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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="realset2.html#V3">trivial</a> <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:42"/>
<font color="Maroon">c<sub>2</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a> 
 ;<br/>

<a NAME="E2:42"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="anproj_1.html#K1" target="_self">Proper_Vectors_of</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="anproj_1.html#T26" target="_self">Th26</a></i>;<br/>
<a NAME="E3:42"/>
 <a href="anproj_1.html#K3" target="_self">Dir</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</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">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_1.html#E2:42"><i><font color="Green">E31</font></i></a>, <a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E4:42"/>
 <a href="anproj_1.html#K3" target="_self">Dir</a> <font color="Maroon">c<sub>2</sub></font> is    <a href="subset_1.html#M1">Element</a> of  <a href="anproj_1.html#K4" target="_self">ProjectivePoints</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="anproj_1.html#D7" target="_self">Def7</a></i>;<br/>


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