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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">o</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>;<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>consider </b><font color="Maroon">p</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font><b> such that </b><br/><a NAME="E2:107"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font> holds <br/> ( <font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">p</font> &amp;  ex <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font> st <br/>( <font color="Maroon">o</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Olive">b</font> implies ( <font color="Maroon">o</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Olive">d</font> &amp; <font color="Maroon">p</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">d</font> ) ) )
 <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">p</font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:107_1"/>
<font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="semi_af1.html#R1" target="_self">is_collinear</a> 
 <b>by </b><i><a class="ref" href="semi_af1.html#T67" target="_self">Th67</a>, </i>;<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>consider </b><font color="Maroon">d</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font><b> such that </b><br/><a NAME="E3:107_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b</font> implies ( <font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">d</font> ) )
 <b>by </b><i><a class="ref" href="semi_af1.html#T67" target="_self">Th67</a></i>;<br/><b>take </b><font color="Maroon">d</font> = <font color="Maroon">d</font>;<br/><b>assume </b><a NAME="E4:107_1"/>
<font color="Maroon">o</font>,<font color="Maroon">p</font>,<font color="Maroon">b</font> <a href="semi_af1.html#R1" target="_self">is_collinear</a> 
 ;<br/><b>hence </b><a NAME="E5:107_1"/>
( <font color="Maroon">o</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="semi_af1.html#R1" target="_self">is_collinear</a>  &amp; <font color="Maroon">p</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="semi_af1.html#T68" target="_self">Th68</a>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:107"/>
( <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="semi_af1.html#R1" target="_self">is_collinear</a>  &amp;  <a href="semi_af1.html#R5" target="_self">qtrap</a> <font color="Maroon">o</font>,<font color="Maroon">p</font> )
 <b>by </b><i><a class="ref" href="semi_af1.html#T56" target="_self">Th56</a></i>;<br/>


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