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<b>let </b><font color="Maroon">SAS</font> be   <a href="semi_af1.html#NM1">Semi_Affine_Space</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>;<br/>









<b>assume </b><a NAME="E1:27"/><i><font color="Green">E29</font></i>: 
( not <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="semi_af1.html#R1" target="_self">is_collinear</a>  &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:27_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="semi_af1.html#R1" target="_self">is_collinear</a>  )
 ;<br/><a NAME="E2:27_1"/><i><font color="Green">E31</font></i>: 
( not <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a</font> )
 <b>by </b><i>, , </i>;<br/><a NAME="E3:27_1"/><b>then </b><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">c</font> )
 <b>by </b><i>, , </i>;<br/><a NAME="E4:27_1"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 <b>by </b><i>, </i>;<br/><a NAME="E5:27_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">a</font>
 <b>by </b><i/>;<br/><a NAME="E6:27_1"/><b>then </b>
( not <font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a</font> &amp; <font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">a</font> )
 <b>by </b><i>, , , , </i>;<br/><b>hence </b><a NAME="E7:27_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:27"/>
not <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="semi_af1.html#R1" target="_self">is_collinear</a> 
 <b>by </b><i/>;<br/>


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