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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="firebrick">::  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#V6" title="ANPROJ_2:attr.6">Pappian</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="firebrick">:: according to </font></span><a class="ref" href="anproj_2.html#D13" target="_self" title="ANPROJ_2:def.13">ANPROJ_2:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="c4">p2</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">p3</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="c5">p3</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="c4">p2</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="c5">p3</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="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="c7">q2</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="c6">q1</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="c6">q1</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="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="c3">p1</font>,<font color="Maroon" title="c4">p2</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="c5">p3</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">q1</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="c6">q1</font>,<font color="Maroon" title="c8">q3</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="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="c6">q1</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="c3">p1</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="c5">p3</font>,<font color="Maroon" title="c6">q1</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="c4">p2</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="c5">p3</font>,<font color="Maroon" title="c7">q2</font>,<font color="Maroon" title="c9">r1</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="E1:87"/><span class="lab"><font color="Green" title="E77">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="c4">p2</font>
 <span class="kw">and </span><br/><a NAME="E2:87"/><span class="lab"><font color="Green" title="E78">A2</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">p3</font>
 <span class="kw">and </span><br/><a NAME="E3:87"/><span class="lab"><font color="Green" title="E79">A3</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="c5">p3</font>
 <span class="kw">and </span><br/><a NAME="E4:87"/><span class="lab"><font color="Green" title="E80">A4</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="c4">p2</font>
 <span class="kw">and </span><br/><a NAME="E5:87"/><span class="lab"><font color="Green" title="E81">A5</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="c5">p3</font>
 <span class="kw">and </span><br/><a NAME="E6:87"/><span class="lab"><font color="Green" title="E82">A6</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="E7:87"/><span class="lab"><font color="Green" title="E83">A7</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="E8:87"/><span class="lab"><font color="Green" title="E84">A8</font></span>: 
<font color="Maroon" title="c7">q2</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="E9:87"/><span class="lab"><font color="Green" title="E85">A9</font></span>: 
<font color="Maroon" title="c6">q1</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="E10:87"/><span class="lab"><font color="Green" title="E86">A10</font></span>: 
<font color="Maroon" title="c6">q1</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="E11:87"/><span class="lab"><font color="Green" title="E87">A11</font></span>: 
 not <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="E12:87"/><span class="lab"><font color="Green" title="E88">A12</font></span>: 
<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="E13:87"/><span class="lab"><font color="Green" title="E89">A13</font></span>: 
<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> 
 <span class="kw">and </span><br/><a NAME="E14:87"/><span class="lab"><font color="Green" title="E90">A14</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">q1</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="E15:87"/><span class="lab"><font color="Green" title="E91">A15</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">q1</font>,<font color="Maroon" title="c8">q3</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E16:87"/><span class="lab"><font color="Green" title="E92">A16</font></span>: 
<font color="Maroon" title="c3">p1</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="E17:87"/><span class="lab"><font color="Green" title="E93">A17</font></span>: 
<font color="Maroon" title="c6">q1</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="E18:87"/><span class="lab"><font color="Green" title="E94">A18</font></span>: 
<font color="Maroon" title="c3">p1</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="E19:87"/><span class="lab"><font color="Green" title="E95">A19</font></span>: 
<font color="Maroon" title="c5">p3</font>,<font color="Maroon" title="c6">q1</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="E20:87"/><span class="lab"><font color="Green" title="E96">A20</font></span>: 
<font color="Maroon" title="c4">p2</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="E21:87"/><span class="lab"><font color="Green" title="E97">A21</font></span>: 
<font color="Maroon" title="c5">p3</font>,<font color="Maroon" title="c7">q2</font>,<font color="Maroon" title="c9">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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">o999</font>, <font color="Maroon" title="c13">q19</font>, <font color="Maroon" title="c14">q29</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="E23:87"/><span class="lab"><font color="Green" title="E98">A22</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="c12">o999</font>
 <span class="kw">and </span><br/><a NAME="E24:87"/><span class="lab"><font color="Green" title="E99">A23</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="c13">q19</font>
 <span class="kw">and </span><br/><a NAME="E25:87"/><span class="lab"><font color="Green" title="E100">A24</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="c14">q29</font>
 <span class="kw">and </span><br/><a NAME="E26:87"/><span class="lab"><font color="Green" title="E101">A25</font></span>: 
 not <font color="Maroon" title="c12">o999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E27:87"/><span class="lab"><font color="Green" title="E102">A26</font></span>: 
 not <font color="Maroon" title="c13">q19</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E28:87"/><span class="lab"><font color="Green" title="E103">A27</font></span>: 
