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







<b>assume </b><a NAME="E1:28"/><i><font color="Green">E23</font></i>: 
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="anproj_1.html#R2" target="_self">are_LinDep</a> 
 ;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</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="E2:28"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>6</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; not  <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>7</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="E4:28"/><i><font color="Green">E24</font></i>: 
not <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="anproj_1.html#R2" target="_self">are_LinDep</a> 
 <b>by </b><i><a class="txt" href="anproj_1.html#E1:28"><i><font color="Green">E23</font></i></a>, <a class="txt" href="anproj_1.html#E32"><i><font color="Green">Lemma22</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<b>thus </b><a NAME="E5:28"/>
<font color="Maroon">c<sub>7</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a> 
 <b>by </b><i><a class="txt" href="anproj_1.html#E4:28"><i><font color="Green">E24</font></i></a>, <a class="ref" href="anproj_1.html#T17" target="_self">Th17</a></i>;<br/>

<b>thus </b><a NAME="E6:28"/>
not <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="anproj_1.html#R2" target="_self">are_LinDep</a> 
 <b>by </b><i><a class="txt" href="anproj_1.html#E4:28"><i><font color="Green">E24</font></i></a></i>;<br/>


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