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<b>consider </b><font color="Maroon" title="c2">Z</font> being   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K1" title="ANPROJ_1:func.1">Proper_Vectors_of</a> <font color="Maroon" title="c1">V</font></span>)</span><b> such that </b><br/><a NAME="E2:41_2_1"/><i><font color="Green" title="E30">A2</font></i>: 
( <font color="Maroon" title="c2">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K9" title="EQREL_1:func.9">Class</a> <span class="p1">(<span class="default"><a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Proportionality_as_EqRel_of</a> <font color="Maroon" title="c1">V</font></span>)</span> &amp;  <a href="anproj_1.html#K4" title="ANPROJ_1:func.4">ProjectivePoints</a> <font color="Maroon" title="c1">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Z</font> )
 <b>by </b><i><a class="ref" href="anproj_1.html#D7" target="_self" title="ANPROJ_1:def.7">Def7</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E4:41_2_1"/><i><font color="Green" title="E31">A3</font></i>: 
<font color="Maroon" title="c3">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="ref" href="anproj_1.html#D8" target="_self" title="ANPROJ_1:def.8">Def8</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">u</font> = <font color="Maroon" title="c3">u</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font> ;<br/>
<a NAME="E6:41_2_1"/><i><font color="Green" title="E32">A4</font></i>: 
<font color="Maroon" title="c4">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="anproj_1.html#K1" title="ANPROJ_1:func.1">Proper_Vectors_of</a> <font color="Maroon" title="c1">V</font>
 
<b>by </b><i><a class="txt" href="anproj_1.html#E4:41_2_1"><i><font color="Green" title="E31">A3</font></i></a>, <a class="ref" href="anproj_1.html#D4" target="_self" title="ANPROJ_1:def.4">Def4</a></i>;<br/>
<b>set </b><font color="Maroon" title="c5">Y</font> =  <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c4">u</font>;<br/>
<a NAME="E7:41_2_1"/>
 <a href="anproj_1.html#K3" title="ANPROJ_1:func.3">Dir</a> <font color="Maroon" title="c4">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Z</font>
 
<b>by </b><i><a class="txt" href="anproj_1.html#E2:41_2_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="txt" href="anproj_1.html#E6:41_2_1"><i><font color="Green" title="E32">A4</font></i></a>, <a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E8:41_2_1"/>
not  <a href="anproj_1.html#K4" title="ANPROJ_1:func.4">ProjectivePoints</a> <font color="Maroon" title="c1">V</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="txt" href="anproj_1.html#E2:41_2_1"><i><font color="Green" title="E30">A2</font></i></a></i>;<br/>


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