 not <font color="Maroon" title="c14">q29</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E29:87"/><span class="lab"><font color="Green" title="E104">A28</font></span>: 
<font color="Maroon" title="c12">o999</font>,<font color="Maroon" title="c13">q19</font>,<font color="Maroon" title="c14">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="#E14:87"><span class="lab"><font color="Green" title="E90">A14</font></span></a>, <a class="ref" href="anproj_2.html#T23" target="_self" title="ANPROJ_2:th.23">Th24</a></span>;<br/>
<a NAME="E30:87"/><span class="lab"><font color="Green" title="E105">A29</font></span>: 
 not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c13">q19</font>,<font color="Maroon" title="c14">q29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:87"><span class="lab"><font color="Green" title="E85">A9</font></span></a>, <a class="txt" href="#E24:87"><span class="lab"><font color="Green" title="E99">A23</font></span></a>, <a class="txt" href="#E25:87"><span class="lab"><font color="Green" title="E100">A24</font></span></a>, <a class="txt" href="#E27:87"><span class="lab"><font color="Green" title="E102">A26</font></span></a>, <a class="txt" href="#E28:87"><span class="lab"><font color="Green" title="E103">A27</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c15">o9999</font>, <font color="Maroon" title="c16">q199</font>, <font color="Maroon" title="c17">q39</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="E32:87"/><span class="lab"><font color="Green" title="E106">A30</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="c15">o9999</font>
 <span class="kw">and </span><br/><a NAME="E33:87"/><span class="lab"><font color="Green" title="E107">A31</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="c16">q199</font>
 <span class="kw">and </span><br/><a NAME="E34:87"/><span class="lab"><font color="Green" title="E108">A32</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="c17">q39</font>
 <span class="kw">and </span><br/><a NAME="E35:87"/><span class="lab"><font color="Green" title="E109">A33</font></span>: 
 not <font color="Maroon" title="c15">o9999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E36:87"/><span class="lab"><font color="Green" title="E110">A34</font></span>: 
 not <font color="Maroon" title="c16">q199</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E37:87"/><span class="lab"><font color="Green" title="E111">A35</font></span>: 
 not <font color="Maroon" title="c17">q39</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E38:87"/><span class="lab"><font color="Green" title="E112">A36</font></span>: 
<font color="Maroon" title="c15">o9999</font>,<font color="Maroon" title="c16">q199</font>,<font color="Maroon" title="c17">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="#E15:87"><span class="lab"><font color="Green" title="E91">A15</font></span></a>, <a class="ref" href="anproj_2.html#T23" target="_self" title="ANPROJ_2:th.23">Th24</a></span>;<br/>
<a NAME="E39:87"/><span class="lab"><font color="Green" title="E113">A37</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c16">q199</font>,<font color="Maroon" title="c13">q19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:87"><span class="lab"><font color="Green" title="E99">A23</font></span></a>, <a class="txt" href="#E27:87"><span class="lab"><font color="Green" title="E102">A26</font></span></a>, <a class="txt" href="#E33:87"><span class="lab"><font color="Green" title="E107">A31</font></span></a>, <a class="txt" href="#E36:87"><span class="lab"><font color="Green" title="E110">A34</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c18">o99</font>, <font color="Maroon" title="c19">p199</font>, <font color="Maroon" title="c20">p39</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="E41:87"/><span class="lab"><font color="Green" title="E114">A38</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="c18">o99</font> &amp; <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="c19">p199</font> )
 <span class="kw">and </span><br/><a NAME="E42:87"/><span class="lab"><font color="Green" title="E115">A39</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="c20">p39</font>
 <span class="kw">and </span><br/><a NAME="E43:87"/><span class="lab"><font color="Green" title="E116">A40</font></span>: 
(  not <font color="Maroon" title="c18">o99</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  &amp;  not <font color="Maroon" title="c19">p199</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  )
 <span class="kw">and </span><br/><a NAME="E44:87"/><span class="lab"><font color="Green" title="E117">A41</font></span>: 
 not <font color="Maroon" title="c20">p39</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E45:87"/><span class="lab"><font color="Green" title="E118">A42</font></span>: 
<font color="Maroon" title="c18">o99</font>,<font color="Maroon" title="c19">p199</font>,<font color="Maroon" title="c20">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="#E13:87"><span class="lab"><font color="Green" title="E89">A13</font></span></a>, <a class="ref" href="anproj_2.html#T23" target="_self" title="ANPROJ_2:th.23">Th24</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c21">o9</font>, <font color="Maroon" title="c22">p19</font>, <font color="Maroon" title="c23">p29</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="E47:87"/><span class="lab"><font color="Green" title="E119">A43</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="c21">o9</font>
 <span class="kw">and </span><br/><a NAME="E48:87"/><span class="lab"><font color="Green" title="E120">A44</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="c22">p19</font>
 <span class="kw">and </span><br/><a NAME="E49:87"/><span class="lab"><font color="Green" title="E121">A45</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="c23">p29</font>
 <span class="kw">and </span><br/><a NAME="E50:87"/><span class="lab"><font color="Green" title="E122">A46</font></span>: 
 not <font color="Maroon" title="c21">o9</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E51:87"/><span class="lab"><font color="Green" title="E123">A47</font></span>: 
 not <font color="Maroon" title="c22">p19</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E52:87"/><span class="lab"><font color="Green" title="E124">A48</font></span>: 
 not <font color="Maroon" title="c23">p29</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E53:87"/><span class="lab"><font color="Green" title="E125">A49</font></span>: 
