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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be  non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</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"> for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">r2</font>, <font color="Olive" title="b3">q</font>, <font color="Olive" title="b4">r1</font>, <font color="Olive" title="b5">q1</font>, <font color="Olive" title="b6">p</font>, <font color="Olive" title="b7">r</font> being  <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>  st <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">r2</font>,<font color="Olive" title="b3">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b4">r1</font>,<font color="Olive" title="b5">q1</font>,<font color="Olive" title="b3">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b4">r1</font>,<font color="Olive" title="b6">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">r2</font>,<font color="Olive" title="b5">q1</font>,<font color="Olive" title="b6">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b5">q1</font>,<font color="Olive" title="b7">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">r2</font>,<font color="Olive" title="b4">r1</font>,<font color="Olive" title="b7">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b6">p</font>,<font color="Olive" title="b3">q</font>,<font color="Olive" title="b7">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">r2</font>,<font color="Olive" title="b5">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">r2</font>,<font color="Olive" title="b4">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b4">r1</font>,<font color="Olive" title="b5">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  holds <br/><font color="Olive" title="b2">r2</font>,<font color="Olive" title="b4">r1</font>,<font color="Olive" title="b5">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">p1</font>, <font color="Maroon" title="c3">r2</font>, <font color="Maroon" title="c4">q</font>, <font color="Maroon" title="c5">r1</font>, <font color="Maroon" title="c6">q1</font>, <font color="Maroon" title="c7">p</font>, <font color="Maroon" title="c8">r</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>; <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">p1</font>,<font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c4">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c6">q1</font>,<font color="Maroon" title="c4">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c7">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c6">q1</font>,<font color="Maroon" title="c7">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c6">q1</font>,<font color="Maroon" title="c8">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c8">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c8">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c6">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c5">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; not <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c6">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  implies <font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c6">q1</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="E1:86"/><span class="lab"><font color="Green" title="E74">A1</font></span>: 
<font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c4">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E2:86"/><span class="lab"><font color="Green" title="E75">A2</font></span>: 
<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c6">q1</font>,<font color="Maroon" title="c4">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E3:86"/><span class="lab"><font color="Green" title="E76">A3</font></span>: 
<font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c7">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E4:86"/><span class="lab"><font color="Green" title="E77">A4</font></span>: 
<font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c6">q1</font>,<font color="Maroon" title="c7">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E5:86"/><span class="lab"><font color="Green" title="E78">A5</font></span>: 
<font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c6">q1</font>,<font color="Maroon" title="c8">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E6:86"/><span class="lab"><font color="Green" title="E79">A6</font></span>: 
<font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c8">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E7:86"/><span class="lab"><font color="Green" title="E80">A7</font></span>: 
<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c8">r</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="c2">p1</font>,<font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c6">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c5">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c6">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c6">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c9">u1</font>, <font color="Maroon" title="c10">w1</font>, <font color="Maroon" title="c11">x</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="E9:86"/><span class="lab"><font color="Green" title="E81">A8</font></span>: 
