"><span class="lab"><font color="Green" title="E114">A39</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E105:88"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c21">p199</font>,<font color="Maroon" title="c25">p19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E60:88"><span class="lab"><font color="Green" title="E128">A53</font></span></a>, <a class="txt" href="#E63:88"><span class="lab"><font color="Green" title="E131">A56</font></span></a>, <a class="txt" href="#E47:88"><span class="lab"><font color="Green" title="E117">A42</font></span></a>, <a class="txt" href="#E50:88"><span class="lab"><font color="Green" title="E120">A45</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E106:88"/><span class="kw">then </span>
<font color="Maroon" title="c25">p19</font>,<font color="Maroon" title="c19">p39</font>,<font color="Maroon" title="c23">r29</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:88"><span class="lab"><font color="Green" title="E123">A48</font></span></a>, <a class="txt" href="#E54:88"><span class="lab"><font color="Green" title="E124">A49</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E107:88"/><span class="kw">then </span><span class="lab"><font color="Green" title="E167">A92</font></span>: 
<font color="Maroon" title="c25">p19</font>,<font color="Maroon" title="c26">p29</font>,<font color="Maroon" title="c19">p39</font>,<font color="Maroon" title="c20">r19</font>,<font color="Maroon" title="c23">r29</font>,<font color="Maroon" title="c27">r39</font> <a href="anproj_2.html#R2" title="ANPROJ_2:pred.2">lie_on_a_triangle</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E66:88"><span class="lab"><font color="Green" title="E134">A59</font></span></a>, <a class="txt" href="#E104:88"><span class="lab"><font color="Green" title="E166">A91</font></span></a>, <a class="ref" href="anproj_2.html#D2" target="_self" title="ANPROJ_2:def.2">Def2</a></span>;<br/>
<a NAME="E108:88"/><span class="lab"><font color="Green" title="E168">A93</font></span>: 
<font color="Maroon" title="c12">q19</font>,<font color="Maroon" title="c13">q29</font>,<font color="Maroon" title="c16">q39</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:88"><span class="lab"><font color="Green" title="E96">A21</font></span></a>, <a class="txt" href="#E23:88"><span class="lab"><font color="Green" title="E97">A22</font></span></a>, <a class="txt" href="#E31:88"><span class="lab"><font color="Green" title="E104">A29</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c37">o99</font>, <font color="Maroon" title="c38">p1999</font>, <font color="Maroon" title="c39">q1999</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E110:88"/><span class="lab"><font color="Green" title="E169">A94</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c37">o99</font>
 <span class="kw">and </span><br/><a NAME="E111:88"/><span class="lab"><font color="Green" title="E170">A95</font></span>: 
<font color="Maroon" title="c3">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c38">p1999</font>
 <span class="kw">and </span><br/><a NAME="E112:88"/><span class="lab"><font color="Green" title="E171">A96</font></span>: 
<font color="Maroon" title="c6">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c39">q1999</font>
 <span class="kw">and </span><br/><a NAME="E113:88"/><span class="lab"><font color="Green" title="E172">A97</font></span>: 
not <font color="Maroon" title="c37">o99</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E114:88"/><span class="lab"><font color="Green" title="E173">A98</font></span>: 
not <font color="Maroon" title="c38">p1999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E115:88"/><span class="lab"><font color="Green" title="E174">A99</font></span>: 
not <font color="Maroon" title="c39">q1999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E116:88"/><span class="lab"><font color="Green" title="E175">A100</font></span>: 
<font color="Maroon" title="c37">o99</font>,<font color="Maroon" title="c38">p1999</font>,<font color="Maroon" title="c39">q1999</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:88"><span class="lab"><font color="Green" title="E90">A15</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E117:88"/><span class="lab"><font color="Green" title="E176">A101</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c39">q1999</font>,<font color="Maroon" title="c12">q19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:88"><span class="lab"><font color="Green" title="E93">A18</font></span></a>, <a class="txt" href="#E22:88"><span class="lab"><font color="Green" title="E96">A21</font></span></a>, <a class="txt" href="#E112:88"><span class="lab"><font color="Green" title="E171">A96</font></span></a>, <a class="txt" href="#E115:88"><span class="lab"><font color="Green" title="E174">A99</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E118:88"/><span class="lab"><font color="Green" title="E177">A102</font></span>: 