<font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c22">p19</font>,<font color="Maroon" title="c23">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="#E12:87"><span class="lab"><font color="Green" title="E88">A12</font></span></a>, <a class="ref" href="anproj_2.html#T23" target="_self" title="ANPROJ_2:th.23">Th24</a></span>;<br/>
<a NAME="E54:87"/><span class="lab"><font color="Green" title="E126">A50</font></span>: 
(  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c20">p39</font> &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c22">p19</font>,<font color="Maroon" title="c20">p39</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:87"><span class="lab"><font color="Green" title="E78">A2</font></span></a>, <a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E81">A5</font></span></a>, <a class="txt" href="#E47:87"><span class="lab"><font color="Green" title="E119">A43</font></span></a>, <a class="txt" href="#E48:87"><span class="lab"><font color="Green" title="E120">A44</font></span></a>, <a class="txt" href="#E50:87"><span class="lab"><font color="Green" title="E122">A46</font></span></a>, <a class="txt" href="#E51:87"><span class="lab"><font color="Green" title="E123">A47</font></span></a>, <a class="txt" href="#E42:87"><span class="lab"><font color="Green" title="E115">A39</font></span></a>, <a class="txt" href="#E44:87"><span class="lab"><font color="Green" title="E117">A41</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E55:87"/><span class="lab"><font color="Green" title="E127">A51</font></span>: 
(  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c13">q19</font>,<font color="Maroon" title="c17">q39</font> &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c14">q29</font>,<font color="Maroon" title="c17">q39</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:87"><span class="lab"><font color="Green" title="E84">A8</font></span></a>, <a class="txt" href="#E10:87"><span class="lab"><font color="Green" title="E86">A10</font></span></a>, <a class="txt" href="#E24:87"><span class="lab"><font color="Green" title="E99">A23</font></span></a>, <a class="txt" href="#E25:87"><span class="lab"><font color="Green" title="E100">A24</font></span></a>, <a class="txt" href="#E27:87"><span class="lab"><font color="Green" title="E102">A26</font></span></a>, <a class="txt" href="#E28:87"><span class="lab"><font color="Green" title="E103">A27</font></span></a>, <a class="txt" href="#E34:87"><span class="lab"><font color="Green" title="E108">A32</font></span></a>, <a class="txt" href="#E37:87"><span class="lab"><font color="Green" title="E111">A35</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E56:87"/><span class="lab"><font color="Green" title="E128">A52</font></span>: 
 not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c23">p29</font>,<font color="Maroon" title="c20">p39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E79">A3</font></span></a>, <a class="txt" href="#E49:87"><span class="lab"><font color="Green" title="E121">A45</font></span></a>, <a class="txt" href="#E52:87"><span class="lab"><font color="Green" title="E124">A48</font></span></a>, <a class="txt" href="#E42:87"><span class="lab"><font color="Green" title="E115">A39</font></span></a>, <a class="txt" href="#E44:87"><span class="lab"><font color="Green" title="E117">A41</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E57:87"/><span class="lab"><font color="Green" title="E129">A53</font></span>: 
 not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c17">q39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:87"><span class="lab"><font color="Green" title="E83">A7</font></span></a>, <a class="txt" href="#E47:87"><span class="lab"><font color="Green" title="E119">A43</font></span></a>, <a class="txt" href="#E50:87"><span class="lab"><font color="Green" title="E122">A46</font></span></a>, <a class="txt" href="#E34:87"><span class="lab"><font color="Green" title="E108">A32</font></span></a>, <a class="txt" href="#E37:87"><span class="lab"><font color="Green" title="E111">A35</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E58:87"/><span class="lab"><font color="Green" title="E130">A54</font></span>: 
 not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c14">q29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E82">A6</font></span></a>, <a class="txt" href="#E47:87"><span class="lab"><font color="Green" title="E119">A43</font></span></a>, <a class="txt" href="#E50:87"><span class="lab"><font color="Green" title="E122">A46</font></span></a>, <a class="txt" href="#E25:87"><span class="lab"><font color="Green" title="E100">A24</font></span></a>, <a class="txt" href="#E28:87"><span class="lab"><font color="Green" title="E103">A27</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E59:87"/>
(  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c23">p29</font> &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c22">p19</font>,<font color="Maroon" title="c23">p29</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E77">A1</font></span></a>, <a class="txt" href="#E4:87"><span class="lab"><font color="Green" title="E80">A4</font></span></a>, <a class="txt" href="#E47:87"><span class="lab"><font color="Green" title="E119">A43</font></span></a>, <a class="txt" href="#E48:87"><span class="lab"><font color="Green" title="E120">A44</font></span></a>, <a class="txt" href="#E49:87"><span class="lab"><font color="Green" title="E121">A45</font></span></a>, <a class="txt" href="#E50:87"><span class="lab"><font color="Green" title="E122">A46</font></span></a>, <a class="txt" href="#E51:87"><span class="lab"><font color="Green" title="E123">A47</font></span></a>, <a class="txt" href="#E52:87"><span class="lab"><font color="Green" title="E124">A48</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E60:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E131">A55</font></span>: 
<font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c22">p19</font>,<font color="Maroon" title="c23">p29</font>,<font color="Maroon" title="c20">p39</font>,<font color="Maroon" title="c13">q19</font>,<font color="Maroon" title="c14">q29</font>,<font color="Maroon" title="c17">q39</font> <a href="anproj_2.html#R5" title="ANPROJ_2:pred.5">are_half_mutually_not_Prop</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E58:87"><span class="lab"><font color="Green" title="E130">A54</font></span></a>, <a class="txt" href="#E57:87"><span class="lab"><font color="Green" title="E129">A53</font></span></a>, <a class="txt" href="#E54:87"><span class="lab"><font color="Green" title="E126">A50</font></span></a>, <a class="txt" href="#E30:87"><span class="lab"><font color="Green" title="E105">A29</font></span></a>, <a class="txt" href="#E56:87"><span class="lab"><font color="Green" title="E128">A52</font></span></a>, <a class="txt" href="#E55:87"><span class="lab"><font color="Green" title="E127">A51</font></span></a>, <a class="ref" href="anproj_2.html#D5" target="_self" title="ANPROJ_2:def.5">Def5</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c24">q1999</font>, <font color="Maroon" title="c25">p2999</font>, <font color="Maroon" title="c26">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="E62:87"/><span class="lab"><font color="Green" title="E132">A56</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="c24">q1999</font>
