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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">b1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PCPP</font>;<br/><b>let </b><font color="Maroon">b2</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>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PCPP</font>;<br/>













<b>assume </b><a NAME="E1:14"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a2</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2</font> &amp; <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">x</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">y</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">x</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">y</font> <a href="collsp.html#R1">is_collinear</a>  &amp; not <font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">b1</font> <a href="collsp.html#R1">is_collinear</a>  )
 ;<br/>

<b>assume </b><a NAME="E2:14"/><i><font color="Green">E35</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/>

<a NAME="E3:14"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">a1</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">a2</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">b1</font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/>
<a NAME="E4:14"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">b1</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i>, <a class="ref" href="anproj_2.html#D8">ANPROJ_2:def 8</a></i>;<br/>
<a NAME="E5:14"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">a1</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i>, , <a class="ref" href="anproj_2.html#D8">ANPROJ_2:def 8</a></i>;<br/>
<a NAME="E6:14"/>
<font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">a2</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i>, , <a class="ref" href="anproj_2.html#D8">ANPROJ_2:def 8</a></i>;<br/>
<b>hence </b><a NAME="E7:14"/>
contradiction
 <b>by </b><i>, , , , <a class="ref" href="anproj_2.html#D8">ANPROJ_2:def 8</a></i>;<br/>


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