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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="E1:21"/><i><font color="Green">E19</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/>

<a NAME="E2:21"/><b>then </b>
( <font color="Maroon">c<sub>2</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> &amp; <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> &amp; <font color="Maroon">c<sub>4</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#T15" target="_self">Th15</a></i>;<br/>
<b>hence </b><a NAME="E3:21"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  )
 <b>by </b><i><a class="ref" href="rlvect_1.html#D13">RLVECT_1:def 13</a></i>;<br/>

<b>thus </b><a NAME="E4:21"/>
( not  <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; not  <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="anproj_1.html#E1:21"><i><font color="Green">E19</font></i></a>, <a class="ref" href="anproj_1.html#T16" target="_self">Th16</a></i>;<br/>


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