<font color="Maroon" title="c2">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="c9">u1</font>
 <span class="kw">and </span><br/><a NAME="E10:86"/><span class="lab"><font color="Green" title="E82">A9</font></span>: 
<font color="Maroon" title="c5">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="c10">w1</font>
 <span class="kw">and </span><br/><a NAME="E11:86"/><span class="lab"><font color="Green" title="E83">A10</font></span>: 
<font color="Maroon" title="c7">p</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="c11">x</font>
 <span class="kw">and </span><br/><a NAME="E12:86"/><span class="lab"><font color="Green" title="E84">A11</font></span>: 
not <font color="Maroon" title="c9">u1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E13:86"/><span class="lab"><font color="Green" title="E85">A12</font></span>: 
not <font color="Maroon" title="c10">w1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E14:86"/><span class="lab"><font color="Green" title="E86">A13</font></span>: 
not <font color="Maroon" title="c11">x</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E15:86"/><span class="lab"><font color="Green" title="E87">A14</font></span>: 
<font color="Maroon" title="c9">u1</font>,<font color="Maroon" title="c10">w1</font>,<font color="Maroon" title="c11">x</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="#E3:86"><span class="lab"><font color="Green" title="E76">A3</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="c12">u</font>, <font color="Maroon" title="c13">v</font>, <font color="Maroon" title="c14">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E17:86"/><span class="lab"><font color="Green" title="E88">A15</font></span>: 
<font color="Maroon" title="c2">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="c12">u</font>
 <span class="kw">and </span><br/><a NAME="E18:86"/><span class="lab"><font color="Green" title="E89">A16</font></span>: 
<font color="Maroon" title="c3">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="c13">v</font>
 <span class="kw">and </span><br/><a NAME="E19:86"/><span class="lab"><font color="Green" title="E90">A17</font></span>: 
<font color="Maroon" title="c4">q</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">z</font>
 <span class="kw">and </span><br/><a NAME="E20:86"/><span class="lab"><font color="Green" title="E91">A18</font></span>: 
not <font color="Maroon" title="c12">u</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E21:86"/><span class="lab"><font color="Green" title="E92">A19</font></span>: 
not <font color="Maroon" title="c13">v</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E22:86"/><span class="lab"><font color="Green" title="E93">A20</font></span>: 
not <font color="Maroon" title="c14">z</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E23:86"/><span class="lab"><font color="Green" title="E94">A21</font></span>: 
<font color="Maroon" title="c12">u</font>,<font color="Maroon" title="c13">v</font>,<font color="Maroon" title="c14">z</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="#E1:86"><span class="lab"><font color="Green" title="E74">A1</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">w</font>, <font color="Maroon" title="c16">y</font>, <font color="Maroon" title="c17">z1</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="E25:86"/><span class="lab"><font color="Green" title="E95">A22</font></span>: 
<font color="Maroon" title="c5">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="c15">w</font>
 <span class="kw">and </span><br/><a NAME="E26:86"/><span class="lab"><font color="Green" title="E96">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="c16">y</font>
 <span class="kw">and </span><br/><a NAME="E27:86"/><span class="lab"><font color="Green" title="E97">A24</font></span>: 
<font color="Maroon" title="c4">q</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">z1</font>
 <span class="kw">and </span><br/><a NAME="E28:86"/><span class="lab"><font color="Green" title="E98">A25</font></span>: 
not <font color="Maroon" title="c15">w</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E29:86"/><span class="lab"><font color="Green" title="E99">A26</font></span>: 
not <font color="Maroon" title="c16">y</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E30:86"/><span class="lab"><font color="Green" title="E100">A27</font></span>: 
not <font color="Maroon" title="c17">z1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E31:86"/><span class="lab"><font color="Green" title="E101">A28</font></span>: 
