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<b>let </b><font color="Maroon">PCPP</font> be   <a href="anproj_2.html#NM1">CollProjectiveSpace</a>;<br/><b>let </b><font color="Maroon">a1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PCPP</font>;<br/><b>let </b><font color="Maroon">a2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PCPP</font>;<br/><b>let </b><font color="Maroon">a3</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PCPP</font>;<br/><b>let </b><font color="Maroon">c3</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PCPP</font>;<br/><b>let </b><font color="Maroon">c1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PCPP</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PCPP</font>;<br/>













<b>assume </b><a NAME="E1:9"/><i><font color="Green">E34</font></i>: 
( not <font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">a3</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">c3</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a2</font>,<font color="Maroon">a3</font>,<font color="Maroon">c1</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a1</font>,<font color="Maroon">a3</font>,<font color="Maroon">x</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c1</font>,<font color="Maroon">c3</font>,<font color="Maroon">x</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a1</font> &amp; <font color="Maroon">c3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a2</font> &amp; <font color="Maroon">c1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a2</font> &amp; <font color="Maroon">c1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3</font> )
 ;<br/>

<a NAME="E2:9"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:9_1"/>
not <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:9_1"/><b>then </b>
( <font color="Maroon">a1</font>,<font color="Maroon">c3</font>,<font color="Maroon">c1</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a1</font>,<font color="Maroon">c3</font>,<font color="Maroon">a2</font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:9_1"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">c1</font>,<font color="Maroon">a2</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:9_1"/><b>then </b>
( <font color="Maroon">a2</font>,<font color="Maroon">c1</font>,<font color="Maroon">a1</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a2</font>,<font color="Maroon">c1</font>,<font color="Maroon">a3</font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:9_1"/><b>then </b>
<font color="Maroon">a2</font>,<font color="Maroon">a1</font>,<font color="Maroon">a3</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:9_1"/>
contradiction
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:9"/>
<font color="Maroon">a3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:9_2"/>
not <font color="Maroon">a3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:9_2"/><b>then </b>
( <font color="Maroon">a3</font>,<font color="Maroon">c1</font>,<font color="Maroon">c3</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a3</font>,<font color="Maroon">c1</font>,<font color="Maroon">a2</font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:9_2"/><b>then </b>
<font color="Maroon">a3</font>,<font color="Maroon">a2</font>,<font color="Maroon">c3</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:9_2"/><b>then </b>
( <font color="Maroon">a2</font>,<font color="Maroon">c3</font>,<font color="Maroon">a3</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a2</font>,<font color="Maroon">c3</font>,<font color="Maroon">a1</font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:9_2"/><b>then </b>
<font color="Maroon">a2</font>,<font color="Maroon">a1</font>,<font color="Maroon">a3</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:9_2"/>
contradiction
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:9"/>
( <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> &amp; <font color="Maroon">a3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> )
 <b>by </b><i/>;<br/>


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