 <span class="kw">and </span><br/><a NAME="E63:87"/><span class="lab"><font color="Green" title="E133">A57</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="c25">p2999</font>
 <span class="kw">and </span><br/><a NAME="E64:87"/><span class="lab"><font color="Green" title="E134">A58</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="c26">r399</font>
 <span class="kw">and </span><br/><a NAME="E65:87"/><span class="lab"><font color="Green" title="E135">A59</font></span>: 
 not <font color="Maroon" title="c24">q1999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E66:87"/><span class="lab"><font color="Green" title="E136">A60</font></span>: 
 not <font color="Maroon" title="c25">p2999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E67:87"/><span class="lab"><font color="Green" title="E137">A61</font></span>: 
 not <font color="Maroon" title="c26">r399</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E68:87"/><span class="lab"><font color="Green" title="E138">A62</font></span>: 
<font color="Maroon" title="c24">q1999</font>,<font color="Maroon" title="c25">p2999</font>,<font color="Maroon" title="c26">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="#E17:87"><span class="lab"><font color="Green" title="E93">A17</font></span></a>, <a class="ref" href="anproj_2.html#T23" target="_self" title="ANPROJ_2:th.23">Th24</a></span>;<br/>
<a NAME="E69:87"/><span class="lab"><font color="Green" title="E139">A63</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c24">q1999</font>,<font color="Maroon" title="c13">q19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:87"><span class="lab"><font color="Green" title="E99">A23</font></span></a>, <a class="txt" href="#E27:87"><span class="lab"><font color="Green" title="E102">A26</font></span></a>, <a class="txt" href="#E62:87"><span class="lab"><font color="Green" title="E132">A56</font></span></a>, <a class="txt" href="#E65:87"><span class="lab"><font color="Green" title="E135">A59</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c27">p29999</font>, <font color="Maroon" title="c28">q3999</font>, <font color="Maroon" title="c29">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="E71:87"/><span class="lab"><font color="Green" title="E140">A64</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="c27">p29999</font>
 <span class="kw">and </span><br/><a NAME="E72:87"/><span class="lab"><font color="Green" title="E141">A65</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="c28">q3999</font>
 <span class="kw">and </span><br/><a NAME="E73:87"/><span class="lab"><font color="Green" title="E142">A66</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="c29">r19</font>
 <span class="kw">and </span><br/><a NAME="E74:87"/><span class="lab"><font color="Green" title="E143">A67</font></span>: 
 not <font color="Maroon" title="c27">p29999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E75:87"/><span class="lab"><font color="Green" title="E144">A68</font></span>: 
 not <font color="Maroon" title="c28">q3999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E76:87"/><span class="lab"><font color="Green" title="E145">A69</font></span>: 
 not <font color="Maroon" title="c29">r19</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E77:87"/><span class="lab"><font color="Green" title="E146">A70</font></span>: 
<font color="Maroon" title="c27">p29999</font>,<font color="Maroon" title="c28">q3999</font>,<font color="Maroon" title="c29">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="#E20:87"><span class="lab"><font color="Green" title="E96">A20</font></span></a>, <a class="ref" href="anproj_2.html#T23" target="_self" title="ANPROJ_2:th.23">Th24</a></span>;<br/>
<a NAME="E78:87"/><span class="lab"><font color="Green" title="E147">A71</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c28">q3999</font>,<font color="Maroon" title="c17">q39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:87"><span class="lab"><font color="Green" title="E108">A32</font></span></a>, <a class="txt" href="#E37:87"><span class="lab"><font color="Green" title="E111">A35</font></span></a>, <a class="txt" href="#E72:87"><span class="lab"><font color="Green" title="E141">A65</font></span></a>, <a class="txt" href="#E75:87"><span class="lab"><font color="Green" title="E144">A68</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E79:87"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c12">o999</font>,<font color="Maroon" title="c21">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:87"><span class="lab"><font color="Green" title="E119">A43</font></span></a>, <a class="txt" href="#E50:87"><span class="lab"><font color="Green" title="E122">A46</font></span></a>, <a class="txt" href="#E23:87"><span class="lab"><font color="Green" title="E98">A22</font></span></a>, <a class="txt" href="#E26:87"><span class="lab"><font color="Green" title="E101">A25</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E80:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E148">A72</font></span>: 
<font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c13">q19</font>,<font color="Maroon" title="c14">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="#E29:87"><span class="lab"><font color="Green" title="E104">A28</font></span></a>, <a class="ref" href="anproj_1.html#T4" title="ANPROJ_1:th.4">ANPROJ_1:4</a></span>;<br/>
<a NAME="E81:87"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c15">o9999</font>,<font color="Maroon" title="c21">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:87"><span class="lab"><font color="Green" title="E119">A43</font></span></a>, <a class="txt" href="#E50:87"><span class="lab"><font color="Green" title="E122">A46</font></span></a>, <a class="txt" href="#E32:87"><span class="lab"><font color="Green" title="E106">A30</font></span></a>, <a class="txt" href="#E35:87"><span class="lab"><font color="Green" title="E109">A33</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E82:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E149">A73</font></span>: 