<font color="Maroon" title="c15">w</font>,<font color="Maroon" title="c16">y</font>,<font color="Maroon" title="c17">z1</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="#E2:86"><span class="lab"><font color="Green" title="E75">A2</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E32:86"/><span class="lab"><font color="Green" title="E102">A29</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c10">w1</font>,<font color="Maroon" title="c15">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:86"><span class="lab"><font color="Green" title="E95">A22</font></span></a>, <a class="txt" href="#E28:86"><span class="lab"><font color="Green" title="E98">A25</font></span></a>, <a class="txt" href="#E10:86"><span class="lab"><font color="Green" title="E82">A9</font></span></a>, <a class="txt" href="#E13:86"><span class="lab"><font color="Green" title="E85">A12</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E33:86"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c17">z1</font>,<font color="Maroon" title="c14">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:86"><span class="lab"><font color="Green" title="E90">A17</font></span></a>, <a class="txt" href="#E22:86"><span class="lab"><font color="Green" title="E93">A20</font></span></a>, <a class="txt" href="#E27:86"><span class="lab"><font color="Green" title="E97">A24</font></span></a>, <a class="txt" href="#E30:86"><span class="lab"><font color="Green" title="E100">A27</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E34:86"/><span class="kw">then </span><span class="lab"><font color="Green" title="E103">A30</font></span>: 
<font color="Maroon" title="c15">w</font>,<font color="Maroon" title="c16">y</font>,<font color="Maroon" title="c14">z</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="#E31:86"><span class="lab"><font color="Green" title="E101">A28</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="c18">x2</font>, <font color="Maroon" title="c19">z2</font>, <font color="Maroon" title="c20">t2</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="E36:86"/><span class="lab"><font color="Green" title="E104">A31</font></span>: 
<font color="Maroon" title="c7">p</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">x2</font>
 <span class="kw">and </span><br/><a NAME="E37:86"/><span class="lab"><font color="Green" title="E105">A32</font></span>: 
<font color="Maroon" title="c4">q</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">z2</font>
 <span class="kw">and </span><br/><a NAME="E38:86"/><span class="lab"><font color="Green" title="E106">A33</font></span>: 
<font color="Maroon" title="c8">r</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">t2</font>
 <span class="kw">and </span><br/><a NAME="E39:86"/><span class="lab"><font color="Green" title="E107">A34</font></span>: 
not <font color="Maroon" title="c18">x2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E40:86"/><span class="lab"><font color="Green" title="E108">A35</font></span>: 
not <font color="Maroon" title="c19">z2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E41:86"/><span class="lab"><font color="Green" title="E109">A36</font></span>: 
not <font color="Maroon" title="c20">t2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E42:86"/><span class="lab"><font color="Green" title="E110">A37</font></span>: 
<font color="Maroon" title="c18">x2</font>,<font color="Maroon" title="c19">z2</font>,<font color="Maroon" title="c20">t2</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="#E7:86"><span class="lab"><font color="Green" title="E80">A7</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E43:86"/><span class="lab"><font color="Green" title="E111">A38</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c18">x2</font>,<font color="Maroon" title="c11">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:86"><span class="lab"><font color="Green" title="E83">A10</font></span></a>, <a class="txt" href="#E14:86"><span class="lab"><font color="Green" title="E86">A13</font></span></a>, <a class="txt" href="#E36:86"><span class="lab"><font color="Green" title="E104">A31</font></span></a>, <a class="txt" href="#E39:86"><span class="lab"><font color="Green" title="E107">A34</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="c21">u2</font>, <font color="Maroon" title="c22">y2</font>, <font color="Maroon" title="c23">t</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="E45:86"/><span class="lab"><font color="Green" title="E112">A39</font></span>: 
<font color="Maroon" title="c2">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">u2</font>
 <span class="kw">and </span><br/><a NAME="E46:86"/><span class="lab"><font color="Green" title="E113">A40</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="c22">y2</font>
 <span class="kw">and </span><br/><a NAME="E47:86"/><span class="lab"><font color="Green" title="E114">A41</font></span>: 
<font color="Maroon" title="c8">r</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">t</font>
 <span class="kw">and </span><br/><a NAME="E48:86"/><span class="lab"><font color="Green" title="E115">A42</font></span>: 
not <font color="Maroon" title="c21">u2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E49:86"/><span class="lab"><font color="Green" title="E116">A43</font></span>: 
not <font color="Maroon" title="c22">y2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E50:86"/><span class="lab"><font color="Green" title="E117">A44</font></span>: 
not <font color="Maroon" title="c23">t</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E51:86"/><span class="lab"><font color="Green" title="E118">A45</font></span>: 
