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<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">r</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/>







<b>assume </b><a NAME="E1:27"/><i><font color="Green">E40</font></i>: 
not <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font> <a href="anproj_1.html#R2" target="_self">are_LinDep</a> 
 ;<br/>

<b>let </b><font color="Maroon">u</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/>



<b>assume </b><a NAME="E2:27"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">u</font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">v</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">u</font>,<font color="Maroon">v</font> )
 ;<br/>

<b>assume </b><a NAME="E3:27"/>
for <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> holds  <font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Olive">y</font> <a href="anproj_1.html#R2" target="_self">are_LinDep</a> 
 ;<br/>

<a NAME="E4:27"/><b>then </b>
( <font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">p</font> <a href="anproj_1.html#R2" target="_self">are_LinDep</a>  &amp; <font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">q</font> <a href="anproj_1.html#R2" target="_self">are_LinDep</a>  &amp; <font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">r</font> <a href="anproj_1.html#R2" target="_self">are_LinDep</a>  )
 
;<br/>
<b>hence </b><a NAME="E5:27"/>
contradiction
 <b>by </b><i>, , </i>;<br/>


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