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<b>let </b><font color="Maroon">CS</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="collsp.html#L1">CollStr</a> ;<br/>

<b>thus </b><a NAME="E1:103"/>
( <font color="Maroon">CS</font> is  <a href="anproj_2.html#V7" target="_self">2-dimensional</a> <a href="anproj_2.html#NM1">CollProjectiveSpace</a> implies ( <font color="Maroon">CS</font> is  <a href="collsp.html#V4">proper</a> <a href="anproj_2.html#V3" target="_self">at_least_3rank</a> <a href="collsp.html#NM2">CollSp</a> &amp; ( for <font color="Olive">p</font>, <font color="Olive">p1</font>, <font color="Olive">q</font>, <font color="Olive">q1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>  ex <font color="Olive">r</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font> st <br/>( <font color="Olive">p</font>,<font color="Olive">p1</font>,<font color="Olive">r</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">q</font>,<font color="Olive">q1</font>,<font color="Olive">r</font> <a href="collsp.html#R1">is_collinear</a>  ) ) ) )
 <b>by </b><i/>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:103"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">CS</font> is  <a href="collsp.html#V4">proper</a> <a href="anproj_2.html#V3" target="_self">at_least_3rank</a> <a href="collsp.html#NM2">CollSp</a>
 <b>and </b><br/><a NAME="E3:103"/><i><font color="Green">E59</font></i>: 
for <font color="Olive">p</font>, <font color="Olive">p1</font>, <font color="Olive">q</font>, <font color="Olive">q1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>  ex <font color="Olive">r</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font> st <br/>( <font color="Olive">p</font>,<font color="Olive">p1</font>,<font color="Olive">r</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">q</font>,<font color="Olive">q1</font>,<font color="Olive">r</font> <a href="collsp.html#R1">is_collinear</a>  )
 ;<br/>

<a NAME="E4:103"/>
<font color="Maroon">CS</font> is <a href="anproj_2.html#V2" target="_self">Vebleian</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="103_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>, <font color="Maroon">p1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>, <font color="Maroon">p2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>, <font color="Maroon">r</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>, <font color="Maroon">r1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="anproj_2.html#D9" target="_self">ANPROJ_2:def 9</a><br/>

<b>assume </b><a NAME="E1:103_1"/>
( <font color="Maroon">p</font>,<font color="Maroon">p1</font>,<font color="Maroon">r</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">p1</font>,<font color="Maroon">p2</font>,<font color="Maroon">r1</font> <a href="collsp.html#R1">is_collinear</a>  )
 ;<br/>

<b>thus </b><a NAME="E2:103_1"/>
 ex <font color="Olive">r2</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font> st <br/>( <font color="Maroon">p</font>,<font color="Maroon">p2</font>,<font color="Olive">r2</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">r</font>,<font color="Maroon">r1</font>,<font color="Olive">r2</font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:103"/>
<font color="Maroon">CS</font> is  <a href="anproj_2.html#V7" target="_self">2-dimensional</a> <a href="anproj_2.html#NM1">CollProjectiveSpace</a>
 <b>by </b><i>, , </i>;<br/>


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