<font color="Maroon" title="c21">u2</font>,<font color="Maroon" title="c22">y2</font>,<font color="Maroon" title="c23">t</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="#E5:86"><span class="lab"><font color="Green" title="E78">A5</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E52:86"/><span class="lab"><font color="Green" title="E119">A46</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c22">y2</font>,<font color="Maroon" title="c16">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:86"><span class="lab"><font color="Green" title="E96">A23</font></span></a>, <a class="txt" href="#E29:86"><span class="lab"><font color="Green" title="E99">A26</font></span></a>, <a class="txt" href="#E46:86"><span class="lab"><font color="Green" title="E113">A40</font></span></a>, <a class="txt" href="#E49:86"><span class="lab"><font color="Green" title="E116">A43</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E53:86"/><span class="lab"><font color="Green" title="E120">A47</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c20">t2</font>,<font color="Maroon" title="c23">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:86"><span class="lab"><font color="Green" title="E114">A41</font></span></a>, <a class="txt" href="#E50:86"><span class="lab"><font color="Green" title="E117">A44</font></span></a>, <a class="txt" href="#E38:86"><span class="lab"><font color="Green" title="E106">A33</font></span></a>, <a class="txt" href="#E41:86"><span class="lab"><font color="Green" title="E109">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="E54:86"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c19">z2</font>,<font color="Maroon" title="c14">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:86"><span class="lab"><font color="Green" title="E90">A17</font></span></a>, <a class="txt" href="#E22:86"><span class="lab"><font color="Green" title="E93">A20</font></span></a>, <a class="txt" href="#E37:86"><span class="lab"><font color="Green" title="E105">A32</font></span></a>, <a class="txt" href="#E40:86"><span class="lab"><font color="Green" title="E108">A35</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E55:86"/><span class="kw">then </span><span class="lab"><font color="Green" title="E121">A48</font></span>: 
<font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c14">z</font>,<font color="Maroon" title="c23">t</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="#E42:86"><span class="lab"><font color="Green" title="E110">A37</font></span></a>, <a class="txt" href="#E43:86"><span class="lab"><font color="Green" title="E111">A38</font></span></a>, <a class="txt" href="#E53:86"><span class="lab"><font color="Green" title="E120">A47</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E56:86"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c21">u2</font>,<font color="Maroon" title="c12">u</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:86"><span class="lab"><font color="Green" title="E88">A15</font></span></a>, <a class="txt" href="#E20:86"><span class="lab"><font color="Green" title="E91">A18</font></span></a>, <a class="txt" href="#E45:86"><span class="lab"><font color="Green" title="E112">A39</font></span></a>, <a class="txt" href="#E48:86"><span class="lab"><font color="Green" title="E115">A42</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E57:86"/><span class="kw">then </span><span class="lab"><font color="Green" title="E122">A49</font></span>: 
<font color="Maroon" title="c12">u</font>,<font color="Maroon" title="c16">y</font>,<font color="Maroon" title="c23">t</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="#E51:86"><span class="lab"><font color="Green" title="E118">A45</font></span></a>, <a class="txt" href="#E52:86"><span class="lab"><font color="Green" title="E119">A46</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="c24">v2</font>, <font color="Maroon" title="c25">w2</font>, <font color="Maroon" title="c26">t1</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="E59:86"/><span class="lab"><font color="Green" title="E123">A50</font></span>: 
<font color="Maroon" title="c3">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="c24">v2</font>
 <span class="kw">and </span><br/><a NAME="E60:86"/><span class="lab"><font color="Green" title="E124">A51</font></span>: 
<font color="Maroon" title="c5">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="c25">w2</font>
 <span class="kw">and </span><br/><a NAME="E61:86"/><span class="lab"><font color="Green" title="E125">A52</font></span>: 
<font color="Maroon" title="c8">r</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">t1</font>
 <span class="kw">and </span><br/><a NAME="E62:86"/><span class="lab"><font color="Green" title="E126">A53</font></span>: 
not <font color="Maroon" title="c24">v2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E63:86"/><span class="lab"><font color="Green" title="E127">A54</font></span>: 
not <font color="Maroon" title="c25">w2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E64:86"/><span class="lab"><font color="Green" title="E128">A55</font></span>: 
not <font color="Maroon" title="c26">t1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E65:86"/><span class="lab"><font color="Green" title="E129">A56</font></span>: 