( not <font color="Maroon" title="c24">o9</font>,<font color="Maroon" title="c25">p19</font>,<font color="Maroon" title="c19">p39</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; not <font color="Maroon" title="c24">o9</font>,<font color="Maroon" title="c26">p29</font>,<font color="Maroon" title="c19">p39</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:88"><span class="lab"><font color="Green" title="E83">A8</font></span></a>, <a class="txt" href="#E56:88"><span class="lab"><font color="Green" title="E125">A50</font></span></a>, <a class="txt" href="#E57:88"><span class="lab"><font color="Green" title="E126">A51</font></span></a>, <a class="txt" href="#E60:88"><span class="lab"><font color="Green" title="E128">A53</font></span></a>, <a class="txt" href="#E61:88"><span class="lab"><font color="Green" title="E129">A54</font></span></a>, <a class="txt" href="#E63:88"><span class="lab"><font color="Green" title="E131">A56</font></span></a>, <a class="txt" href="#E64:88"><span class="lab"><font color="Green" title="E132">A57</font></span></a>, <a class="txt" href="#E37:88"><span class="lab"><font color="Green" title="E109">A34</font></span></a>, <a class="txt" href="#E40:88"><span class="lab"><font color="Green" title="E112">A37</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E119:88"/><span class="lab"><font color="Green" title="E178">A103</font></span>: 
<font color="Maroon" title="c25">p19</font>,<font color="Maroon" title="c26">p29</font>,<font color="Maroon" title="c19">p39</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E63:88"><span class="lab"><font color="Green" title="E131">A56</font></span></a>, <a class="txt" href="#E64:88"><span class="lab"><font color="Green" title="E132">A57</font></span></a>, <a class="txt" href="#E40:88"><span class="lab"><font color="Green" title="E112">A37</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E120:88"/><span class="lab"><font color="Green" title="E179">A104</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c34">o9999</font>,<font color="Maroon" title="c24">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:88"><span class="lab"><font color="Green" title="E125">A50</font></span></a>, <a class="txt" href="#E57:88"><span class="lab"><font color="Green" title="E126">A51</font></span></a>, <a class="txt" href="#E95:88"><span class="lab"><font color="Green" title="E158">A83</font></span></a>, <a class="txt" href="#E98:88"><span class="lab"><font color="Green" title="E161">A86</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E121:88"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c35">p3999</font>,<font color="Maroon" title="c19">p39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:88"><span class="lab"><font color="Green" title="E109">A34</font></span></a>, <a class="txt" href="#E40:88"><span class="lab"><font color="Green" title="E112">A37</font></span></a>, <a class="txt" href="#E96:88"><span class="lab"><font color="Green" title="E159">A84</font></span></a>, <a class="txt" href="#E99:88"><span class="lab"><font color="Green" title="E162">A87</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E122:88"/><span class="kw">then </span><span class="lab"><font color="Green" title="E180">A105</font></span>: 
<font color="Maroon" title="c24">o9</font>,<font color="Maroon" title="c19">p39</font>,<font color="Maroon" title="c16">q39</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E101:88"><span class="lab"><font color="Green" title="E164">A89</font></span></a>, <a class="txt" href="#E120:88"><span class="lab"><font color="Green" title="E179">A104</font></span></a>, <a class="txt" href="#E102:88"><span class="lab"><font color="Green" title="E165">A90</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E123:88"/><span class="lab"><font color="Green" title="E181">A106</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c37">o99</font>,<font color="Maroon" title="c24">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:88"><span class="lab"><font color="Green" title="E125">A50</font></span></a>, <a class="txt" href="#E57:88"><span class="lab"><font color="Green" title="E126">A51</font></span></a>, <a class="txt" href="#E110:88"><span class="lab"><font color="Green" title="E169">A94</font></span></a>, <a class="txt" href="#E113:88"><span class="lab"><font color="Green" title="E172">A97</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E124:88"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c38">p1999</font>,<font color="Maroon" title="c25">p19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E60:88"><span class="lab"><font color="Green" title="E128">A53</font></span></a>, <a class="txt" href="#E63:88"><span class="lab"><font color="Green" title="E131">A56</font></span></a>, <a class="txt" href="#E111:88"><span class="lab"><font color="Green" title="E170">A95</font></span></a>, <a class="txt" href="#E114:88"><span class="lab"><font color="Green" title="E173">A98</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E125:88"/><span class="kw">then </span>
<font color="Maroon" title="c24">o9</font>,<font color="Maroon" title="c25">p19</font>,<font color="Maroon" title="c12">q19</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E116:88"><span class="lab"><font color="Green" title="E175">A100</font></span></a>, <a class="txt" href="#E123:88"><span class="lab"><font color="Green" title="E181">A106</font></span></a>, <a class="txt" href="#E117:88"><span class="lab"><font color="Green" title="E176">A101</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E126:88"/><span class="kw">then </span><span class="lab"><font color="Green" title="E182">A107</font></span>: 