<font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c13">q19</font>,<font color="Maroon" title="c17">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="#E38:87"><span class="lab"><font color="Green" title="E112">A36</font></span></a>, <a class="txt" href="#E39:87"><span class="lab"><font color="Green" title="E113">A37</font></span></a>, <a class="ref" href="anproj_1.html#T4" title="ANPROJ_1:th.4">ANPROJ_1:4</a></span>;<br/>
<a NAME="E83:87"/>
(  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c18">o99</font>,<font color="Maroon" title="c21">o9</font> &amp;  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c19">p199</font>,<font color="Maroon" title="c22">p19</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:87"><span class="lab"><font color="Green" title="E119">A43</font></span></a>, <a class="txt" href="#E48:87"><span class="lab"><font color="Green" title="E120">A44</font></span></a>, <a class="txt" href="#E50:87"><span class="lab"><font color="Green" title="E122">A46</font></span></a>, <a class="txt" href="#E51:87"><span class="lab"><font color="Green" title="E123">A47</font></span></a>, <a class="txt" href="#E41:87"><span class="lab"><font color="Green" title="E114">A38</font></span></a>, <a class="txt" href="#E43:87"><span class="lab"><font color="Green" title="E116">A40</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E84:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E150">A74</font></span>: 
<font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c22">p19</font>,<font color="Maroon" title="c20">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="#E45:87"><span class="lab"><font color="Green" title="E118">A42</font></span></a>, <a class="ref" href="anproj_1.html#T4" title="ANPROJ_1:th.4">ANPROJ_1:4</a></span>;<br/>
<a NAME="E85:87"/>
 not <font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c22">p19</font>,<font color="Maroon" title="c13">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="#E11:87"><span class="lab"><font color="Green" title="E87">A11</font></span></a>, <a class="txt" href="#E47:87"><span class="lab"><font color="Green" title="E119">A43</font></span></a>, <a class="txt" href="#E48:87"><span class="lab"><font color="Green" title="E120">A44</font></span></a>, <a class="txt" href="#E50:87"><span class="lab"><font color="Green" title="E122">A46</font></span></a>, <a class="txt" href="#E51:87"><span class="lab"><font color="Green" title="E123">A47</font></span></a>, <a class="txt" href="#E24:87"><span class="lab"><font color="Green" title="E99">A23</font></span></a>, <a class="txt" href="#E27:87"><span class="lab"><font color="Green" title="E102">A26</font></span></a>, <a class="ref" href="anproj_2.html#T23" target="_self" title="ANPROJ_2:th.23">Th24</a></span>;<br/>
<a NAME="E86:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E151">A75</font></span>: 
<font color="Maroon" title="c21">o9</font>,<font color="Maroon" title="c22">p19</font>,<font color="Maroon" title="c23">p29</font>,<font color="Maroon" title="c20">p39</font>,<font color="Maroon" title="c13">q19</font>,<font color="Maroon" title="c14">q29</font>,<font color="Maroon" title="c17">q39</font> <a href="anproj_2.html#R4" title="ANPROJ_2:pred.4">lie_on_an_angle</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:87"><span class="lab"><font color="Green" title="E125">A49</font></span></a>, <a class="txt" href="#E84:87"><span class="lab"><font color="Green" title="E150">A74</font></span></a>, <a class="txt" href="#E80:87"><span class="lab"><font color="Green" title="E148">A72</font></span></a>, <a class="txt" href="#E82:87"><span class="lab"><font color="Green" title="E149">A73</font></span></a>, <a class="ref" href="anproj_2.html#D4" target="_self" title="ANPROJ_2:def.4">Def4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c30">p19999</font>, <font color="Maroon" title="c31">q399</font>, <font color="Maroon" title="c32">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="E88:87"/><span class="lab"><font color="Green" title="E152">A76</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="c30">p19999</font>
 <span class="kw">and </span><br/><a NAME="E89:87"/><span class="lab"><font color="Green" title="E153">A77</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="c31">q399</font>
 <span class="kw">and </span><br/><a NAME="E90:87"/><span class="lab"><font color="Green" title="E154">A78</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="c32">r29</font>
 <span class="kw">and </span><br/><a NAME="E91:87"/><span class="lab"><font color="Green" title="E155">A79</font></span>: 
 not <font color="Maroon" title="c30">p19999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E92:87"/><span class="lab"><font color="Green" title="E156">A80</font></span>: 
 not <font color="Maroon" title="c31">q399</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E93:87"/><span class="lab"><font color="Green" title="E157">A81</font></span>: 
 not <font color="Maroon" title="c32">r29</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E94:87"/><span class="lab"><font color="Green" title="E158">A82</font></span>: 
<font color="Maroon" title="c30">p19999</font>,<font color="Maroon" title="c31">q399</font>,<font color="Maroon" title="c32">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="#E18:87"><span class="lab"><font color="Green" title="E94">A18</font></span></a>, <a class="ref" href="anproj_2.html#T23" target="_self" title="ANPROJ_2:th.23">Th24</a></span>;<br/>
<a NAME="E95:87"/><span class="lab"><font color="Green" title="E159">A83</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c31">q399</font>,<font color="Maroon" title="c17">q39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:87"><span class="lab"><font color="Green" title="E108">A32</font></span></a>, <a class="txt" href="#E37:87"><span class="lab"><font color="Green" title="E111">A35</font></span></a>, <a class="txt" href="#E89:87"><span class="lab"><font color="Green" title="E153">A77</font></span></a>, <a class="txt" href="#E92:87"><span class="lab"><font color="Green" title="E156">A80</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c33">p3999</font>, <font color="Maroon" title="c34">q29999</font>, <font color="Maroon" title="c35">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="E97:87"/><span class="lab"><font color="Green" title="E160">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="c33">p3999</font>
 <span class="kw">and </span><br/><a NAME="E98:87"/><span class="lab"><font color="Green" title="E161">A85</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="c34">q29999</font>