<font color="Maroon" title="c24">v2</font>,<font color="Maroon" title="c25">w2</font>,<font color="Maroon" title="c26">t1</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="#E6:86"><span class="lab"><font color="Green" title="E79">A6</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E66:86"/><span class="lab"><font color="Green" title="E130">A57</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c26">t1</font>,<font color="Maroon" title="c23">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:86"><span class="lab"><font color="Green" title="E114">A41</font></span></a>, <a class="txt" href="#E50:86"><span class="lab"><font color="Green" title="E117">A44</font></span></a>, <a class="txt" href="#E61:86"><span class="lab"><font color="Green" title="E125">A52</font></span></a>, <a class="txt" href="#E64:86"><span class="lab"><font color="Green" title="E128">A55</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E67:86"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c9">u1</font>,<font color="Maroon" title="c12">u</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:86"><span class="lab"><font color="Green" title="E88">A15</font></span></a>, <a class="txt" href="#E20:86"><span class="lab"><font color="Green" title="E91">A18</font></span></a>, <a class="txt" href="#E9:86"><span class="lab"><font color="Green" title="E81">A8</font></span></a>, <a class="txt" href="#E12:86"><span class="lab"><font color="Green" title="E84">A11</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E68:86"/><span class="kw">then </span><span class="lab"><font color="Green" title="E131">A58</font></span>: 
<font color="Maroon" title="c12">u</font>,<font color="Maroon" title="c15">w</font>,<font color="Maroon" title="c11">x</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="#E15:86"><span class="lab"><font color="Green" title="E87">A14</font></span></a>, <a class="txt" href="#E32:86"><span class="lab"><font color="Green" title="E102">A29</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="c27">v1</font>, <font color="Maroon" title="c28">y1</font>, <font color="Maroon" title="c29">x1</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="E70:86"/><span class="lab"><font color="Green" title="E132">A59</font></span>: 
<font color="Maroon" title="c3">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="c27">v1</font>
 <span class="kw">and </span><br/><a NAME="E71:86"/><span class="lab"><font color="Green" title="E133">A60</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="c28">y1</font>
 <span class="kw">and </span><br/><a NAME="E72:86"/><span class="lab"><font color="Green" title="E134">A61</font></span>: 
<font color="Maroon" title="c7">p</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">x1</font>
 <span class="kw">and </span><br/><a NAME="E73:86"/><span class="lab"><font color="Green" title="E135">A62</font></span>: 
not <font color="Maroon" title="c27">v1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E74:86"/><span class="lab"><font color="Green" title="E136">A63</font></span>: 
not <font color="Maroon" title="c28">y1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E75:86"/><span class="lab"><font color="Green" title="E137">A64</font></span>: 
not <font color="Maroon" title="c29">x1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E76:86"/><span class="lab"><font color="Green" title="E138">A65</font></span>: 
<font color="Maroon" title="c27">v1</font>,<font color="Maroon" title="c28">y1</font>,<font color="Maroon" title="c29">x1</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="#E4:86"><span class="lab"><font color="Green" title="E77">A4</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E77:86"/><span class="lab"><font color="Green" title="E139">A66</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c29">x1</font>,<font color="Maroon" title="c11">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:86"><span class="lab"><font color="Green" title="E83">A10</font></span></a>, <a class="txt" href="#E14:86"><span class="lab"><font color="Green" title="E86">A13</font></span></a>, <a class="txt" href="#E72:86"><span class="lab"><font color="Green" title="E134">A61</font></span></a>, <a class="txt" href="#E75:86"><span class="lab"><font color="Green" title="E137">A64</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E78:86"/><span class="lab"><font color="Green" title="E140">A67</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c25">w2</font>,<font color="Maroon" title="c15">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:86"><span class="lab"><font color="Green" title="E95">A22</font></span></a>, <a class="txt" href="#E28:86"><span class="lab"><font color="Green" title="E98">A25</font></span></a>, <a class="txt" href="#E60:86"><span class="lab"><font color="Green" title="E124">A51</font></span></a>, <a class="txt" href="#E63:86"><span class="lab"><font color="Green" title="E127">A54</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E79:86"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c24">v2</font>,<font color="Maroon" title="c13">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:86"><span class="lab"><font color="Green" title="E89">A16</font></span></a>, <a class="txt" href="#E21:86"><span class="lab"><font color="Green" title="E92">A19</font></span></a>, <a class="txt" href="#E59:86"><span class="lab"><font color="Green" title="E123">A50</font></span></a>, <a class="txt" href="#E62:86"><span class="lab"><font color="Green" title="E126">A53</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E80:86"/><span class="kw">then </span><span class="lab"><font color="Green" title="E141">A68</font></span>: 
