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<b>let </b><font color="Maroon" title="c1">PCPP</font> be   <a href="anproj_2.html#NM1" title="ANPROJ_2:NM.1">CollProjectiveSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c6">r</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PCPP</font>;<br/>











<b>assume </b><a NAME="E1:3"/><i><font color="Green" title="E3">A1</font></i>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">q</font> &amp; <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c6">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:3_1"/><i><font color="Green" title="E4">A2</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font>
 ;<br/><a NAME="E2:3_1"/><i><font color="Green" title="E5">A3</font></i>: 
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:3"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></i>;<br/><a NAME="E3:3_1"/>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:3"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></i>;<br/><a NAME="E4:3_1"/><b>then </b>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:3_1"><i><font color="Green" title="E4">A2</font></i></a>, <a class="txt" href="hessenbe.html#E2:3_1"><i><font color="Green" title="E5">A3</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></i>;<br/><a NAME="E5:3_1"/><b>then </b><i><font color="Green" title="E6">A4</font></i>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">b</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></i>;<br/><a NAME="E6:3_1"/>
<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:3"><i><font color="Green" title="E3">A1</font></i></a>, <a class="txt" href="hessenbe.html#E1:3_1"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></i>;<br/><a NAME="E7:3_1"/><b>then </b>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">a</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></i>;<br/><b>hence </b><a NAME="E8:3_1"/>
<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:3"><i><font color="Green" title="E3">A1</font></i></a>, <a class="txt" href="hessenbe.html#E5:3_1"><i><font color="Green" title="E6">A4</font></i></a>, <a class="ref" href="anproj_2.html#D8" title="ANPROJ_2:def.8">ANPROJ_2:def 8</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:3"/>
<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</a></i>;<br/>


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