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

<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>given </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E1:94"/><i><font color="Green">E84</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="real_1.html#NM1">Real</a> st <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<a NAME="E2:94"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="anproj_2.html#V1" target="_self">up-3-dimensional</a>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E1:94"><i><font color="Green">E84</font></i></a>, <a class="txt" href="anproj_2.html#E89"><i><font color="Green">Lemma82</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:94"/>
(  <a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font> is <a href="collsp.html#V4">proper</a> &amp;  <a href="anproj_1.html#K6">ProjectiveSpace</a> <font color="Maroon">c<sub>1</sub></font> is <a href="anproj_2.html#V3" target="_self">at_least_3rank</a> )
 <b>by </b><i><a class="txt" href="anproj_2.html#E72"><i><font color="Green">Lemma68</font></i></a>, <a class="txt" href="anproj_2.html#E74"><i><font color="Green">Lemma70</font></i></a></i>;<br/>


</div>
