<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">CLSP</font> be   <a href="collsp.html#NM2">CollSp</a>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">CLSP</font>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">CLSP</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">CLSP</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">CLSP</font>;<br/><b>let </b><font color="Maroon">r</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">CLSP</font>;<br/>











<b>assume </b><a NAME="E1:17"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font> <a href="collsp.html#R1" target="_self">is_collinear</a>  &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font> <a href="collsp.html#R1" target="_self">is_collinear</a>  &amp; <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font> <a href="collsp.html#R1" target="_self">is_collinear</a>  )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E2:17_1"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="collsp.html#R1" target="_self">is_collinear</a> 
 <b>by </b><i><a class="ref" href="collsp.html#D1" target="_self">Def1</a>, </i>;<br/><a NAME="E3:17_1"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">b</font> <a href="collsp.html#R1" target="_self">is_collinear</a> 
 <b>by </b><i/>;<br/><a NAME="E4:17_1"/><b>then </b>
( <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">a</font> <a href="collsp.html#R1" target="_self">is_collinear</a>  &amp; <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">b</font> <a href="collsp.html#R1" target="_self">is_collinear</a>  )
 <b>by </b><i><a class="ref" href="collsp.html#D1" target="_self">Def1</a>, <a class="ref" href="collsp.html#T2" target="_self">Th2</a>, , , </i>;<br/><b>hence </b><a NAME="E5:17_1"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">r</font> <a href="collsp.html#R1" target="_self">is_collinear</a> 
 <b>by </b><i><a class="ref" href="collsp.html#D1" target="_self">Def1</a>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:17"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">r</font> <a href="collsp.html#R1" target="_self">is_collinear</a> 
 <b>by </b><i/>;<br/>


</div>