 <span class="kw">and </span><br/><a NAME="E99:87"/><span class="lab"><font color="Green" title="E162">A86</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="c35">r199</font>
 <span class="kw">and </span><br/><a NAME="E100:87"/><span class="lab"><font color="Green" title="E163">A87</font></span>: 
 not <font color="Maroon" title="c33">p3999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E101:87"/><span class="lab"><font color="Green" title="E164">A88</font></span>: 
 not <font color="Maroon" title="c34">q29999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E102:87"/><span class="lab"><font color="Green" title="E165">A89</font></span>: 
 not <font color="Maroon" title="c35">r199</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E103:87"/><span class="lab"><font color="Green" title="E166">A90</font></span>: 
<font color="Maroon" title="c33">p3999</font>,<font color="Maroon" title="c34">q29999</font>,<font color="Maroon" title="c35">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="#E21:87"><span class="lab"><font color="Green" title="E97">A21</font></span></a>, <a class="ref" href="anproj_2.html#T23" target="_self" title="ANPROJ_2:th.23">Th24</a></span>;<br/>
<a NAME="E104:87"/><span class="lab"><font color="Green" title="E167">A91</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c33">p3999</font>,<font color="Maroon" title="c20">p39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:87"><span class="lab"><font color="Green" title="E115">A39</font></span></a>, <a class="txt" href="#E44:87"><span class="lab"><font color="Green" title="E117">A41</font></span></a>, <a class="txt" href="#E97:87"><span class="lab"><font color="Green" title="E160">A84</font></span></a>, <a class="txt" href="#E100:87"><span class="lab"><font color="Green" title="E163">A87</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E105:87"/><span class="lab"><font color="Green" title="E168">A92</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c34">q29999</font>,<font color="Maroon" title="c14">q29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:87"><span class="lab"><font color="Green" title="E100">A24</font></span></a>, <a class="txt" href="#E28:87"><span class="lab"><font color="Green" title="E103">A27</font></span></a>, <a class="txt" href="#E98:87"><span class="lab"><font color="Green" title="E161">A85</font></span></a>, <a class="txt" href="#E101:87"><span class="lab"><font color="Green" title="E164">A88</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E106:87"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c35">r199</font>,<font color="Maroon" title="c29">r19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E73:87"><span class="lab"><font color="Green" title="E142">A66</font></span></a>, <a class="txt" href="#E76:87"><span class="lab"><font color="Green" title="E145">A69</font></span></a>, <a class="txt" href="#E99:87"><span class="lab"><font color="Green" title="E162">A86</font></span></a>, <a class="txt" href="#E102:87"><span class="lab"><font color="Green" title="E165">A89</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E107:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E169">A93</font></span>: 
<font color="Maroon" title="c20">p39</font>,<font color="Maroon" title="c14">q29</font>,<font color="Maroon" title="c29">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="#E103:87"><span class="lab"><font color="Green" title="E166">A90</font></span></a>, <a class="txt" href="#E104:87"><span class="lab"><font color="Green" title="E167">A91</font></span></a>, <a class="txt" href="#E105:87"><span class="lab"><font color="Green" title="E168">A92</font></span></a>, <a class="ref" href="anproj_1.html#T4" title="ANPROJ_1:th.4">ANPROJ_1:4</a></span>;<br/>
<a NAME="E108:87"/><span class="lab"><font color="Green" title="E170">A94</font></span>: 
<font color="Maroon" title="c13">q19</font>,<font color="Maroon" title="c14">q29</font>,<font color="Maroon" title="c17">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="#E27:87"><span class="lab"><font color="Green" title="E102">A26</font></span></a>, <a class="txt" href="#E28:87"><span class="lab"><font color="Green" title="E103">A27</font></span></a>, <a class="txt" href="#E37:87"><span class="lab"><font color="Green" title="E111">A35</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E109:87"/><span class="lab"><font color="Green" title="E171">A95</font></span>: 
<font color="Maroon" title="c22">p19</font>,<font color="Maroon" title="c23">p29</font>,<font color="Maroon" title="c20">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="#E51:87"><span class="lab"><font color="Green" title="E123">A47</font></span></a>, <a class="txt" href="#E52:87"><span class="lab"><font color="Green" title="E124">A48</font></span></a>, <a class="txt" href="#E44:87"><span class="lab"><font color="Green" title="E117">A41</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E110:87"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c27">p29999</font>,<font color="Maroon" title="c23">p29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:87"><span class="lab"><font color="Green" title="E121">A45</font></span></a>, <a class="txt" href="#E52:87"><span class="lab"><font color="Green" title="E124">A48</font></span></a>, <a class="txt" href="#E71:87"><span class="lab"><font color="Green" title="E140">A64</font></span></a>, <a class="txt" href="#E74:87"><span class="lab"><font color="Green" title="E143">A67</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E111:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E172">A96</font></span>: 
<font color="Maroon" title="c23">p29</font>,<font color="Maroon" title="c17">q39</font>,<font color="Maroon" title="c29">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="#E77:87"><span class="lab"><font color="Green" title="E146">A70</font></span></a>, <a class="txt" href="#E78:87"><span class="lab"><font color="Green" title="E147">A71</font></span></a>, <a class="ref" href="anproj_1.html#T4" title="ANPROJ_1:th.4">ANPROJ_1:4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c36">p399</font>, <font color="Maroon" title="c37">q1999</font>, <font color="Maroon" title="c38">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="E113:87"/><span class="lab"><font color="Green" title="E173">A97</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="c36">p399</font>
 <span class="kw">and </span><br/><a NAME="E114:87"/><span class="lab"><font color="Green" title="E174">A98</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="c37">q1999</font>
