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

<b>consider </b><font color="Maroon">Z</font> being   <a href="setfam_1.html#NM1">Subset-Family</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K1" target="_self">Proper_Vectors_of</a> <font color="Maroon">V</font></span>)</span><b> such that </b><br/><a NAME="E2:41_2_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><a href="anproj_1.html#K2" target="_self">Proportionality_as_EqRel_of</a> <font color="Maroon">V</font></span>)</span> &amp;  <a href="anproj_1.html#K4" target="_self">ProjectivePoints</a> <font color="Maroon">V</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Z</font> )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">u</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E4:41_2_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font>
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">u</font> = <font color="Maroon">u</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> ;<br/>
<a NAME="E6:41_2_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="anproj_1.html#K1" target="_self">Proper_Vectors_of</a> <font color="Maroon">V</font>
 
<b>by </b><i>, </i>;<br/>
<b>set </b><font color="Maroon">Y</font> =  <a href="anproj_1.html#K3" target="_self">Dir</a> <font color="Maroon">u</font>;<br/>
<a NAME="E7:41_2_1"/>
 <a href="anproj_1.html#K3" target="_self">Dir</a> <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, , <a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E8:41_2_1"/>
not  <a href="anproj_1.html#K4" target="_self">ProjectivePoints</a> <font color="Maroon">V</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i/>;<br/>


</div>
