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<b>consider </b><font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E2:41_2_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font></span>)</span> &amp;  <a href="anproj_1.html#K4" target="_self">ProjectivePoints</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="anproj_1.html#D7" target="_self">Def7</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:41_2_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="anproj_1.html#D8" target="_self">Def8</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E6:41_2_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>4</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="txt" href="anproj_1.html#E4:41_2_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="anproj_1.html#D4" target="_self">Def4</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="anproj_1.html#K3" target="_self">Dir</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<a NAME="E7:41_2_1"/>
 <a href="anproj_1.html#K3" target="_self">Dir</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="anproj_1.html#E2:41_2_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="anproj_1.html#E6:41_2_1"><i><font color="Green">E32</font></i></a>, <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">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="txt" href="anproj_1.html#E2:41_2_1"><i><font color="Green">E30</font></i></a></i>;<br/>


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