 <span class="kw">and </span><br/><a NAME="E115:87"/><span class="lab"><font color="Green" title="E175">A99</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="c38">r299</font>
 <span class="kw">and </span><br/><a NAME="E116:87"/><span class="lab"><font color="Green" title="E176">A100</font></span>: 
 not <font color="Maroon" title="c36">p399</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E117:87"/><span class="lab"><font color="Green" title="E177">A101</font></span>: 
 not <font color="Maroon" title="c37">q1999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E118:87"/><span class="lab"><font color="Green" title="E178">A102</font></span>: 
 not <font color="Maroon" title="c38">r299</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E119:87"/><span class="lab"><font color="Green" title="E179">A103</font></span>: 
<font color="Maroon" title="c36">p399</font>,<font color="Maroon" title="c37">q1999</font>,<font color="Maroon" title="c38">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="#E19:87"><span class="lab"><font color="Green" title="E95">A19</font></span></a>, <a class="ref" href="anproj_2.html#T23" target="_self" title="ANPROJ_2:th.23">Th24</a></span>;<br/>
<a NAME="E120:87"/><span class="lab"><font color="Green" title="E180">A104</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c37">q1999</font>,<font color="Maroon" title="c13">q19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:87"><span class="lab"><font color="Green" title="E99">A23</font></span></a>, <a class="txt" href="#E27:87"><span class="lab"><font color="Green" title="E102">A26</font></span></a>, <a class="txt" href="#E114:87"><span class="lab"><font color="Green" title="E174">A98</font></span></a>, <a class="txt" href="#E117:87"><span class="lab"><font color="Green" title="E177">A101</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E121:87"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c30">p19999</font>,<font color="Maroon" title="c22">p19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:87"><span class="lab"><font color="Green" title="E120">A44</font></span></a>, <a class="txt" href="#E51:87"><span class="lab"><font color="Green" title="E123">A47</font></span></a>, <a class="txt" href="#E88:87"><span class="lab"><font color="Green" title="E152">A76</font></span></a>, <a class="txt" href="#E91:87"><span class="lab"><font color="Green" title="E155">A79</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E122:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E181">A105</font></span>: 
<font color="Maroon" title="c22">p19</font>,<font color="Maroon" title="c17">q39</font>,<font color="Maroon" title="c32">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="#E94:87"><span class="lab"><font color="Green" title="E158">A82</font></span></a>, <a class="txt" href="#E95:87"><span class="lab"><font color="Green" title="E159">A83</font></span></a>, <a class="ref" href="anproj_1.html#T4" title="ANPROJ_1:th.4">ANPROJ_1:4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c39">p1999</font>, <font color="Maroon" title="c40">q2999</font>, <font color="Maroon" title="c41">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="E124:87"/><span class="lab"><font color="Green" title="E182">A106</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="c39">p1999</font>
 <span class="kw">and </span><br/><a NAME="E125:87"/><span class="lab"><font color="Green" title="E183">A107</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="c40">q2999</font>
 <span class="kw">and </span><br/><a NAME="E126:87"/><span class="lab"><font color="Green" title="E184">A108</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="c41">r39</font>
 <span class="kw">and </span><br/><a NAME="E127:87"/><span class="lab"><font color="Green" title="E185">A109</font></span>: 
 not <font color="Maroon" title="c39">p1999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E128:87"/><span class="lab"><font color="Green" title="E186">A110</font></span>: 
 not <font color="Maroon" title="c40">q2999</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E129:87"/><span class="lab"><font color="Green" title="E187">A111</font></span>: 
 not <font color="Maroon" title="c41">r39</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E130:87"/><span class="lab"><font color="Green" title="E188">A112</font></span>: 
<font color="Maroon" title="c39">p1999</font>,<font color="Maroon" title="c40">q2999</font>,<font color="Maroon" title="c41">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="#E16:87"><span class="lab"><font color="Green" title="E92">A16</font></span></a>, <a class="ref" href="anproj_2.html#T23" target="_self" title="ANPROJ_2:th.23">Th24</a></span>;<br/>
<a NAME="E131:87"/><span class="lab"><font color="Green" title="E189">A113</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c40">q2999</font>,<font color="Maroon" title="c14">q29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:87"><span class="lab"><font color="Green" title="E100">A24</font></span></a>, <a class="txt" href="#E28:87"><span class="lab"><font color="Green" title="E103">A27</font></span></a>, <a class="txt" href="#E125:87"><span class="lab"><font color="Green" title="E183">A107</font></span></a>, <a class="txt" href="#E128:87"><span class="lab"><font color="Green" title="E186">A110</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E132:87"/><span class="lab"><font color="Green" title="E190">A114</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c25">p2999</font>,<font color="Maroon" title="c23">p29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:87"><span class="lab"><font color="Green" title="E121">A45</font></span></a>, <a class="txt" href="#E52:87"><span class="lab"><font color="Green" title="E124">A48</font></span></a>, <a class="txt" href="#E63:87"><span class="lab"><font color="Green" title="E133">A57</font></span></a>, <a class="txt" href="#E66:87"><span class="lab"><font color="Green" title="E136">A60</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E133:87"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c26">r399</font>,<font color="Maroon" title="c41">r39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E126:87"><span class="lab"><font color="Green" title="E184">A108</font></span></a>, <a class="txt" href="#E129:87"><span class="lab"><font color="Green" title="E187">A111</font></span></a>, <a class="txt" href="#E64:87"><span class="lab"><font color="Green" title="E134">A58</font></span></a>, <a class="txt" href="#E67:87"><span class="lab"><font color="Green" title="E137">A61</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E134:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E191">A115</font></span>: 