<font color="Maroon" title="c24">o9</font>,<font color="Maroon" title="c25">p19</font>,<font color="Maroon" title="c26">p29</font>,<font color="Maroon" title="c19">p39</font>,<font color="Maroon" title="c12">q19</font>,<font color="Maroon" title="c13">q29</font>,<font color="Maroon" title="c16">q39</font> <a href="anproj_2.html#R3" title="ANPROJ_2:pred.3">are_perspective</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E80:88"><span class="lab"><font color="Green" title="E146">A71</font></span></a>, <a class="txt" href="#E122:88"><span class="lab"><font color="Green" title="E180">A105</font></span></a>, <a class="ref" href="anproj_2.html#D3" target="_self" title="ANPROJ_2:def.3">Def3</a></span>;<br/>
<a NAME="E127:88"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c33">r299</font>,<font color="Maroon" title="c23">r29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:88"><span class="lab"><font color="Green" title="E119">A44</font></span></a>, <a class="txt" href="#E52:88"><span class="lab"><font color="Green" title="E122">A47</font></span></a>, <a class="txt" href="#E84:88"><span class="lab"><font color="Green" title="E149">A74</font></span></a>, <a class="txt" href="#E87:88"><span class="lab"><font color="Green" title="E152">A77</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E128:88"/><span class="kw">then </span>
<font color="Maroon" title="c12">q19</font>,<font color="Maroon" title="c16">q39</font>,<font color="Maroon" title="c23">r29</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E88:88"><span class="lab"><font color="Green" title="E153">A78</font></span></a>, <a class="txt" href="#E89:88"><span class="lab"><font color="Green" title="E154">A79</font></span></a>, <a class="txt" href="#E93:88"><span class="lab"><font color="Green" title="E157">A82</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E129:88"/><span class="kw">then </span><span class="lab"><font color="Green" title="E183">A108</font></span>: 
<font color="Maroon" title="c12">q19</font>,<font color="Maroon" title="c13">q29</font>,<font color="Maroon" title="c16">q39</font>,<font color="Maroon" title="c20">r19</font>,<font color="Maroon" title="c23">r29</font>,<font color="Maroon" title="c27">r39</font> <a href="anproj_2.html#R2" title="ANPROJ_2:pred.2">lie_on_a_triangle</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E92:88"><span class="lab"><font color="Green" title="E156">A81</font></span></a>, <a class="txt" href="#E45:88"><span class="lab"><font color="Green" title="E116">A41</font></span></a>, <a class="ref" href="anproj_2.html#D2" target="_self" title="ANPROJ_2:def.2">Def2</a></span>;<br/>
<a NAME="E130:88"/>
<font color="Maroon" title="c20">r19</font>,<font color="Maroon" title="c23">r29</font>,<font color="Maroon" title="c27">r39</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E65:88"><span class="lab"><font color="Green" title="E133">A58</font></span></a>, <a class="txt" href="#E41:88"><span class="lab"><font color="Green" title="E113">A38</font></span></a>, <a class="txt" href="#E52:88"><span class="lab"><font color="Green" title="E122">A47</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E131:88"/><span class="kw">then </span>
<font color="Maroon" title="c20">r19</font>,<font color="Maroon" title="c23">r29</font>,<font color="Maroon" title="c27">r39</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:88"><span class="lab"><font color="Green" title="E125">A50</font></span></a>, <a class="txt" href="#E68:88"><span class="lab"><font color="Green" title="E136">A61</font></span></a>, <a class="txt" href="#E58:88"><span class="lab"><font color="Green" title="E127">A52</font></span></a>, <a class="txt" href="#E67:88"><span class="lab"><font color="Green" title="E135">A60</font></span></a>, <a class="txt" href="#E43:88"><span class="lab"><font color="Green" title="E115">A40</font></span></a>, <a class="txt" href="#E119:88"><span class="lab"><font color="Green" title="E178">A103</font></span></a>, <a class="txt" href="#E108:88"><span class="lab"><font color="Green" title="E168">A93</font></span></a>, <a class="txt" href="#E126:88"><span class="lab"><font color="Green" title="E182">A107</font></span></a>, <a class="txt" href="#E90:88"><span class="lab"><font color="Green" title="E155">A80</font></span></a>, <a class="txt" href="#E118:88"><span class="lab"><font color="Green" title="E177">A102</font></span></a>, <a class="txt" href="#E107:88"><span class="lab"><font color="Green" title="E167">A92</font></span></a>, <a class="txt" href="#E129:88"><span class="lab"><font color="Green" title="E183">A108</font></span></a>, <a class="ref" href="anproj_2.html#T8" target="_self" title="ANPROJ_2:th.8">Th8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E132:88"/>
<font color="Maroon" title="c9">r1</font>,<font color="Maroon" title="c10">r2</font>,<font color="Maroon" title="c11">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="#E62:88"><span class="lab"><font color="Green" title="E130">A55</font></span></a>, <a class="txt" href="#E65:88"><span class="lab"><font color="Green" title="E133">A58</font></span></a>, <a class="txt" href="#E38:88"><span class="lab"><font color="Green" title="E110">A35</font></span></a>, <a class="txt" href="#E41:88"><span class="lab"><font color="Green" title="E113">A38</font></span></a>, <a class="txt" href="#E49:88"><span class="lab"><font color="Green" title="E119">A44</font></span></a>, <a class="txt" href="#E52:88"><span class="lab"><font color="Green" title="E122">A47</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</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>
