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<b>let </b><font color="Maroon">S</font> be   <a href="analoaf.html#NM1">OAffinSpace</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">t</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/>











<b>assume </b><a NAME="E1:42"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> &amp; <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="diraf.html#NR4" target="_self">is_collinear</a>  &amp; <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">t</font> <a href="diraf.html#NR4" target="_self">is_collinear</a>  &amp; <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font> <a href="diraf.html#NR4" target="_self">is_collinear</a>  )
 ;<br/>

<div><i><font color="Green">E26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:42_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font>
 ;<br/><a NAME="E2:42_1"/><b>then </b>
( <font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> &amp; <font color="Maroon">z</font>,<font color="Maroon">y</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">z</font>,<font color="Maroon">t</font> &amp; <font color="Maroon">z</font>,<font color="Maroon">y</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">z</font>,<font color="Maroon">u</font> )
 <b>by </b><i>, </i>;<br/><a NAME="E3:42_1"/><b>then </b>
<font color="Maroon">z</font>,<font color="Maroon">t</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">z</font>,<font color="Maroon">u</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:42_1"/>
<font color="Maroon">z</font>,<font color="Maroon">t</font>,<font color="Maroon">u</font> <a href="diraf.html#NR4" target="_self">is_collinear</a> 
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:42_2"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">z</font>
 ;<br/><a NAME="E2:42_2"/>
( <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Maroon">z</font> &amp; <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Maroon">t</font> &amp; <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Maroon">u</font> )
 <b>by </b><i>, </i>;<br/><a NAME="E3:42_2"/><b>then </b>
( <font color="Maroon">x</font>,<font color="Maroon">z</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Maroon">t</font> &amp; <font color="Maroon">x</font>,<font color="Maroon">z</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Maroon">u</font> )
 <b>by </b><i>, </i>;<br/><a NAME="E4:42_2"/><b>then </b>
( <font color="Maroon">z</font>,<font color="Maroon">x</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">z</font>,<font color="Maroon">t</font> &amp; <font color="Maroon">z</font>,<font color="Maroon">x</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">z</font>,<font color="Maroon">u</font> )
 <b>by </b><i/>;<br/><a NAME="E5:42_2"/><b>then </b>
<font color="Maroon">z</font>,<font color="Maroon">t</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">z</font>,<font color="Maroon">u</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E6:42_2"/>
<font color="Maroon">z</font>,<font color="Maroon">t</font>,<font color="Maroon">u</font> <a href="diraf.html#NR4" target="_self">is_collinear</a> 
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:42"/>
<font color="Maroon">z</font>,<font color="Maroon">t</font>,<font color="Maroon">u</font> <a href="diraf.html#NR4" target="_self">is_collinear</a> 
 <b>by </b><i/>;<br/>


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