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<b>let </b><font color="Maroon" title="c1">V</font> be  non <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a> <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><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#K6" title="ANPROJ_1:func.6">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>;<br/>















<b>assume </b><a NAME="E1:85"/><i><font color="Green" title="E76">A1</font></i>: 
( <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>  )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c9">u</font>, <font color="Maroon" title="c10">v</font>, <font color="Maroon" title="c11">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E3:85"/><i><font color="Green" title="E77">A2</font></i>: 
( <font color="Maroon" title="c2">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c9">u</font> &amp; <font color="Maroon" title="c3">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c10">v</font> &amp; <font color="Maroon" title="c4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c11">z</font> &amp; <font color="Maroon" title="c9">u</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c10">v</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c11">z</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c11">z</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )
 <b>by </b><i><a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c12">w</font>, <font color="Maroon" title="c13">y</font>, <font color="Maroon" title="c14">z1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E5:85"/><i><font color="Green" title="E78">A3</font></i>: 
( <font color="Maroon" title="c5">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c12">w</font> &amp; <font color="Maroon" title="c6">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c13">y</font> &amp; <font color="Maroon" title="c4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c14">z1</font> &amp; <font color="Maroon" title="c12">w</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c13">y</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c14">z1</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c12">w</font>,<font color="Maroon" title="c13">y</font>,<font color="Maroon" title="c14">z1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:85"><i><font color="Green" title="E76">A1</font></i></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c15">u1</font>, <font color="Maroon" title="c16">w1</font>, <font color="Maroon" title="c17">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E7:85"/><i><font color="Green" title="E79">A4</font></i>: 
( <font color="Maroon" title="c2">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c15">u1</font> &amp; <font color="Maroon" title="c5">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c16">w1</font> &amp; <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c17">x</font> &amp; <font color="Maroon" title="c15">u1</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c16">w1</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c17">x</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c15">u1</font>,<font color="Maroon" title="c16">w1</font>,<font color="Maroon" title="c17">x</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:85"><i><font color="Green" title="E76">A1</font></i></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c18">v1</font>, <font color="Maroon" title="c19">y1</font>, <font color="Maroon" title="c20">x1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E9:85"/><i><font color="Green" title="E80">A5</font></i>: 
( <font color="Maroon" title="c3">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c18">v1</font> &amp; <font color="Maroon" title="c6">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c19">y1</font> &amp; <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c20">x1</font> &amp; <font color="Maroon" title="c18">v1</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c19">y1</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c20">x1</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c18">v1</font>,<font color="Maroon" title="c19">y1</font>,<font color="Maroon" title="c20">x1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:85"><i><font color="Green" title="E76">A1</font></i></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></i>;<br/>
<b>consider </b><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><b> such that </b><br/><a NAME="E11:85"/><i><font color="Green" title="E81">A6</font></i>: 
( <font color="Maroon" title="c2">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c21">u2</font> &amp; <font color="Maroon" title="c6">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c22">y2</font> &amp; <font color="Maroon" title="c8">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c23">t</font> &amp; <font color="Maroon" title="c21">u2</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c22">y2</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c23">t</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <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>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:85"><i><font color="Green" title="E76">A1</font></i></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></i>;<br/>
<b>consider </b><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><b> such that </b><br/><a NAME="E13:85"/><i><font color="Green" title="E82">A7</font></i>: 
( <font color="Maroon" title="c3">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c24">v2</font> &amp; <font color="Maroon" title="c5">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c25">w2</font> &amp; <font color="Maroon" title="c8">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c26">t1</font> &amp; <font color="Maroon" title="c24">v2</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c25">w2</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c26">t1</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <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>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:85"><i><font color="Green" title="E76">A1</font></i></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c27">x2</font>, <font color="Maroon" title="c28">z2</font>, <font color="Maroon" title="c29">t2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E15:85"/><i><font color="Green" title="E83">A8</font></i>: 
( <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c27">x2</font> &amp; <font color="Maroon" title="c4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c28">z2</font> &amp; <font color="Maroon" title="c8">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c29">t2</font> &amp; <font color="Maroon" title="c27">x2</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c28">z2</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c29">t2</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c27">x2</font>,<font color="Maroon" title="c28">z2</font>,<font color="Maroon" title="c29">t2</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:85"><i><font color="Green" title="E76">A1</font></i></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></i>;<br/>
<a NAME="E16:85"/>
( <font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c11">z</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Maroon" title="c12">w</font>,<font color="Maroon" title="c13">y</font>,<font color="Maroon" title="c11">z</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c12">w</font>,<font color="Maroon" title="c17">x</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c13">y</font>,<font color="Maroon" title="c17">x</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c13">y</font>,<font color="Maroon" title="c23">t</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c12">w</font>,<font color="Maroon" title="c23">t</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp; <font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c11">z</font>,<font color="Maroon" title="c23">t</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_1"><b>proof </b></a><div class="add">

