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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">L</font> be    <a href="rlvect_2.html#M1">Linear_Combination</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:3_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="rlvect_2.html#K3">Carrier</a> <font color="Maroon">L</font>
 ;<br/><a NAME="E2:3_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">w</font> where <font color="Olive">w</font> is   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font> : <font color="Maroon">L</font> <a href="funct_2.html#K3">.</a> <font color="Olive">w</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 </span>}</span> 
 <b>by </b><i><a class="ref" href="rlvect_2.html#D6">RLVECT_2:def 6</a></i>;<br/><b>hence </b><a NAME="E3:3_1"/>
 ex <font color="Olive">v</font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">v</font> &amp; <font color="Maroon">L</font> <a href="funct_2.html#K3">.</a> <font color="Olive">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 ;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">v</font> being   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font><b> such that </b><a NAME="E2:3"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> &amp; <font color="Maroon">L</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 ;<br/>

<a NAME="E3:3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">w</font> where <font color="Olive">w</font> is   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font> : <font color="Maroon">L</font> <a href="funct_2.html#K3">.</a> <font color="Olive">w</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="rlvect_2.html#K3">Carrier</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="rlvect_2.html#D6">RLVECT_2:def 6</a></i>;<br/>


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