<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="vectsp_6.html#M1">Linear_Combination</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E2:8"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>and </b><br/><a NAME="E3:8"/><i><font color="Green">E8</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="vectsp_6.html#K1">Carrier</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E4:8"/><i><font color="Green">E9</font></i>: 
 <a href="vectsp_6.html#K4">Sum</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vectsp_6.html#K3">(#)</a> <font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></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">c<sub>4</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="vectsp_6.html#M2">Linear_Combination</a> of <font color="Maroon">c<sub>4</sub></font><b> such that </b><br/><a NAME="E7:8"/><i><font color="Green">E10</font></i>: 
 <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vectsp_6.html#K3">(#)</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="vectsp_6.html#K4">Sum</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="vectsp_9.html#E3:8"><i><font color="Green">E8</font></i></a>, <a class="ref" href="vectsp_9.html#T9" target="_self">Th9</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>thus </b><a NAME="E8:8"/>
 <a href="vectsp_6.html#K4">Sum</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="vectsp_6.html#K4">Sum</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="vectsp_9.html#E4:8"><i><font color="Green">E9</font></i></a>, <a class="txt" href="vectsp_9.html#E7:8"><i><font color="Green">E10</font></i></a></i>;<br/>


</div>