<a NAME="E1:85_1"/><i><font color="Green" title="E84">A9</font></i>: 
(  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c14">z1</font>,<font color="Maroon" title="c11">z</font> &amp;  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c16">w1</font>,<font color="Maroon" title="c12">w</font> &amp;  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c15">u1</font>,<font color="Maroon" title="c9">u</font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E3:85"><i><font color="Green" title="E77">A2</font></i></a>, <a class="txt" href="anproj_2.html#E5:85"><i><font color="Green" title="E78">A3</font></i></a>, <a class="txt" href="anproj_2.html#E7:85"><i><font color="Green" title="E79">A4</font></i></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></i>;<br/>
<a NAME="E2:85_1"/><i><font color="Green" title="E85">A10</font></i>: 
(  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c19">y1</font>,<font color="Maroon" title="c13">y</font> &amp;  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c20">x1</font>,<font color="Maroon" title="c17">x</font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E5:85"><i><font color="Green" title="E78">A3</font></i></a>, <a class="txt" href="anproj_2.html#E7:85"><i><font color="Green" title="E79">A4</font></i></a>, <a class="txt" href="anproj_2.html#E9:85"><i><font color="Green" title="E80">A5</font></i></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></i>;<br/>
<a NAME="E3:85_1"/><i><font color="Green" title="E86">A11</font></i>: 
(  <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="c9">u</font> &amp;  <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="c13">y</font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E3:85"><i><font color="Green" title="E77">A2</font></i></a>, <a class="txt" href="anproj_2.html#E5:85"><i><font color="Green" title="E78">A3</font></i></a>, <a class="txt" href="anproj_2.html#E11:85"><i><font color="Green" title="E81">A6</font></i></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></i>;<br/>
<a NAME="E4:85_1"/><i><font color="Green" title="E87">A12</font></i>: 
(  <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="c10">v</font> &amp;  <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="c12">w</font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E3:85"><i><font color="Green" title="E77">A2</font></i></a>, <a class="txt" href="anproj_2.html#E5:85"><i><font color="Green" title="E78">A3</font></i></a>, <a class="txt" href="anproj_2.html#E13:85"><i><font color="Green" title="E82">A7</font></i></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></i>;<br/>
<a NAME="E5:85_1"/><i><font color="Green" title="E88">A13</font></i>: 
(  <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> &amp;  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c27">x2</font>,<font color="Maroon" title="c17">x</font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E7:85"><i><font color="Green" title="E79">A4</font></i></a>, <a class="txt" href="anproj_2.html#E11:85"><i><font color="Green" title="E81">A6</font></i></a>, <a class="txt" href="anproj_2.html#E13:85"><i><font color="Green" title="E82">A7</font></i></a>, <a class="txt" href="anproj_2.html#E15:85"><i><font color="Green" title="E83">A8</font></i></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></i>;<br/>
<a NAME="E6:85_1"/><i><font color="Green" title="E89">A14</font></i>: 
(  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c28">z2</font>,<font color="Maroon" title="c11">z</font> &amp;  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c29">t2</font>,<font color="Maroon" title="c23">t</font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E3:85"><i><font color="Green" title="E77">A2</font></i></a>, <a class="txt" href="anproj_2.html#E11:85"><i><font color="Green" title="E81">A6</font></i></a>, <a class="txt" href="anproj_2.html#E15:85"><i><font color="Green" title="E83">A8</font></i></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></i>;<br/>
<a NAME="E7:85_1"/><i><font color="Green" title="E90">A15</font></i>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c18">v1</font>,<font color="Maroon" title="c10">v</font>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E3:85"><i><font color="Green" title="E77">A2</font></i></a>, <a class="txt" href="anproj_2.html#E9:85"><i><font color="Green" title="E80">A5</font></i></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></i>;<br/>
<b>thus </b><a NAME="E8:85_1"/>
<font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c11">z</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E3:85"><i><font color="Green" title="E77">A2</font></i></a></i>;<br/>