<font color="Maroon" title="c13">v</font>,<font color="Maroon" title="c15">w</font>,<font color="Maroon" title="c23">t</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="#E65:86"><span class="lab"><font color="Green" title="E129">A56</font></span></a>, <a class="txt" href="#E78:86"><span class="lab"><font color="Green" title="E140">A67</font></span></a>, <a class="txt" href="#E66:86"><span class="lab"><font color="Green" title="E130">A57</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E81:86"/><span class="lab"><font color="Green" title="E142">A69</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c28">y1</font>,<font color="Maroon" title="c16">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:86"><span class="lab"><font color="Green" title="E96">A23</font></span></a>, <a class="txt" href="#E29:86"><span class="lab"><font color="Green" title="E99">A26</font></span></a>, <a class="txt" href="#E71:86"><span class="lab"><font color="Green" title="E133">A60</font></span></a>, <a class="txt" href="#E74:86"><span class="lab"><font color="Green" title="E136">A63</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E82:86"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c27">v1</font>,<font color="Maroon" title="c13">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:86"><span class="lab"><font color="Green" title="E89">A16</font></span></a>, <a class="txt" href="#E21:86"><span class="lab"><font color="Green" title="E92">A19</font></span></a>, <a class="txt" href="#E70:86"><span class="lab"><font color="Green" title="E132">A59</font></span></a>, <a class="txt" href="#E73:86"><span class="lab"><font color="Green" title="E135">A62</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E83:86"/><span class="kw">then </span>
<font color="Maroon" title="c13">v</font>,<font color="Maroon" title="c16">y</font>,<font color="Maroon" title="c11">x</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="#E76:86"><span class="lab"><font color="Green" title="E138">A65</font></span></a>, <a class="txt" href="#E81:86"><span class="lab"><font color="Green" title="E142">A69</font></span></a>, <a class="txt" href="#E77:86"><span class="lab"><font color="Green" title="E139">A66</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E84:86"/><span class="kw">then </span>
( <font color="Maroon" title="c12">u</font>,<font color="Maroon" title="c13">v</font>,<font color="Maroon" title="c16">y</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  or <font color="Maroon" title="c12">u</font>,<font color="Maroon" title="c13">v</font>,<font color="Maroon" title="c15">w</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  or <font color="Maroon" title="c12">u</font>,<font color="Maroon" title="c15">w</font>,<font color="Maroon" title="c16">y</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  or <font color="Maroon" title="c13">v</font>,<font color="Maroon" title="c15">w</font>,<font color="Maroon" title="c16">y</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="#E22:86"><span class="lab"><font color="Green" title="E93">A20</font></span></a>, <a class="txt" href="#E23:86"><span class="lab"><font color="Green" title="E94">A21</font></span></a>, <a class="txt" href="#E14:86"><span class="lab"><font color="Green" title="E86">A13</font></span></a>, <a class="txt" href="#E50:86"><span class="lab"><font color="Green" title="E117">A44</font></span></a>, <a class="txt" href="#E34:86"><span class="lab"><font color="Green" title="E103">A30</font></span></a>, <a class="txt" href="#E68:86"><span class="lab"><font color="Green" title="E131">A58</font></span></a>, <a class="txt" href="#E57:86"><span class="lab"><font color="Green" title="E122">A49</font></span></a>, <a class="txt" href="#E80:86"><span class="lab"><font color="Green" title="E141">A68</font></span></a>, <a class="txt" href="#E55:86"><span class="lab"><font color="Green" title="E121">A48</font></span></a>, <a class="ref" href="anproj_1.html#T23" title="ANPROJ_1:th.23">ANPROJ_1:23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E85:86"/>
( <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c6">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c5">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c6">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or <font color="Maroon" title="c3">r2</font>,<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c6">q1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:86"><span class="lab"><font color="Green" title="E88">A15</font></span></a>, <a class="txt" href="#E18:86"><span class="lab"><font color="Green" title="E89">A16</font></span></a>, <a class="txt" href="#E20:86"><span class="lab"><font color="Green" title="E91">A18</font></span></a>, <a class="txt" href="#E21:86"><span class="lab"><font color="Green" title="E92">A19</font></span></a>, <a class="txt" href="#E25:86"><span class="lab"><font color="Green" title="E95">A22</font></span></a>, <a class="txt" href="#E26:86"><span class="lab"><font color="Green" title="E96">A23</font></span></a>, <a class="txt" href="#E28:86"><span class="lab"><font color="Green" title="E98">A25</font></span></a>, <a class="txt" href="#E29:86"><span class="lab"><font color="Green" title="E99">A26</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/>


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