<font color="Maroon" title="c13">q19</font>,<font color="Maroon" title="c23">p29</font>,<font color="Maroon" title="c41">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="#E68:87"><span class="lab"><font color="Green" title="E138">A62</font></span></a>, <a class="txt" href="#E69:87"><span class="lab"><font color="Green" title="E139">A63</font></span></a>, <a class="txt" href="#E132:87"><span class="lab"><font color="Green" title="E190">A114</font></span></a>, <a class="ref" href="anproj_1.html#T4" title="ANPROJ_1:th.4">ANPROJ_1:4</a></span>;<br/>
<a NAME="E135:87"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c39">p1999</font>,<font color="Maroon" title="c22">p19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:87"><span class="lab"><font color="Green" title="E120">A44</font></span></a>, <a class="txt" href="#E51:87"><span class="lab"><font color="Green" title="E123">A47</font></span></a>, <a class="txt" href="#E124:87"><span class="lab"><font color="Green" title="E182">A106</font></span></a>, <a class="txt" href="#E127:87"><span class="lab"><font color="Green" title="E185">A109</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E136:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E192">A116</font></span>: 
<font color="Maroon" title="c22">p19</font>,<font color="Maroon" title="c14">q29</font>,<font color="Maroon" title="c41">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="#E130:87"><span class="lab"><font color="Green" title="E188">A112</font></span></a>, <a class="txt" href="#E131:87"><span class="lab"><font color="Green" title="E189">A113</font></span></a>, <a class="ref" href="anproj_1.html#T4" title="ANPROJ_1:th.4">ANPROJ_1:4</a></span>;<br/>
<a NAME="E137:87"/><span class="lab"><font color="Green" title="E193">A117</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c36">p399</font>,<font color="Maroon" title="c20">p39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:87"><span class="lab"><font color="Green" title="E115">A39</font></span></a>, <a class="txt" href="#E44:87"><span class="lab"><font color="Green" title="E117">A41</font></span></a>, <a class="txt" href="#E113:87"><span class="lab"><font color="Green" title="E173">A97</font></span></a>, <a class="txt" href="#E116:87"><span class="lab"><font color="Green" title="E176">A100</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E138:87"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c38">r299</font>,<font color="Maroon" title="c32">r29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E90:87"><span class="lab"><font color="Green" title="E154">A78</font></span></a>, <a class="txt" href="#E93:87"><span class="lab"><font color="Green" title="E157">A81</font></span></a>, <a class="txt" href="#E115:87"><span class="lab"><font color="Green" title="E175">A99</font></span></a>, <a class="txt" href="#E118:87"><span class="lab"><font color="Green" title="E178">A102</font></span></a>, <a class="ref" href="anproj_1.html#T22" title="ANPROJ_1:th.22">ANPROJ_1:22</a></span>;<br/>
<a NAME="E139:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E194">A118</font></span>: 
<font color="Maroon" title="c20">p39</font>,<font color="Maroon" title="c13">q19</font>,<font color="Maroon" title="c32">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="#E119:87"><span class="lab"><font color="Green" title="E179">A103</font></span></a>, <a class="txt" href="#E137:87"><span class="lab"><font color="Green" title="E193">A117</font></span></a>, <a class="txt" href="#E120:87"><span class="lab"><font color="Green" title="E180">A104</font></span></a>, <a class="ref" href="anproj_1.html#T4" title="ANPROJ_1:th.4">ANPROJ_1:4</a></span>;<br/>
<a NAME="E140:87"/>
<font color="Maroon" title="c29">r19</font>,<font color="Maroon" title="c32">r29</font>,<font color="Maroon" title="c41">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="#E129:87"><span class="lab"><font color="Green" title="E187">A111</font></span></a>, <a class="txt" href="#E93:87"><span class="lab"><font color="Green" title="E157">A81</font></span></a>, <a class="txt" href="#E76:87"><span class="lab"><font color="Green" title="E145">A69</font></span></a>, <a class="ref" href="anproj_2.html#D1" target="_self" title="ANPROJ_2:def.1">Def1</a></span>;<br/>
<a NAME="E141:87"/><span class="kw">then </span>
<font color="Maroon" title="c29">r19</font>,<font color="Maroon" title="c32">r29</font>,<font color="Maroon" title="c41">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="#E50:87"><span class="lab"><font color="Green" title="E122">A46</font></span></a>, <a class="txt" href="#E86:87"><span class="lab"><font color="Green" title="E151">A75</font></span></a>, <a class="txt" href="#E60:87"><span class="lab"><font color="Green" title="E131">A55</font></span></a>, <a class="txt" href="#E109:87"><span class="lab"><font color="Green" title="E171">A95</font></span></a>, <a class="txt" href="#E108:87"><span class="lab"><font color="Green" title="E170">A94</font></span></a>, <a class="txt" href="#E136:87"><span class="lab"><font color="Green" title="E192">A116</font></span></a>, <a class="txt" href="#E134:87"><span class="lab"><font color="Green" title="E191">A115</font></span></a>, <a class="txt" href="#E122:87"><span class="lab"><font color="Green" title="E181">A105</font></span></a>, <a class="txt" href="#E139:87"><span class="lab"><font color="Green" title="E194">A118</font></span></a>, <a class="txt" href="#E111:87"><span class="lab"><font color="Green" title="E172">A96</font></span></a>, <a class="txt" href="#E107:87"><span class="lab"><font color="Green" title="E169">A93</font></span></a>, <a class="ref" href="anproj_2.html#T9" target="_self" title="ANPROJ_2:th.9">Th9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E142:87"/>
<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="#E126:87"><span class="lab"><font color="Green" title="E184">A108</font></span></a>, <a class="txt" href="#E129:87"><span class="lab"><font color="Green" title="E187">A111</font></span></a>, <a class="txt" href="#E90:87"><span class="lab"><font color="Green" title="E154">A78</font></span></a>, <a class="txt" href="#E93:87"><span class="lab"><font color="Green" title="E157">A81</font></span></a>, <a class="txt" href="#E73:87"><span class="lab"><font color="Green" title="E142">A66</font></span></a>, <a class="txt" href="#E76:87"><span class="lab"><font color="Green" title="E145">A69</font></span></a>, <a class="ref" href="anproj_2.html#T23" target="_self" title="ANPROJ_2:th.23">Th24</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
