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<b>let </b><font color="Maroon">GF</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">GF</font>;<br/><b>let </b><font color="Maroon">L</font> be    <a href="vectsp_6.html#M1">Linear_Combination</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font>;<br/>







<b>consider </b><font color="Maroon">F</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E2:8"/>
<font color="Maroon">F</font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>and </b><br/><a NAME="E3:8"/><i><font color="Green">E32</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_6.html#K1">Carrier</a> <font color="Maroon">L</font>
 <b>and </b><br/><a NAME="E4:8"/><i><font color="Green">E40</font></i>: 
 <a href="vectsp_6.html#K4">Sum</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="vectsp_6.html#K3">(#)</a> <font color="Maroon">F</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_6.html#D9">VECTSP_6:def 9</a></i>;<br/>
<b>assume </b><a NAME="E5:8"/>
 <a href="vectsp_6.html#K1">Carrier</a> <font color="Maroon">L</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp_7.html#K1">Lin</a> <font color="Maroon">A</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">K</font> being    <a href="vectsp_6.html#M2">Linear_Combination</a> of <font color="Maroon">A</font><b> such that </b><br/><a NAME="E7:8"/><i><font color="Green">E42</font></i>: 
 <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="vectsp_6.html#K3">(#)</a> <font color="Maroon">F</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="vectsp_6.html#K4">Sum</a> <font color="Maroon">K</font>
 <b>by </b><i>, </i>;<br/>
<b>take </b>
<font color="Maroon">K</font>
;<br/>

<b>thus </b><a NAME="E8:8"/>
 <a href="vectsp_6.html#K4">Sum</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_6.html#K4">Sum</a> <font color="Maroon">K</font>
 <b>by </b><i>, </i>;<br/>


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