<b>thus </b><a NAME="E9:85_1"/>
<font color="Maroon" title="c12">w</font>,<font color="Maroon" title="c13">y</font>,<font color="Maroon" title="c11">z</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:85"><i><font color="Green" title="E78">A3</font></i></a>, <a class="txt" href="anproj_2.html#E1:85_1"><i><font color="Green" title="E84">A9</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>

<b>thus </b><a NAME="E10:85_1"/>
<font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c12">w</font>,<font color="Maroon" title="c17">x</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E7:85"><i><font color="Green" title="E79">A4</font></i></a>, <a class="txt" href="anproj_2.html#E1:85_1"><i><font color="Green" title="E84">A9</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>

<b>thus </b><a NAME="E11:85_1"/>
<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c13">y</font>,<font color="Maroon" title="c17">x</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E9:85"><i><font color="Green" title="E80">A5</font></i></a>, <a class="txt" href="anproj_2.html#E2:85_1"><i><font color="Green" title="E85">A10</font></i></a>, <a class="txt" href="anproj_2.html#E7:85_1"><i><font color="Green" title="E90">A15</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>

<b>thus </b><a NAME="E12:85_1"/>
<font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c13">y</font>,<font color="Maroon" title="c23">t</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E11:85"><i><font color="Green" title="E81">A6</font></i></a>, <a class="txt" href="anproj_2.html#E3:85_1"><i><font color="Green" title="E86">A11</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>

<b>thus </b><a NAME="E13:85_1"/>
<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c12">w</font>,<font color="Maroon" title="c23">t</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E13:85"><i><font color="Green" title="E82">A7</font></i></a>, <a class="txt" href="anproj_2.html#E4:85_1"><i><font color="Green" title="E87">A12</font></i></a>, <a class="txt" href="anproj_2.html#E5:85_1"><i><font color="Green" title="E88">A13</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>

<b>thus </b><a NAME="E14:85_1"/>
<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c11">z</font>,<font color="Maroon" title="c23">t</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E15:85"><i><font color="Green" title="E83">A8</font></i></a>, <a class="txt" href="anproj_2.html#E5:85_1"><i><font color="Green" title="E88">A13</font></i></a>, <a class="txt" href="anproj_2.html#E6:85_1"><i><font color="Green" title="E89">A14</font></i></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E17:85"/><b>then </b>
( <font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c13">y</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  or <font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c12">w</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  or <font color="Maroon" title="c9">u</font>,<font color="Maroon" title="c12">w</font>,<font color="Maroon" title="c13">y</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  or <font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c12">w</font>,<font color="Maroon" title="c13">y</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E3:85"><i><font color="Green" title="E77">A2</font></i></a>, <a class="txt" href="anproj_2.html#E7:85"><i><font color="Green" title="E79">A4</font></i></a>, <a class="txt" href="anproj_2.html#E11:85"><i><font color="Green" title="E81">A6</font></i></a>, <a class="ref" href="anproj_1.html#T23" title="ANPROJ_1:th.23">ANPROJ_1:23</a></i>;<br/>
<b>hence </b><a NAME="E18:85"/>
( <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>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E3:85"><i><font color="Green" title="E77">A2</font></i></a>, <a class="txt" href="anproj_2.html#E5:85"><i><font color="Green" title="E78">A3</font></i></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></i>;<br/>


</div>
