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<b>let </b><font color="Maroon" title="c1">V</font> be  non <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a> <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6" title="ANPROJ_1:func.6">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="anproj_2.html#D9" target="_self" title="ANPROJ_2:def.9">ANPROJ_2:def 9</a><br/><b>let </b><font color="Maroon" title="c3">p1</font>, <font color="Maroon" title="c4">p2</font>, <font color="Maroon" title="c5">r</font>, <font color="Maroon" title="c6">r1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6" title="ANPROJ_1:func.6">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>;<br/>











<b>assume </b><a NAME="E1:72"/><i><font color="Green" title="E68">A1</font></i>: 
( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font>,<font color="Maroon" title="c6">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 ;<br/>

<a NAME="E2:72"/><b>then </b>
( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  implies  ex <font color="Olive" title="b1">r2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6" title="ANPROJ_1:func.6">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span> st <br/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">p2</font>,<font color="Olive" title="b1">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">r1</font>,<font color="Olive" title="b1">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  ) )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E69"><i><font color="Green" title="E65">Lm34</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:72"/>
 ex <font color="Olive" title="b1">r2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K6" title="ANPROJ_1:func.6">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span> st <br/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">p2</font>,<font color="Olive" title="b1">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">r1</font>,<font color="Olive" title="b1">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:72"><i><font color="Green" title="E68">A1</font></i></a>, <a class="txt" href="anproj_2.html#E70"><i><font color="Green" title="E66">Lm35</font></i></a></i>;<br/>


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